Density Functional Theory (DFT)¶
Overview¶
The NWChem density functional theory (DFT) module uses the Gaussian basis set approach to compute closed shell and open shell densities and KohnSham orbitals in the:
 local density approximation (LDA),
 nonlocal density approximation (NLDA),
 local spindensity approximation (LSD),
 nonlocal spindensity approximation (NLSD),
 nonlocal metaGGA approximation (metaGGA),
 any empirical mixture of local and nonlocal approximations (including exact exchange), and
 asymptotically corrected exchangecorrelation potentials.
 spinorbit effects
The formal scaling of the DFT computation can be reduced by choosing to use auxiliary Gaussian basis sets to fit the charge density (CD) and/or fit the exchangecorrelation (XC) potential.
DFT input is provided using the compound DFT directive
DFT
...
END
The actual DFT calculation will be performed when the input module encounters the TASK directive.
TASK DFT
Once a user has specified a geometry and a KohnSham orbital basis set the DFT module can be invoked with no input directives (defaults invoked throughout). There are subdirectives which allow for customized application; those currently provided as options for the DFT module are:
VECTORS [[input] (<string input_movecs default atomic>)  \
(project <string basisname> <string filename>)] \
[swap [alphabeta] <integer vec1 vec2> ...] \
[output <string output_filename default input_movecs>] \
XC [[acm] [b3lyp] [beckehandh] [pbe0]\
[becke97] [becke971] [becke972] [becke973] [becke97d] [becke98] \
[hcth] [hcth120] [hcth147] [hcth147@tz2p]\
[hcth407] [becke97gga1] [hcth407p]\
[mpw91] [mpw1k] [xft97] [cft97] [ft97] [op] [bop] [pbeop]\
[xpkzb99] [cpkzb99] [xtpss03] [ctpss03] [xctpssh]\
[b1b95] [bb1k] [mpw1b95] [mpwb1k] [pw6b95] [pwb6k] [m05] [m052x] [vs98] \
[m06] [m06hf] [m06L] [m062x] \
[HFexch <real prefactor default 1.0>] \
[becke88 [nonlocal] <real prefactor default 1.0>] \
[xperdew91 [nonlocal] <real prefactor default 1.0>] \
[xpbe96 [nonlocal] <real prefactor default 1.0>] \
[gill96 [nonlocal] <real prefactor default 1.0>] \
[lyp <real prefactor default 1.0>] \
[perdew81 <real prefactor default 1.0>] \
[perdew86 [nonlocal] <real prefactor default 1.0>] \
[perdew91 [nonlocal] <real prefactor default 1.0>] \
[cpbe96 [nonlocal] <real prefactor default 1.0>] \
[pw91lda <real prefactor default 1.0>] \
[slater <real prefactor default 1.0>] \
[vwn_1 <real prefactor default 1.0>] \
[vwn_2 <real prefactor default 1.0>] \
[vwn_3 <real prefactor default 1.0>] \
[vwn_4 <real prefactor default 1.0>] \
[vwn_5 <real prefactor default 1.0>] \
[vwn_1_rpa <real prefactor default 1.0>] \
[xtpss03 [nonlocal] <real prefactor default 1.0>] \
[ctpss03 [nonlocal] <real prefactor default 1.0>] \
[bc95 [nonlocal] <real prefactor default 1.0>] \
[xpw6b95 [nonlocal] <real prefactor default 1.0>] \
[xpwb6k [nonlocal] <real prefactor default 1.0>] \
[xm05 [nonlocal] <real prefactor default 1.0>] \
[xm052x [nonlocal] <real prefactor default 1.0>] \
[cpw6b95 [nonlocal] <real prefactor default 1.0>] \
[cpwb6k [nonlocal] <real prefactor default 1.0>] \
[cm05 [nonlocal] <real prefactor default 1.0>] \
[cm052x [nonlocal] <real prefactor default 1.0>]] \
[xvs98 [nonlocal] <real prefactor default 1.0>]] \
[cvs98 [nonlocal] <real prefactor default 1.0>]] \
[xm06L [nonlocal] <real prefactor default 1.0>]] \
[xm06hf [nonlocal] <real prefactor default 1.0>]] \
[xm06 [nonlocal] <real prefactor default 1.0>]] \
[xm062x [nonlocal] <real prefactor default 1.0>]] \
[cm06L [nonlocal] <real prefactor default 1.0>]] \
[cm06hf [nonlocal] <real prefactor default 1.0>]] \
[cm06 [nonlocal] <real prefactor default 1.0>]] \
[cm062x [nonlocal] <real prefactor default 1.0>]]
CONVERGENCE [[energy <real energy default 1e7>] \
[density <real density default 1e5>] \
[gradient <real gradient default 5e4>] \
[dampon <real dampon default 0.0>] \
[dampoff <real dampoff default 0.0>] \
[diison <real diison default 0.0>] \
[diisoff <real diisoff default 0.0>] \
[levlon <real levlon default 0.0>] \
[levloff <real levloff default 0.0>] \
[ncydp <integer ncydp default 2>] \
[ncyds <integer ncyds default 30>] \
[ncysh <integer ncysh default 30>] \
[damp <integer ndamp default 0>] [nodamping] \
[diis [nfock <integer nfock default 10>]] \
[nodiis] [lshift <real lshift default 0.5>] \
[nolevelshifting] \
[hl_tol <real hl_tol default 0.1>] \
[rabuck [n_rabuck <integer n_rabuck default 25>]\
[fast] ]
GRID [(xcoarsecoarsemediumfinexfinehuge) default medium] \
[(gausleglebedev ) default lebedev ] \
[(beckeerf1erf2ssf) default erf1] \
[(eulermuratreutler) default mura] \
[rm <real rm default 2.0>] \
[nodisk]
TOLERANCES [[tight] [tol_rho <real tol_rho default 1e10>] \
[accCoul <integer accCoul default 8>] \
[radius <real radius default 25.0>]]
[(LB94CS00 <real shift default none>)]
DECOMP
ODFT
DIRECT
SEMIDIRECT [filesize <integer filesize default disksize>]
[memsize <integer memsize default available>]
[filename <string filename default $file_prefix.aoints$>]
INCORE
ITERATIONS <integer iterations default 30>
MAX_OVL
CGMIN
RODFT
MULLIKEN
DISP
XDM [ a1 <real a1> ] [ a2 <real a2> ]
MULT <integer mult default 1>
NOIO
PRINTNOPRINT
SYM <string (ONOFF) default ON>
ADAPT <string (ONOFF) default ON>
The following sections describe these keywords and optional subdirectives that can be specified for a DFT calculation in NWChem.
Specification of Basis Sets for the DFT Module¶
The DFT module requires at a minimum the basis set for the KohnSham molecular orbitals. This basis set must be in the default basis set named “ao basis”, or it must be assigned to this default name using the SET directive.
In addition to the basis set for the KohnSham orbitals, the charge
density fitting basis set can also be specified in the input directives
for the DFT module. This basis set is used for the evaluation of the
Coulomb potential in the Dunlap scheme. The charge density fitting basis
set must have the name cd basis
. This can be the actual name of a
basis set, or a basis set can be assigned this name using the
SET directive. If this basis set is not
defined by input, the O(N^{4}) exact Coulomb contribution is computed.
The user also has the option of specifying a third basis set for the
evaluation of the exchangecorrelation potential. This basis set must
have the name xc basis
. If this basis set is not specified by input,
the exchange contribution (XC) is evaluated by numerical quadrature. In
most applications, this approach is efficient enough, so the “xc basis”
basis set is not required.
For the DFT module, the input options for defining the basis sets in a given calculation can be summarized as follows:
ao basis
 KohnSham molecular orbitals; required for all calculationscd basis
 charge density fitting basis set; optional, but recommended for evaluation of the Coulomb potential “xc basis”  exchangecorrelation (XC) fitting basis set; optional, and not recommended
ADFT New in NWChem 7.2.0:¶
Use of the auxiliary density functional theory method (ADFT)^{1} can be triggered by means of the adft
keyword. This can result in a large speedup when using “pure” GGA functionals (e.g. PBE96) and Laplaciandependent mGGA functionals (e.g. SCANL). The speedup comes from the use of the fitted density obtained with the charge density fitting technique to approximate both the Coulomb and ExchangeCorrelation contributions.
The ADFT method is similar in spirit to the exchangecorrelation fitting technique triggered by specifying an xc basis without the adft
keyword. It is important to note that, different to straight exchangecorrelation fitting, energy derivatives are welldefined within the ADFT framework. As a consequence, geometry optimizations and harmonic vibrational frequencies are wellbehaved.
The ADFT method requires a charge density fitting basis set (see DFT basis set section). If not cd basis
set is provided, the weigend coulomb fitting
basis set will be loaded.
VECTORS and MAX_OVL: KSMO Vectors¶
The VECTORS directive is the same as that in the SCF module. Currently, the LOCK keyword is not supported by the DFT module, however the directive
MAX_OVL
has the same effect.
XC and DECOMP: ExchangeCorrelation Potentials¶
XC [[acm] [b3lyp] [beckehandh] [pbe0] [bhlyp]\
[becke97] [becke971] [becke972] [becke973] [becke98] [hcth] [hcth120] [hcth147] [hcth147@tz2p] \
[hcth407] [becke97gga1] [hcth407p] \
[optx] [hcthp14] [mpw91] [mpw1k] [xft97] [cft97] [ft97] [op] [bop] [pbeop]\
[m05] [m052x] [m06] [m06l] [m062x] [m06hf] [m08hx] [m08so] [m11] [m11l]\
[HFexch <real prefactor default 1.0>] \
[becke88 [nonlocal] <real prefactor default 1.0>] \
[xperdew91 [nonlocal] <real prefactor default 1.0>] \
[xpbe96 [nonlocal] <real prefactor default 1.0>] \
[gill96 [nonlocal] <real prefactor default 1.0>] \
[lyp <real prefactor default 1.0>] \
[perdew81 <real prefactor default 1.0>] \
[perdew86 [nonlocal] <real prefactor default 1.0>] \
[perdew91 [nonlocal] <real prefactor default 1.0>] \
[cpbe96 [nonlocal] <real prefactor default 1.0>] \
[pw91lda <real prefactor default 1.0>] \
[slater <real prefactor default 1.0>] \
[vwn_1 <real prefactor default 1.0>] \
[vwn_2 <real prefactor default 1.0>] \
[vwn_3 <real prefactor default 1.0>] \
[vwn_4 <real prefactor default 1.0>] \
[vwn_5 <real prefactor default 1.0>] \
[vwn_1_rpa <real prefactor default 1.0>]]
The user has the option of specifying the exchangecorrelation treatment in the DFT Module (see table below for full list of functionals). The default exchangecorrelation functional is defined as the local density approximation (LDA) for closed shell systems and its counterpart the local spindensity (LSD) approximation for open shell systems. Within this approximation, the exchange functional is the Slater ρ^{1/3} functional^{2}^{3}, and the correlation functional is the VoskoWilkNusair (VWN) functional (functional V)^{4}. The parameters used in this formula are obtained by fitting to the Ceperley and Alder Quantum MonteCarlo solution of the homogeneous electron gas.
These defaults can be invoked explicitly by specifying the following
keywords within the DFT module input directive, XC slater vwn_5
.
That is, this statement in the input file
dft
XC slater vwn_5
end
task dft
is equivalent to the simple line
task dft
The DECOMP
directive causes the components of the energy corresponding
to each functional to be printed, rather than just the total
exchangecorrelation energy that is the default. You can see an example
of this directive in the sample
input.
Many alternative exchange and correlation functionals are available to the user as listed in the table below. The following sections describe how to use these options.
Libxc interface New in NWChem 7.2.0:¶
If NWChem is compiled by linking it with the libxc DFT library
(as described in the Interfaces with External Software section),
the user will be able to use most of the XC functionals available in libxc.
The input syntax requires to use the xc keyword followed by
the functionals name from
list available in Libxc
For example, the following input for the NWChem libxc interface
dft
xc gga_x_pbe 1.0 gga_x_pbe 1.0
end
while trigger use of the same PBE96 functionals as in the NWChem builtin interface
dft
xc xpbe96 1.0 cpbe96 1.0
end
ExchangeCorrelation Functionals¶
There are several Exchange and Correlation functionals in addition to
the default slater
and vwn_5
functionals. These are either local or
gradientcorrected functionals (GCA); a full list can be found in the
table below.
The HartreeFock exact exchange functional, (which has O(N^{4}) computation expense), is invoked by specifying
XC HFexch
Note that the user also has the ability to include only the local or
nonlocal contributions of a given functional. In addition, the user can
specify a multiplicative prefactor (the variable
XC becke88 nonlocal 0.72
The user should be aware that the Becke88 local component is simply the Slater exchange and should be input as such.
Any combination of the supported exchange functional options can be used. For example, the popular Gaussian B3 exchange could be specified as:
XC slater 0.8 becke88 nonlocal 0.72 HFexch 0.2
Any combination of the supported correlation functional options can be used. For example, B3LYP could be specified as:
XC vwn_1_rpa 0.19 lyp 0.81 HFexch 0.20 slater 0.80 becke88 nonlocal 0.72
and X3LYP as:
xc vwn_1_rpa 0.129 lyp 0.871 hfexch 0.218 slater 0.782 \
becke88 nonlocal 0.542 xperdew91 nonlocal 0.167
Setting up common exchangecorrelation functionals¶
 B3LYP:
xc b3lyp
 PBE0:
xc pbe0
 PBE96:
xc xpbe96 cpbe96
 PW91:
xc xperdew91 perdew91
 BHLYP:
xc bhlyp
 Becke Half and Half:
xc beckehandh
 BP86:
xc becke88 perdew86
 BP91:
xc becke88 perdew91
 BLYP:
xc becke88 lyp
Minnesota Functionals
 xc m05
 xc m052x
 xc m06
 xc m06l
 xc m062x
 xc m06hf
 xc m08hx
 xc m08so
 xc m11
 xc m11l
Analytic second derivatives are not supported with the Minnesota functionals yet.
Combined Exchange and Correlation Functionals¶
In addition to the options listed above for the exchange and correlation functionals, the user has the alternative of specifying combined exchange and correlation functionals.
The available hybrid functionals (where a HartreeFock Exchange component is present) consist of the Becke “half and half”^{5}, the adiabatic connection method^{6}, Becke 1997 (“Becke V” paper^{7}).
The keyword beckehandh
specifies that the exchangecorrelation energy
will be computed
as
E_{XC} ≈ ½E_{X}^{HF} + ½E_{X}^{Slater} + ½E_{C}^{PW91LDA}
We know this is NOT the correct Becke prescribed implementation that requires the XC potential in the energy expression. But this is what is currently implemented as an approximation to it.
The keyword acm
specifies that the exchangecorrelation energy is
computed as
E_{XC} = a_{0}E_{X}^{HF} + (1  a_{0})E_{X}^{Slater} + a_{X}δE_{X}^{Becke88} + E_{C}^{VWN} + a_{C}δE_{C}^{Perdew91}
where
a_{0} = 0.20, a_{X} = 0.72, a_{C} = 0.81
and δ stands for a nonlocal component.
The keyword b3lyp
specifies that the exchangecorrelation energy is
computed as
E_{XC} = a_{0}E_{X}^{HF} + (1  a_{0})E_{X}^{Slater} + a_{X}δE_{X}^{Becke88} + (1  a_{C})E_{C}^{VWN_1_RPA} + a_{C}δE_{C}^{LYP}
where
a_{0} = 0.20, a_{X} = 0.72, a_{C} = 0.81
XC Functionals Summary¶
Keyword  X  C  GGA  Meta  Hybr.  2nd  Ref. 

slater  *  Y  ^{2}^{3}  
vwn_1  *  Y  ^{4}  
vwn_2  *  Y  ^{4}  
vwn_3  *  Y  ^{4}  
vwn_4  *  Y  ^{4}  
vwn_5  *  Y  ^{4}  
vwn_1_rpa  *  Y  ^{4}  
perdew81  *  Y  ^{8}  
pw91lda  *  Y  ^{9}  
xbecke86b  *  *  N  ^{10}  
becke88  *  *  Y  ^{11}  
xperdew86  *  *  N  ^{12}  
xperdew91  *  *  Y  ^{9}  
xpbe96  *  *  Y  ^{13}^{14}  
gill96  *  *  Y  ^{15}  
optx  *  *  N  ^{16}  
mpw91  *  *  Y  ^{17}^{18}  
xft97  *  *  N  ^{19}^{20}  
rpbe  *  *  Y  ^{21}  
revpbe  *  *  Y  ^{22}  
xpw6b95  *  *  N  ^{23}  
xpwb6k  *  *  N  ^{23}  
perdew86  *  *  Y  ^{12}  
lyp  *  *  Y  ^{24}  
perdew91  *  *  Y  ^{25}^{26}  
cpbe96  *  *  Y  ^{13}^{14}  
cft97  *  *  N  ^{19}^{20}  
op  *  *  N  ^{27}  
hcth  *  *  *  N  ^{28}  
hcth120  *  *  *  N  ^{29}  
hcth147  *  *  *  N  ^{29}  
hcth147@tz2p  *  *  *  N  ^{30}  
hcth407  *  *  *  N  ^{31}  
becke97gga1  *  *  *  N  ^{32}  
hcthp14  *  *  *  N  ^{33}  
ft97  *  *  *  N  ^{19}^{20}  
htch407p  *  *  *  N  ^{34}  
bop  *  *  *  N  ^{27}  
pbeop  *  *  *  N  ^{35}  
xpkzb99  *  *  N  ^{36}  
cpkzb99  *  *  N  ^{36}  
xtpss03  *  *  N  ^{37}  
ctpss03  *  *  N  ^{37}  
bc95  *  *  N  ^{21}  
cpw6b95  *  *  N  ^{23}  
cpwb6k  *  *  N  ^{23}  
xm05  *  *  *  N  ^{38}^{39}  
cm05  *  *  N  ^{38}^{39}  
m052x  *  *  *  *  N  ^{40}  
xm052x  *  *  *  N  ^{40}  
cm052x  *  *  N  ^{40}  
xctpssh  *  *  N  ^{41}  
bb1k  *  *  N  ^{22}  
mpw1b95  *  *  N  ^{42}  
mpwb1k  *  *  N  ^{42}  
pw6b95  *  *  N  ^{23}  
pwb6k  *  *  N  ^{23}  
m05  *  *  N  ^{38}  
vs98  *  *  N  ^{43}  
xvs98  *  *  N  ^{43}  
cvs98  *  *  N  ^{43}  
m06L  *  *  *  N  ^{44}  
xm06L  *  *  N  ^{44}  
cm06L  *  *  N  ^{44}  
m06hf  *  *  N  ^{45}  
xm06hf  *  *  *  N  ^{45}  
cm06hf  *  *  N  ^{45}  
m06  *  *  N  ^{46}  
xm06  *  *  *  N  ^{46}  
cm06  *  *  N  ^{46}  
m062x  *  *  N  ^{44}  
xm062x  *  *  *  N  ^{44}  
cm062x  *  *  N  ^{44}  
cm08hx  *  *  N  ^{47}  
xm08hx  *  *  N  ^{47}  
m08hx  *  *  *  *  N  ^{47}  
cm08so  *  *  N  ^{47}  
xm08so  *  *  N  ^{47}  
m08so  *  *  *  *  N  ^{47}  
cm11  *  *  N  ^{48}  
xm11  *  *  N  ^{48}  
m11  *  *  *  *  N  ^{48}  
cm11l  *  *  N  ^{49}  
xm11l  *  *  N  ^{49}  
m11l  *  *  *  N  ^{49}  
csogga  *  *  N  ^{47}  
xsogga  *  *  N  ^{47}  
sogga  *  *  *  N  ^{47}  
csogga11  *  *  N  ^{50}  
xsogga11  *  *  N  ^{50}  
sogga11  *  *  *  N  ^{50}  
csogga11x  *  N  ^{51}  
xsogga11x  *  *  N  ^{51}  
sogga11x  *  *  *  *  N  ^{51}  
dldf  *  *  *  *  N  ^{52}  
beckehandh  *  *  *  Y  ^{5}  
b3lyp  *  *  *  *  Y  ^{6}  
acm  *  *  *  *  Y  ^{6}  
becke97  *  *  *  *  N  ^{7}  
becke971  *  *  *  *  N  ^{28}  
becke972  *  *  *  *  N  ^{53}  
becke973  *  *  *  *  N  ^{54}  
becke97d  *  *  *  *  N  ^{55}  
becke98  *  *  *  *  N  ^{56}  
pbe0  *  *  *  *  Y  ^{57}  
mpw1k  *  *  *  *  Y  ^{58}  
xmvs15  *  *  N  ^{59}  
hle16  *  *  *  *  Y  ^{60}  
scan  *  *  *  *  N  ^{61}  
scanl  *  *  *  *  N  ^{62}  
revm06L  *  *  *  *  N  ^{63}  
revm06  *  *  *  *  *  N  ^{64} 
wb97x  *  *  *  *  N  ^{65}  
wb97xd3  *  *  *  *  N  ^{66}  
rscan  *  *  *  *  N  ^{67}  
r2scan  *  *  *  *  N  ^{68}  
r2scan0  *  *  *  *  *  N  ^{69} 
r2scanl  *  *  *  *  N  ^{70}^{71}  
ncap  *  *  *  Y  ^{72}  
MetaGGA Functionals¶
One way to calculate metaGGA energies is to use orbitals and densities from fully selfconsistent GGA or LDA calculations and run them in one iteration in the metaGGA functional. It is expected that metaGGA energies obtained this way will be close to fully self consistent metaGGA calculations.
It is possible to calculate metaGGA energies both ways in NWChem, that is, selfconsistently or with GGA/LDA orbitals and densities. However, since second derivatives are not available for metaGGAs, in order to calculate frequencies, one must use task dft freq numerical. A sample file with this is shown below, in Sample input file. In this instance, the energy is calculated selfconsistently and geometry is optimized using the analytical gradients.
(For more information on metaGGAs, see Kurth et al 1999 ^{73} for a brief description of metaGGAs, and citations 1427 therein for thorough background)
Note: both TPSS and PKZB correlation require the PBE GGA CORRELATION (which is itself dependent on an LDA). The decision has been made to use these functionals with the accompanying local PW91LDA. The user cannot set the local part of these metaGGA functionals.
RangeSeparated Functionals¶
Using the Ewald decomposition
we can split the the Exchange interaction as
Therefore, the longrange HF Exchange energy becomes
cam <real cam> cam_alpha <real cam_alpha> cam_beta <cam_beta>
cam
represents the attenuation parameter μ, cam_alpha
and
cam_beta
are the α and β parameters that control the
amount of shortrange DFT and longrange HF Exchange according to the
Ewald decomposition. As r_{12} → 0, the HF exchange
fraction is α,
while the DFT exchange fraction is 1  α.
As r_{12} → ∞,
the HF exchange fraction approaches α + β and the DFT exchange fraction
approaches 1  α  β. In the HSE functional, the HF part
is shortranged and DFT is longranged.
Range separated functionals (or longrange corrected or LC) can be specified as follows:
CAMB3LYP:
xc xcamb88 1.00 lyp 0.81 vwn_5 0.19 hfexch 1.00
cam 0.33 cam_alpha 0.19 cam_beta 0.46
LCBLYP:
xc xcamb88 1.00 lyp 1.0 hfexch 1.00
cam 0.33 cam_alpha 0.0 cam_beta 1.0
LCPBE:
xc xcampbe96 1.0 cpbe96 1.0 HFexch 1.0
cam 0.30 cam_alpha 0.0 cam_beta 1.0
LCPBE0 or CAMPBE0:
xc xcampbe96 1.0 cpbe96 1.0 HFexch 1.0
cam 0.30 cam_alpha 0.25 cam_beta 0.75
BNL (Baer, Neuhauser, Lifshifts):
xc xbnl07 0.90 lyp 1.00 hfexch 1.00
cam 0.33 cam_alpha 0.0 cam_beta 1.0
LCwPBE:
xc xwpbe 1.00 cpbe96 1.0 hfexch 1.00
cam 0.4 cam_alpha 0.00 cam_beta 1.00
LRCwPBEh:
xc xwpbe 0.80 cpbe96 1.0 hfexch 1.00
cam 0.2 cam_alpha 0.20 cam_beta 0.80
QTP00
xc xcamb88 1.00 lyp 0.80 vwn_5 0.2 hfexch 1.00
cam 0.29 cam_alpha 0.54 cam_beta 0.37
rCAMB3LYP
xc xcamb88 1.00 lyp 1.0 vwn_5 0. hfexch 1.00 becke88 nonlocal 0.13590
cam 0.33 cam_alpha 0.18352 cam_beta 0.94979
HSE03 functional: 0.25*Ex(HFSR)  0.25*Ex(PBESR) + Ex(PBE) + Ec(PBE), where gamma(HFSR) = gamma(PBESR)
xc hse03
or it can be explicitly set as
xc xpbe96 1.0 xcampbe96 0.25 cpbe96 1.0 srhfexch 0.25
cam 0.33 cam_alpha 0.0 cam_beta 1.0
HSE06 functional:
xc xpbe96 1.0 xcampbe96 0.25 cpbe96 1.0 srhfexch 0.25
cam 0.11 cam_alpha 0.0 cam_beta 1.0
Please see references ^{74}^{75}^{76}^{77}^{78}^{79}^{80}^{81}^{82}^{83}^{84}^{85}^{86} (not a complete list) for further details about the theory behind these functionals and applications.
Example illustrating the CAMB3LYP functional:
start h2ocamb3lyp
geometry units angstrom
O 0.00000000 0.00000000 0.11726921
H 0.75698224 0.00000000 0.46907685
H 0.75698224 0.00000000 0.46907685
end
basis spherical
* library augccpvdz
end
dft
xc xcamb88 1.00 lyp 0.81 vwn_5 0.19 hfexch 1.00
cam 0.33 cam_alpha 0.19 cam_beta 0.46
direct
iterations 100
end
task dft energy
Example illustrating the HSE03 functional:
echo
start h2ohse
geometry units angstrom
O 0.00000000 0.00000000 0.11726921
H 0.75698224 0.00000000 0.46907685
H 0.75698224 0.00000000 0.46907685
end
basis spherical
* library augccpvdz
end
dft
xc hse03
iterations 100
direct
end
task dft energy
or alternatively
dft
xc xpbe96 1.0 xcampbe96 0.25 cpbe96 1.0 srhfexch 0.25
cam 0.33 cam_alpha 0.0 cam_beta 1.0
iterations 100
direct
end
task dft energy
SSBD functional¶
The SSBD^{87}^{88} functional is a small correction to the nonempirical PBE functional and includes a portion of Grimme’s dispersion correction (s6=0.847455). It is designed to reproduce the good results of OPBE for spinstate splittings and reaction barriers, and the good results of PBE for weak interactions. The SSBD functional works well for these systems, including for difficult systems for DFT (dimerization of anthracene, branching of octane, waterhexamer isomers, C_{12}H_{12} isomers, stacked adenine dimers), and for NMR chemical shieldings.
It can be specified as
xc ssbd
Semiempirical hybrid DFT combined with perturbative MP2¶
This theory combines hybrid density functional theory with MP2 semiempirically. The B2PLYP functional, which is an example of this approximation, can be specified as:
mp2
freeze atomic
end
dft
xc HFexch 0.53 becke88 0.47 lyp 0.73 mp2 0.27
dftmp2
end
For details of the theory, please see reference^{89}.
LB94 and CS00: Asymptotic correction¶
The keyword LB94
will correct the asymptotic region of the XC definition
of exchangecorrelation potential by the vanLeeuwenBaerends
exchangecorrelation potential that has the correct asymptotic
behavior. The total energy will be computed by the XC definition of
exchangecorrelation functional. This scheme is known to tend to
overcorrect the deficiency of most uncorrected exchangecorrelation
potentials.
The keyword CS00
, when supplied with a real value of shift (in atomic
units), will perform CasidaSalahub ‘00 asymptotic correction. This is
primarily intended for use with
TDDFT. The shift is normally
positive (which means that the original uncorrected exchangecorrelation
potential must be shifted down).
When the keyword CS00
is specified without the value of shift, the
program will automatically supply it according to the semiempirical
formula of Zhan, Nichols, and Dixon (again, see
TDDFT for more details and
references). As the Zhan’s formula is calibrated against B3LYP results,
it is most meaningful to use this with the B3LYP
functional, although the program does not prohibit (or even warn) the
use of any other functional.
Sample input files of asymptotically corrected TDDFT calculations can be found in the corresponding section.
Sample input file¶
A simple example calculates the geometry of water, using the metaGGA
functionals xtpss03
and ctpss03
. This also highlights some of the print
features in the DFT module. Note that you must use the line
task dft freq numerical
because analytic hessians are not available for the
metaGGAs:
title "WATER 6311G* metaGGA XC geometry"
echo
geometry units angstroms
O 0.0 0.0 0.0
H 0.0 0.0 1.0
H 0.0 1.0 0.0
end
basis
H library 6311G*
O library 6311G*
end
dft
iterations 50
print kinetic_energy
xc xtpss03 ctpss03
decomp
end
task dft optimize
task dft freq numerical
ITERATIONS or MAXITER: Number of SCF iterations¶
ITERATIONS or MAXITER <integer iterations default 30>
The default optimization in the DFT module is to iterate on the
KohnSham (SCF) equations for a specified number of iterations (default
30). The keyword that controls this optimization is ITERATIONS
, and has
the following general form,
iterations <integer iterations default 30>
or
maxiter <integer iterations default 30>
The optimization procedure will stop when the specified number of iterations is reached or convergence is met. See an example that uses this directive in Sample input file.
CONVERGENCE: SCF Convergence Control¶
CONVERGENCE [energy <real energy default 1e6>] \
[density <real density default 1e5>] \
[gradient <real gradient default 5e4>] \
[hl_tol <real hl_tol default 0.1>]
[dampon <real dampon default 0.0>] \
[dampoff <real dampoff default 0.0>] \
[ncydp <integer ncydp default 2>] \
[ncyds <integer ncyds default 30>] \
[ncysh <integer ncysh default 30>] \
[damp <integer ndamp default 0>] [nodamping] \
[diison <real diison default 0.0>] \
[diisoff <real diisoff default 0.0>] \
[(diis [nfock <integer nfock default 10>])  nodiis] \
[levlon <real levlon default 0.0>] \
[levloff <real levloff default 0.0>] \
[(lshift <real lshift default 0.5>)  nolevelshifting] \
[rabuck [n_rabuck <integer n_rabuck default 25>] \
[fast] ]
Convergence is satisfied by meeting any or all of three criteria;
 convergence of the total energy; this is defined to be when the total DFT energy at iteration N and at iteration N1 differ by a value less than a threshold value (the default is 1e6). This value can be modified using the key word,
CONVERGENCE energy <real energy default 1e6>
 convergence of the total density; this is defined to be when the total DFT density matrix at iteration N and at iteration N1 have a RMS difference less than some value (the default is 1e5). This value can be modified using the keyword,
CONVERGENCE density <real density default 1e5>
 convergence of the orbital gradient; this is defined to be when the DIIS error vector becomes less than some value (the default is 5e4). This value can be modified using the keyword,
CONVERGENCE gradient <real gradient default 5e4>
The default optimization strategy is to immediately begin direct inversion of the iterative subspace. Damping is also initiated (using 70% of the previous density) for the first 2 iteration. In addition, if the HOMO  LUMO gap is small and the Fock matrix diagonally dominant, then levelshifting is automatically initiated. There are a variety of ways to customize this procedure to whatever is desired.
An alternative optimization strategy is to specify, by using the change in total energy (between iterations N and N1), when to turn damping, levelshifting, and/or DIIS on/off. Start and stop keywords for each of these is available as,
CONVERGENCE [dampon <real dampon default 0.0>] \
[dampoff <real dampoff default 0.0>] \
[diison <real diison default 0.0>] \
[diisoff <real diisoff default 0.0>] \
[levlon <real levlon default 0.0>] \
[levloff <real levloff default 0.0>]
So, for example, damping, DIIS, and/or levelshifting can be turned on/off as desired.
Another strategy can be to specify how many iterations (cycles)
you wish each type of procedure to be used. The necessary keywords to
control the number of damping cycles (ncydp
), the number of DIIS cycles
(ncyds
), and the number of levelshifting cycles (ncysh
) are input as,
CONVERGENCE [ncydp <integer ncydp default 2>] \
[ncyds <integer ncyds default 30>] \
[ncysh <integer ncysh default 0>]
The amount of damping, levelshifting, time at which levelshifting is automatically imposed, and Fock matrices used in the DIIS extrapolation can be modified by the following keywords
CONVERGENCE [damp <integer ndamp default 0>] \
[diis [nfock <integer nfock default 10>]] \
[lshift <real lshift default 0.5>] \
[hl_tol <real hl_tol default 0.1>]]
CONVERGENCE DAMP Keyword¶
Damping is defined to be the percentage of the previous iterations density mixed with the current iterations density. So, for example
CONVERGENCE damp 70
would mix 30% of the current iteration density with 70% of the previous iteration density.
CONVERGENCE LSHIFT Keyword¶
LevelShifting is defined as the amount of shift applied to the diagonal
elements of the unoccupied block of the Fock matrix. The shift is
specified by the keyword lshift
. For example the directive,
CONVERGENCE lshift 0.5
causes the diagonal elements of the Fock matrix corresponding to the virtual orbitals to be shifted by 0.5 a.u. By default, this levelshifting procedure is switched on whenever the HOMOLUMO gap is small. Small is defined by default to be 0.05 au but can be modified by the directive hl_tol. An example of changing the HOMOLUMO gap tolerance to 0.01 would be,
CONVERGENCE hl_tol 0.01
CONVERGENCE DIIS Keyword¶
Direct inversion of the iterative subspace with extrapolation of up to 10 Fock matrices is a default optimization procedure. For large molecular systems the amount of available memory may preclude the ability to store this number of N^{2} arrays in global memory. The user may then specify the number of Fock matrices to be used in the extrapolation (must be greater than three (3) to be effective). To set the number of Fock matrices stored and used in the extrapolation procedure to 3 would take the form,
CONVERGENCE diis 3
The user has the ability to simply turn off any optimization procedures deemed undesirable with the obvious keywords,
CONVERGENCE [nodamping] [nodiis] [nolevelshifting]
For systems where the initial guess is very poor, the user can try using fractional occupation of the orbital levels during the initial cycles of the SCF convergence^{90}. The input has the following form
CONVERGENCE rabuck [n_rabuck <integer n_rabuck default 25>]]
where the optional value n_rabuck
determines the number of SCF cycles
during which the method will be active. For example, to set equal to 30
the number of cycles where the Rabuck method is active, you need to use
the following line
CONVERGENCE rabuck 30
CONVERGENCE FAST Keyword¶
convergence fast
turns on a series of parameters that most often speedup convergence, but not in 100% of the cases.
CONVERGENCE fast
Here is an input snippet that would give you the same result as convergence fast
dft
convergence lshift 0. ncydp 0 dampon 1d99 dampoff 1d4 damp 40
end
set quickguess t
task dft
CDFT: Constrained DFT¶
This option enables the constrained DFT formalism by Wu and Van Voorhis^{91}:
CDFT <integer fatom1 latom1> [<integer fatom2 latom2>] (chargespin <real constaint_value>) \
[pop (beckemullikenlowdin) default lowdin]
Variables fatom1
and latom1
define the first and last atom of the group
of atoms to which the constraint will be applied. Therefore, the atoms in
the same group should be placed continuously in the geometry input. If
fatom2
and latom2
are specified, the difference between group 1 and 2
(i.e. 12) is constrained.
The constraint can be either on the charge or the spin density (number of
alpha  beta electrons) with a user specified constraint_value
. Note:
No gradients have been implemented for the spin constraints case.
Geometry optimizations can only be performed using the charge
constraint.
To calculate the charge or spin density, the Becke, Mulliken, and Lowdin population schemes can be used. The Lowdin scheme is default while the Mulliken scheme is not recommended. If basis sets with many diffuse functions are used, the Becke population scheme is recommended.
Multiple constraints can be defined simultaniously by defining multiple cdft lines in the input. The same population scheme will be used for all constraints and only needs to be specified once. If multiple population options are defined, the last one will be used. When there are convergence problems with multiple constraints, the user is advised to do one constraint first and to use the resulting orbitals for the next step of the constrained calculations.
It is best to put convergence nolevelshifting
in the dft directive to
avoid issues with gradient calculations and convergence in CDFT. Use
orbital swap to get a brokensymmetry solution.
An input example is given below.
geometry
symmetry
C 0.0 0.0 0.0
O 1.2 0.0 0.0
C 0.0 0.0 2.0
O 1.2 0.0 2.0
end
basis
* library 631G*
end
dft
xc b3lyp
convergence nolevelshifting
odft
mult 1
vectors swap beta 14 15
cdft 1 2 charge 1.0
end
task dft
SMEAR: Fractional Occupation of the Molecular Orbitals¶
The SMEAR
keyword is useful in cases with many degenerate states near
the HOMO (eg metallic clusters)
SMEAR <real smear default 0.001>
This option allows fractional occupation of the molecular orbitals. A Gaussian broadening function of exponent smear is used as described in the paper by Warren and Dunlap^{92}. The user must be aware that an additional energy term is added to the total energy in order to have energies and gradients consistent.
FON: Calculations with fractional numbers of electrons¶
Restricted¶
fon partial 3 electrons 1.8 filled 2
Here 1.8 electrons will be equally divided over 3 valence orbitals and 2 orbitals are fully filled. The total number of electrons here is 5.8
Example input:
echo
title "carbon atom"
start carbon_fon
geometry
symmetry c1
C 0.0 0.0 0.0
end
basis
* library 631G
end
dft
direct
grid xfine
convergence energy 1d8
xc pbe0
fon partial 3 electrons 1.8 filled 2
end
task dft energy
Unrestricted¶
fon alpha partial 3 electrons 0.9 filled 2
fon beta partial 3 electrons 0.9 filled 2
Here 0.9 electrons will be equally divided over 3 alpha valence orbitals and 2 alpha orbitals are fully filled. Similarly for beta. The total number of electrons here is 5.8
Example input:
echo
title "carbon atom"
start carbon_fon
geometry
C 0.0 0.0 0.0
end
basis
* library 631G
end
dft
odft
fon alpha partial 3 electrons 0.9 filled 2
fon beta partial 3 electrons 0.9 filled 2
end
task dft energy
To set fractional numbers in the core orbitals, add the following directive in the input file:
set dft:core_fon .true.
Example input:
dft
print "final vectors analysis"
odft
direct
fon alpha partial 2 electrons 1.0 filled 2
fon beta partial 2 electrons 1.0 filled 2
xc pbe0
convergence energy 1d8
end
task dft
OCCUP: Controlling the occupations of molecular orbitals¶
Example:
echo
start h2o_core_hole
memory 1000 mb
geometry units au
O 0 0 0
H 0 1.430 1.107
H 0 1.430 1.107
end
basis
O library 631g*
H library 631g*
end
occup
6 6 # occupation list for 6 alpha and 6 beta orbitals
1.0 0.0 # corehole in the first beta orbital
1.0 1.0
1.0 1.0
1.0 1.0
1.0 1.0
0.0 0.0
end
dft
odft
mult 1
xc beckehandh
end
task dft
GRID: Numerical Integration of the XC Potential¶
GRID [(xcoarsecoarsemediumfinexfinehuge) default medium] \
[(gausleglebedev ) default lebedev ] \
[(beckeerf1erf2ssf) default erf1] \
[(eulermuratreutler) default mura] \
[rm <real rm default 2.0>] \
[nodisk]
A numerical integration is necessary for the evaluation of the
exchangecorrelation contribution to the density functional. The default
quadrature used for the numerical integration is an EulerMacLaurin
scheme for the radial components (with a modified MuraKnowles
transformation) and a Lebedev scheme for the angular components. Within
this numerical integration procedure various levels of accuracy have
been defined and are available to the user. The user can specify the
level of accuracy with the keywords; xcoarse
, coarse
, medium
, fine
, xfine
and
huge
. The default is medium
.
GRID [xcoarsecoarsemediumfinexfinehuge]
Our intent is to have a numerical integration scheme which would give us approximately the accuracy defined below regardless of molecular composition.
Keyword  Total Energy Target Accuracy 

xcoarse  1⋅10^{4} 
coarse  1⋅10^{5} 
medium  1⋅10^{6} 
fine  1⋅10^{7} 
xfine  1⋅10^{8} 
huge  1⋅10^{10} 
In order to determine the level of radial and angular quadrature needed to give us the target accuracy, we computed total DFT energies at the LDA level of theory for many homonuclear atomic, diatomic and triatomic systems in rows 14 of the periodic table. In each case all bond lengths were set to twice the BraggSlater radius. The total DFT energy of the system was computed using the converged SCF density with atoms having radial shells ranging from 35235 (at fixed 48/96 angular quadratures) and angular quadratures of 12/2448/96 (at fixed 235 radial shells). The error of the numerical integration was determined by comparison to a “best” or most accurate calculation in which a grid of 235 radial points 48 theta and 96 phi angular points on each atom was used. This corresponds to approximately 1 million points per atom. The following tables were empirically determined to give the desired target accuracy for DFT total energies. These tables below show the number of radial and angular shells which the DFT module will use for for a given atom depending on the row it is in (in the periodic table) and the desired accuracy. Note, differing atom types in a given molecular system will most likely have differing associated numerical grids. The intent is to generate the desired energy accuracy (at the expense of speed of the calculation).
Keyword  Radial  Angular 

xcoarse  21  194 
coarse  35  302 
medium  49  434 
fine  70  590 
xfine  100  1202 
Program default number of radial and angular shells empirically determined for Row 1 atoms (Li → F) to reach the desired accuracies.
Keyword  Radial  Angular 

xcoarse  42  194 
coarse  70  302 
medium  88  434 
fine  123  770 
xfine  125  1454 
huge  300  1454 
Program default number of radial and angular shells empirically determined for Row 2 atoms (Na → Cl) to reach the desired accuracies.
Keyword  Radial  Angular 

xcoarse  75  194 
coarse  95  302 
medium  112  590 
fine  130  974 
xfine  160  1454 
huge  400  1454 
Program default number of radial and angular shells empirically determined for Row 3 atoms (K → Br) to reach the desired accuracies.
Keyword  Radial  Angular 

xcoarse  84  194 
coarse  104  302 
medium  123  590 
fine  141  974 
xfine  205  1454 
huge  400  1454 
Program default number of radial and angular shells empirically determined for Row 4 atoms (Rb → I) to reach the desired accuracies.
Angular grids¶
In addition to the simple keyword specifying the desired accuracy as
described above, the user has the option of specifying a custom
quadrature of this type in which ALL atoms have the same grid
specification. This is accomplished by using the gausleg
keyword.
GaussLegendre angular grid¶
GRID gausleg <integer nradpts default 50> <integer nagrid default 10>
In this type of grid, the number of phi points is twice the number of theta points. So, for example, a specification of,
GRID gausleg 80 20
would be interpreted as 80 radial points, 20 theta points, and 40 phi points per center (or 64000 points per center before pruning).
Lebedev angular grid¶
A second quadrature is the Lebedev scheme for the angular components. Within this numerical integration procedure various levels of accuracy have also been defined and are available to the user. The input for this type of grid takes the form,
GRID lebedev <integer radpts > <integer iangquad >
In this context the variable iangquad
specifies a certain number of
angular points as indicated by the table below:
IANGQUAD  N_{angular}  l 

1  38  9 
2  50  11 
3  74  13 
4  86  15 
5  110  17 
6  146  19 
7  170  21 
8  194  23 
9  230  25 
10  266  27 
11  302  29 
12  350  31 
13  434  35 
14  590  41 
15  770  47 
16  974  53 
17  1202  59 
18  1454  65 
19  1730  71 
20  2030  77 
21  2354  83 
22  2702  89 
23  3074  95 
24  3470  101 
25  3890  107 
26  4334  113 
27  4802  119 
28  5294  125 
29  5810  131 
Therefore the user can specify any number of radial points along with the level of angular quadrature (129).
The user can also specify grid parameters specific for a given atom type: parameters that must be supplied are: atom tag and number of radial points. As an example, here is a grid input line for the water molecule
grid lebedev 80 11 H 70 8 O 90 11
Partitioning functions¶
GRID [(beckeerf1erf2ssf) default erf1]
 becke : see paper^{93}
 ssf : see paper^{94}
 erf1 : modified ssf
 erf2 : modified ssf
Erfn partitioning functions
Radial grids¶
GRID [[eulermuratreutler] default mura]
 euler : EulerMcLaurin quadrature with the transformation devised by Murray et al^{95}.
 mura : Modification of the MurrayHandyLaming scheme (we are not using the same scaling factors proposed in the paper by Mura and Knowles^{96}).
 treutler : GaussChebyshev using the transformation suggested by Treutler^{97}.
Disk usage for Grid¶
NODISK
This keyword turns off storage of grid points and weights on disk.
TOLERANCES: Screening tolerances¶
TOLERANCES [[tight] [tol_rho <real tol_rho default 1e10>] \
[accCoul <integer accCoul default 8>] \
[radius <real radius default 25.0>]]
The user has the option of controlling screening for the tolerances in the integral evaluations for the DFT module. In most applications, the default values will be adequate for the calculation, but different values can be specified in the input for the DFT module using the keywords described below.
The input parameter accCoul
is used to define the tolerance in Schwarz
screening for the Coulomb integrals. Only integrals with estimated
values greater than 10^{(accCoul)} are evaluated.
TOLERANCES accCoul <integer accCoul default 8>
Screening away needless computation of the XC functional (on the grid) due to negligible density is also possible with the use of,
TOLERANCES tol_rho <real tol_rho default 1e10>
XC functional computation is bypassed if the corresponding density
elements are less than tol_rho
.
A screening parameter, radius, used in the screening of the Becke or Delley spatial weights is also available as,
TOLERANCES radius <real radius default 25.0>
where radius
is the cutoff value in bohr.
The tolerances as discussed previously are insured at convergence. More sleazy tolerances are invoked early in the iterative process which can speed things up a bit. This can also be problematic at times because it introduces a discontinuity in the convergence process. To avoid use of initial sleazy tolerances the user can invoke the tight option:
TOLERANCES tight
This option sets all tolerances to their default/user specified values at the very first iteration.
DIRECT, SEMIDIRECT and NOIO: Hardware Resource Control¶
DIRECTINCORE
SEMIDIRECT [filesize <integer filesize default disksize>]
[memsize <integer memsize default available>]
[filename <string filename default $file_prefix.aoints$]
NOIO
The inverted chargedensity and exchangecorrelation matrices for a DFT
calculation are normally written to disk storage. The user can prevent
this by specifying the keyword noio
within the input for the DFT
directive. The input to exercise this option is as follows,
noio
If this keyword is encountered, then the two matrices (inverted chargedensity and exchangecorrelation) are computed “onthefly” whenever needed.
The INCORE
option is always assumed to be true but can be overridden
with the option DIRECT
in which case all integrals are computed
“onthefly”.
The SEMIDIRECT
option controls caching of integrals. A full description
of this option is described in the HartreeFock section. Some functionality
which is only compatible with the DIRECT
option will not, at present,
work when using SEMIDIRECT
.
ODFT and MULT: Open shell systems¶
ODFT
MULT <integer mult default 1>
Both closedshell and openshell systems can be studied using the DFT
module. Specifying the keyword MULT
within the DFT
directive allows the
user to define the spin multiplicity of the system. The form of the
input line is as follows;
MULT <integer mult default 1>
When the keyword MULT
is specified, the user can define the integer
variable mult
, where mult is equal to the number of alpha electrons
minus beta electrons, plus 1.
When MULT
is set to a negative number. For example, if MULT = 3
, a
triplet calculation will be performed with the beta electrons
preferentially occupied. For MULT = 3
, the alpha electrons will be
preferentially occupied.
The keyword ODFT
is unnecessary except in the context of forcing a
singlet system to be computed as an open shell system (i.e., using a
spinunrestricted wavefunction).
CGMIN: Quadratic convergence algorithm¶
The cgmin
keyword will use the quadratic convergence algorithm. It is
possible to turn the use of the quadratic convergence algorithm off with
the nocgmin
keyword.
RODFT: Restricted openshell DFT¶
The rodft
keyword will perform restricted openshell calculations. This
keyword can only be used with the CGMIN
keyword.
SIC: SelfInteraction Correction¶
sic [perturbative  oep  oeploc ]
<default perturbative>
The Perdew and Zunger^{8} method to remove the selfinteraction contained in many exchangecorrelation functionals has been implemented with the Optimized Effective Potential method^{98}^{99} within the KriegerLiIafrate approximation^{100}^{101}^{102}. Three variants of these methods are included in NWChem:
sic perturbative
This is the default option for the sic directive. After a selfconsistent calculation, the KohnSham orbitals are localized with the FosterBoys algorithm (see section on orbital localization) and the selfinteraction energy is added to the total energy. All exchangecorrelation functionals implemented in the NWChem can be used with this option.sic oep
With this option the optimized effective potential is built in each step of the selfconsistent process. Because the electrostatic potential generated for each orbital involves a numerical integration, this method can be expensive.sic oeploc
This option is similar to the oep option with the addition of localization of the KohnSham orbitals in each step of the selfconsistent process.
With oep
and oeploc
options a xfine grid
(see section about numerical integration ) must be
used in order to avoid numerical noise, furthermore the hybrid
functionals can not be used with these options. More details of the
implementation of this method can be found in the paper by Garza^{103}. The components of the
sic energy can be printed out using:
print "SIC information"
MULLIKEN: Mulliken analysis¶
Mulliken analysis of the charge distribution is invoked by the keyword:
MULLIKEN
When this keyword is encountered, Mulliken analysis of both the input density as well as the output density will occur. For example, to perform a mulliken analysis and print the explicit population analysis of the basis functions, use the following
dft
mulliken
print "mulliken ao"
end
task dft
FUKUI: Fukui Indices¶
Fukui indices analysis is invoked by the keyword:
FUKUI
When this keyword is encounters, the condensed Fukui indices will be calculated and printed in the output. Detailed information about the analysis can be obtained using the following
dft
fukui
print "Fukui information"
end
task dft
The implementation of the Fukui analyis in NWChem was based on the papers by Galvan^{104} and by Chamorro^{105}.
This implementation makes use of the generalized Fukui indices ().
The traditional, spinrestricted, Fukui indices are given by , and their average:
BSSE: Basis Set Superposition Error¶
Particular care is required to compute BSSE by the counterpoise method for the DFT module. In order to include terms deriving from the numerical grid used in the XC integration, the user must label the ghost atoms not just bq, but bq followed by the given atomic symbol. For example, the first component needed to compute the BSSE for the water dimer, should be written as follows
geometry h2o autosym units au
O 0.00000000 0.00000000 0.22143139
H 1.43042868 0.00000000 0.88572555
H 1.43042868 0.00000000 0.88572555
bqH 0.71521434 0.00000000 0.33214708
bqH 0.71521434 0.00000000 0.33214708
bqO 0.00000000 0.00000000 0.88572555
end
basis
H library augccpvdz
O library augccpvdz
bqH library H augccpvdz
bqO library O augccpvdz
end
Please note that the ghost oxygen atom has been labeled bqO
, and
not just bq
.
DISP: Empirical Longrange Contribution (vdW)¶
DISP \
[ vdw <real vdw integer default 2]] \
[[s6 <real s6 default depends on XC functional>] \
[ alpha <real alpha default 20.0d0] \
[ off ]
When systems with high dependence on van der Waals interactions are computed, the dispersion term may be added empirically through longrange contribution DFTD, i.e. E_{DFTD}=E_{DFTKS}+E_{disp}, where:
In this equation, the s_{6} term depends in the functional and basis set used, C_{6}^{ij} is the dispersion coefficient between pairs of atoms. R_{vdw} and R_{ij} are related with van der Waals atom radii and the nucleus distance respectively. The α value contributes to control the corrections at intermediate distances.
There are available three ways to compute C^{6}_{ij}:

where N_{eff} and C_{6} are obtained from references ^{106} and ^{107} (Use
vdw 0
) 
See details in reference^{108}. (Use
vdw 1)

See details in reference^{89}. (Use
vdw 2
)
Note that in each option there is a certain set of C_{6} and R_{vdw}. Also note that Grimme only defined parameters for elements up to Z=54 for the dispersion correction above. C_{6} values for elements above Z=54 have been set to zero.
For options vdw 1
and vdw 2
, there are s_{6} values by default for
some functionals and triplezeta plus double polarization basis set
(TZV2P):
vdw 1
BLYP 1.40, PBE 0.70 and BP86 1.30.vdw 2
BLYP 1.20, PBE 0.75, BP86 1.05, B3LYP 1.05, Becke97D 1.25 and TPSS 1.00.
Grimme’s DFTD3 is also available. Here the dispersion term has the following form:
This new dispersion correction covers elements through Z=94. C^{ij}_{n} (n=6,8) are coordination and geometry dependent. Details about the functional form can be found in reference ^{109}.
To use the Grimme DFTD3 dispersion correction, use the option

vdw 3
(s6
andalpha
cannot be set manually). Functionals for which DFTD3 is available in NWChem are BLYP, B3LYP, BP86, Becke97D, PBE96, TPSS, PBE0, B2PLYP, BHLYP, TPSSH, PWB6K, B1B95, SSBD, MPW1B95, MPWB1K, M05, M052X, M06L, M06, M062X, and M06HF 
vdw 4
triggers the DFTD3BJ dispersion model. Currently only BLYP, B3LYP, BHLYP, TPSS, TPSSh, B2PLYP, B97D, BP86, PBE96, PW6B95, revPBE, B3PW91, pwb6k, b1b95, CAMB3LYP, LCwPBE, HCTH120, MPW1B95, BOP, OLYP, BPBE, OPBE and SSB are supported.
This capability is also supported for energy gradients and Hessian. Is possible to be deactivated with OFF.
NOSCF: Non SelfConsistent Calculations¶
The noscf
keyword can be used to to calculate the non selfconsistent energy
for a set of input vectors. For example, the following input shows how a
non selfconsistent B3LYP energy can be calculated using a
selfconsistent set of vectors calculated at the HartreeFock level.
start h2onoscf
geometry units angstrom
O 0.00000000 0.00000000 0.11726921
H 0.75698224 0.00000000 0.46907685
H 0.75698224 0.00000000 0.46907685
end
basis spherical
* library augccpvdz
end
dft
xc hfexch
vectors output hf.movecs
end
task dft energy
dft
xc b3lyp
vectors input hf.movecs
noscf
end
task dft energy
XDM: Exchangehole dipole moment dispersion model¶
XDM [ a1 <real a1> ] [ a2 <real a2> ]
See details (including list of a1 and a2 parameters) in paper[delaroza2013] and the website http://schooner.chem.dal.ca/wiki/XDM
geometry
O 0.190010095135 1.168397415155 0.925531922479
H 0.124425719598 0.832776238160 1.818190662986
H 0.063897685990 0.392575837594 0.364048725248
O 0.174717244879 1.084630474836 0.860510672419
H 0.566281023931 1.301941006866 1.427261487135
H 0.935093179777 1.047335209207 1.441842151158
end
basis spherical
* library augccpvdz
end
dft
direct
xc b3lyp
xdm a1 0.6224 a2 1.7068
end
task dft optimize
Print Control¶
PRINTNOPRINT
The PRINTNOPRINT
options control the level of output in the DFT.
Please see some examples using this directive in Sample input
file. Known controllable print options
are:
Name  Print Level  Description 

“all vector symmetries”  high  symmetries of all molecular orbitals 
“alpha partner info”  high  unpaired alpha orbital analysis 
“common”  debug  dump of common blocks 
“convergence”  default  convergence of SCF procedure 
“coulomb fit”  high  fitting electronic charge density 
“dft timings”  high  
“final vectors”  high  
“final vectors analysis”  high  print all orbital energies and orbitals 
“final vector symmetries”  default  symmetries of final molecular orbitals 
“information”  low  general information 
“initial vectors”  high  
“intermediate energy info”  high  
“intermediate evals”  high  intermediate orbital energies 
“intermediate fock matrix”  high  
“intermediate overlap”  high  overlaps between the alpha and beta sets 
“intermediate S2”  high  values of S2 
“intermediate vectors”  high  intermediate molecular orbitals 
“interm vector symm”  high  symmetries of intermediate orbitals 
“io info”  debug  reading from and writing to disk 
“kinetic_energy”  high  kinetic energy 
“mulliken ao”  high  mulliken atomic orbital population 
“multipole”  default  moments of alpha, beta, and nuclear charge densities 
“parameters”  default  input parameters 
“quadrature”  high  numerical quadrature 
“schwarz”  high  integral screening info & stats at completion 
“screening parameters”  high  integral accuracies 
“semidirect info”  default  semi direct algorithm 
DFT Print Control Specifications
SpinOrbit Density Functional Theory (SODFT)¶
The spinorbit DFT module (SODFT) in the NWChem code allows for the variational treatment of the oneelectron spinorbit operator within the DFT framework. Calculations can be performed either with an electron relativistic approach (ZORA) or with an effective core potential (ECP) and a matching spinorbit potential (SO). The current implementation does NOT use symmetry.
The actual SODFT calculation will be performed when the input module encounters the TASK directive (TASK).
TASK SODFT
Input parameters are the same as for the DFT. Some of the DFT options
are not available in the SODFT. These are max_ovl
and sic
.
Besides using the standard ECP and basis sets, see Effective Core Potentials for details, one also has to specify a spinorbit (SO) potential. The input specification for the SO potential can be found in Effective Core Potentials. At this time we have not included any spinorbit potentials in the basis set library. However, one can get these from the Stuttgart/Köln web pages http://www.tc.unikoeln.de/PP/clickpse.en.html.
Note: One should use a combination of ECP and SO potentials that were designed for the same size core, i.e., don’t use a small core ECP potential with a large core SO potential (it will produce erroneous results).
The following is an example of a calculation of UO_{2}:
start uo2_sodft
echo
charge 2
geometry
U 0.00000 0.00000 0.00000
O 0.00000 0.00000 1.68000
O 0.00000 0.00000 1.68000
end
basis "ao basis"
* library "stuttgart rlc ecp"
END
ECP
* library "stuttgart rlc ecp"
END
SO
U p
2 3.986181 1.816350
2 2.000160 11.543940
2 0.960841 0.794644
U d
2 4.147972 0.353683
2 2.234563 3.499282
2 0.913695 0.514635
U f
2 3.998938 4.744214
2 1.998840 5.211731
2 0.995641 1.867860
END
dft
mult 1
xc hfexch
end
task sodft
SYM and ADAPT¶
The options SYM
and ADAPT
works the same way as the analogous options for the SCF code.
Therefore please use the following links for SYM and
ADAPT, respectively.
References¶

Köster, A. M.; Reveles, J. U.; Campo, J. M. del. Calculation of ExchangeCorrelation Potentials with Auxiliary Function Densities. The Journal of Chemical Physics 2004, 121 (8), 3417–3424. https://doi.org/10.1063/1.1771638. ↩

Slater, J. C.; Johnson, K. H. SelfConsistentField Xα Cluster Method for Polyatomic Molecules and Solids. Phys. Rev. B 1972, 5, 844–853. https://doi.org/10.1103/PhysRevB.5.844. ↩↩

Slater, J. C. Quantum Theory of Molecules and Solids: The SelfConsistent Field for Molecules and Solids; McGrawHill Education, 1974; p 640. ↩↩

Vosko, S. H.; Wilk, L.; Nusair, M. Accurate SpinDependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis. Canadian Journal of physics 1980, 58 (8), 1200–1211. https://doi.org/10.1139/p80159. ↩↩↩↩↩↩↩

Becke, A. D. A New Mixing of HartreeFock and Local DensityFunctional Theories. The Journal of Chemical Physics 1993, 98 (2), 1372–1377. https://doi.org/https://aip.scitation.org/doi/abs/10.1063/1.464304. ↩↩

Becke, A. D. DensityFunctional Thermochemistry. III. The Role of Exact Exchange. The Journal of Chemical Physics 1993, 98 (7), 5648–5652. https://doi.org/10.1063/1.464913. ↩↩↩

Becke, A. D. DensityFunctional Thermochemistry. V. Systematic Optimization of ExchangeCorrelation Functionals. The Journal of Chemical Physics 1997, 107 (20), 8554–8560. https://doi.org/10.1063/1.475007. ↩↩

Perdew, J. P.; Zunger, A. SelfInteraction Correction to DensityFunctional Approximations for ManyElectron Systems. Phys. Rev. B 1981, 23, 5048–5079. https://doi.org/10.1103/PhysRevB.23.5048. ↩↩

Perdew, J. P.; Wang, Y. Accurate and Simple Analytic Representation of the ElectronGas Correlation Energy. Phys. Rev. B 1992, 45, 13244–13249. https://doi.org/10.1103/PhysRevB.45.13244. ↩↩

Becke, A. D. On the LargeGradient Behavior of the Density Functional Exchange Energy. The Journal of Chemical Physics 1986, 85 (12), 7184–7187. https://doi.org/10.1063/1.451353. ↩

Becke, A. D. DensityFunctional ExchangeEnergy Approximation with Correct Asymptotic Behavior. Physical Review A 1988, 38 (6), 3098–3100. https://doi.org/10.1103/PhysRevA.38.3098. ↩

Perdew, J. P. DensityFunctional Approximation for the Correlation Energy of the Inhomogeneous Electron Gas. Physical Review B 1986, 33 (12), 8822–8824. https://doi.org/10.1103/PhysRevB.33.8822. ↩↩

Perdew, J. P.; Burke, K.; Ernzerhof, M. Errata: Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. https://doi.org/10.1103/PhysRevLett.77.3865. ↩↩

Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1997, 78, 1396–1396. https://doi.org/10.1103/PhysRevLett.78.1396. ↩↩

Gill, P. M. W. A New GradientCorrected Exchange Functional. Molecular Physics 1996, 89 (2), 433–445. https://doi.org/10.1080/002689796173813. ↩

Handy, N. C.; Cohen, A. J. LeftRight Correlation Energy. Molecular Physics 2001, 99 (5), 403–412. https://doi.org/10.1080/00268970010018431. ↩

Adamo, C.; Barone, V. Exchange Functionals with Improved LongRange Behavior and Adiabatic Connection Methods Without Adjustable Parameters: The mPW and mPW1PW Models. The Journal of Chemical Physics 1998, 108 (2), 664–675. https://doi.org/10.1063/1.475428. ↩

Zhao, Y.; Truhlar, D. G. Design of Density Functionals That Are Broadly Accurate for Thermochemistry, Thermochemical Kinetics, and Nonbonded Interactions. The Journal of Physical Chemistry A 2005, 109 (25), 5656–5667. https://doi.org/10.1021/jp050536c. ↩

Filatov, M.; Thiel, W. A New GradientCorrected ExchangeCorrelation Density Functional. Molecular Physics 1997, 91 (5), 847–860. https://doi.org/10.1080/002689797170950. ↩↩↩

Filatov, M.; Thiel, W. A Nonlocal Correlation Energy Density Functional from a Coulomb Hole Model. International Journal of Quantum Chemistry 1997, 62 (6), 603–616. https://doi.org/10.1002/(sici)1097461x(1997)62:6<603::aidqua4>3.0.co;2#. ↩↩↩

Hammer, B.; Hansen, L. B.; Nørskov, J. K. Improved Adsorption Energetics Within DensityFunctional Theory Using Revised PerdewBurkeErnzerhof Functionals. Physical Review B 1999, 59 (11), 7413–7421. https://doi.org/10.1103/physrevb.59.7413. ↩↩

Zhang, Y.; Yang, W. Comment on Generalized Gradient Approximation Made Simple. Physical Review Letters 1998, 80 (4), 890–890. https://doi.org/10.1103/physrevlett.80.890. ↩↩

Zhao, Y.; Lynch, B. J.; Truhlar, D. G. Development and Assessment of a New Hybrid Density Functional Model for Thermochemical Kinetics. The Journal of Physical Chemistry A 2004, 108 (14), 2715–2719. https://doi.org/10.1021/jp049908s. ↩↩↩↩↩↩

Lee, C.; Yang, W.; Parr, R. G. Development of the ColleSalvetti CorrelationEnergy Formula into a Functional of the Electron Density. Physical Review B 1988, 37 (2), 785–789. https://doi.org/10.1103/PhysRevB.37.785. ↩

Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Physical Review B 1992, 46 (11), 6671–6687. https://doi.org/10.1103/PhysRevB.46.6671. ↩

Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Erratum: Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation. Physical Review B 1993, 48 (7), 4978–4978. https://doi.org/10.1103/PhysRevB.48.4978.2. ↩

Tsuneda, T.; Suzumura, T.; Hirao, K. A New OneParameter Progressive CollesalvettiType Correlation Functional. The Journal of Chemical Physics 1999, 110 (22), 10664–10678. https://doi.org/10.1063/1.479012. ↩↩

Hamprecht, F. A.; Cohen, A. J.; Tozer, D. J.; Handy, N. C. Development and Assessment of New ExchangeCorrelation Functionals. The Journal of Chemical Physics 1998, 109 (15), 6264–6271. https://doi.org/10.1063/1.477267. ↩↩

Boese, A. D.; Doltsinis, N. L.; Handy, N. C.; Sprik, M. New Generalized Gradient Approximation Functionals. The Journal of Chemical Physics 2000, 112 (4), 1670–1678. https://doi.org/10.1063/1.480732. ↩↩

Boese, A. D.; Martin, J. M. L.; Handy, N. C. The Role of the Basis Set: Assessing Density Functional Theory. The Journal of Chemical Physics 2003, 119 (6), 3005–3014. https://doi.org/10.1063/1.1589004. ↩

Boese, A. D.; Handy, N. C. A New Parametrization of Exchangecorrelation Generalized Gradient Approximation Functionals. The Journal of Chemical Physics 2001, 114 (13), 5497–5503. https://doi.org/10.1063/1.1347371. ↩

Cohen, A. J.; Handy, N. C. Assessment of Exchange Correlation Functionals. Chemical Physics Letters 2000, 316 (12), 160–166. https://doi.org/10.1016/s00092614(99)012737. ↩

Menconi, G.; Wilson, P. J.; Tozer, D. J. Emphasizing the ExchangeCorrelation Potential in Functional Development. The Journal of Chemical Physics 2001, 114 (9), 3958–3967. https://doi.org/10.1063/1.1342776. ↩

Boese, A. D.; Chandra, A.; Martin, J. M. L.; Marx, D. From Ab Initio Quantum Chemistry to Molecular Dynamics: The Delicate Case of Hydrogen Bonding in Ammonia. The Journal of Chemical Physics 2003, 119 (12), 5965–5980. https://doi.org/10.1063/1.1599338. ↩

Tsuneda, T.; Suzumura, T.; Hirao, K. A Reexamination of Exchange Energy Functionals. The Journal of Chemical Physics 1999, 111 (13), 5656–5667. https://doi.org/10.1063/1.479954. ↩

Perdew, J. P.; Kurth, S.; Zupan, A.; Blaha, P. Accurate Density Functional with Correct Formal Properties: A Step Beyond the Generalized Gradient Approximation. Physical Review Letters 1999, 82 (12), 2544–2547. https://doi.org/10.1103/physrevlett.82.2544. ↩↩

Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Climbing the Density Functional Ladder: Nonempirical MetaGeneralized Gradient Approximation Designed for Molecules and Solids. Physical Review Letters 2003, 91 (14), 146401. https://doi.org/10.1103/physrevlett.91.146401. ↩↩

Zhao, Y.; Truhlar, D. G. Hybrid Meta Density Functional Theory Methods for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions: The MPW1B95 and MPWB1K Models and Comparative Assessments for Hydrogen Bonding and van Der Waals Interactions. The Journal of Physical Chemistry A 2004, 108 (33), 6908–6918. https://doi.org/10.1021/jp048147q. ↩↩↩

Zhao, Y.; Schultz, N. E.; Truhlar, D. G. ExchangeCorrelation Functional with Broad Accuracy for Metallic and Nonmetallic Compounds, Kinetics, and Noncovalent Interactions. The Journal of Chemical Physics 2005, 123 (16), 161103. https://doi.org/10.1063/1.2126975. ↩↩

Zhao, Y.; Schultz, N. E.; Truhlar, D. G. Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions. Journal of Chemical Theory and Computation 2006, 2 (2), 364–382. https://doi.org/10.1021/ct0502763. ↩↩↩

Staroverov, V. N.; Scuseria, G. E.; Tao, J.; Perdew, J. P. Comparative Assessment of a New Nonempirical Density Functional: Molecules and HydrogenBonded Complexes. The Journal of Chemical Physics 2003, 119 (23), 12129–12137. https://doi.org/10.1063/1.1626543. ↩

Becke, A. D. DensityFunctional Thermochemistry. IV. A New Dynamical Correlation Functional and Implications for ExactExchange Mixing. The Journal of Chemical Physics 1996, 104 (3), 1040–1046. https://doi.org/10.1063/1.470829. ↩↩

Voorhis, T. V.; Scuseria, G. E. A Novel Form for the ExchangeCorrelation Energy Functional. The Journal of Chemical Physics 1998, 109 (2), 400–410. https://doi.org/10.1063/1.476577. ↩↩↩

Zhao, Y.; Truhlar, D. G. A New Local Density Functional for MainGroup Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. The Journal of Chemical Physics 2006, 125 (19), 194101. https://doi.org/10.1063/1.2370993. ↩↩↩↩↩↩

Zhao, Y.; Truhlar, D. G. Density Functional for Spectroscopy: No LongRange SelfInteraction Error, Good Performance for Rydberg and ChargeTransfer States, and Better Performance on Average Than B3LYP for Ground States. The Journal of Physical Chemistry A 2006, 110 (49), 13126–13130. https://doi.org/10.1021/jp066479k. ↩↩↩

Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06Class Functionals and 12 Other Functionals. Theoretical Chemistry Accounts 2008, 120 (13), 215–241. https://doi.org/10.1007/s002140070310x. ↩↩↩

Zhao, Y.; Truhlar, D. G. Construction of a Generalized Gradient Approximation by Restoring the DensityGradient Expansion and Enforcing a Tight Lieboxford Bound. The Journal of Chemical Physics 2008, 128 (18), 184109. https://doi.org/10.1063/1.2912068. ↩↩↩↩↩↩↩↩↩

Peverati, R.; Truhlar, D. G. Improving the Accuracy of Hybrid MetaGGA Density Functionals by Range Separation. The Journal of Physical Chemistry Letters 2011, 2 (21), 2810–2817. https://doi.org/10.1021/jz201170d. ↩↩↩

Peverati, R.; Truhlar, D. G. M11l: A Local Density Functional That Provides Improved Accuracy for Electronic Structure Calculations in Chemistry and Physics. The Journal of Physical Chemistry Letters 2012, 3 (1), 117–124. https://doi.org/10.1021/jz201525m. ↩↩↩

Peverati, R.; Zhao, Y.; Truhlar, D. G. Generalized Gradient Approximation That Recovers the SecondOrder DensityGradient Expansion with Optimized AcrosstheBoard Performance. The Journal of Physical Chemistry Letters 2011, 2 (16), 1991–1997. https://doi.org/10.1021/jz200616w. ↩↩↩

Peverati, R.; Truhlar, D. G. Communication: A Global Hybrid Generalized Gradient Approximation to the ExchangeCorrelation Functional That Satisfies the SecondOrder DensityGradient Constraint and Has Broad Applicability in Chemistry. The Journal of Chemical Physics 2011, 135 (19), 191102. https://doi.org/10.1063/1.3663871. ↩↩↩

Pernal, K.; Podeszwa, R.; Patkowski, K.; Szalewicz, K. Dispersionless Density Functional Theory. Physical Review Letters 2009, 103 (26), 263201. https://doi.org/10.1103/physrevlett.103.263201. ↩

Wilson, P. J.; Bradley, T. J.; Tozer, D. J. Hybrid ExchangeCorrelation Functional Determined from Thermochemical Data and Ab Initio Potentials. The Journal of Chemical Physics 2001, 115 (20), 9233–9242. https://doi.org/10.1063/1.1412605. ↩

Keal, T. W.; Tozer, D. J. Semiempirical Hybrid Functional with Improved Performance in an Extensive Chemical Assessment. The Journal of Chemical Physics 2005, 123 (12), 121103. https://doi.org/10.1063/1.2061227. ↩

Grimme, S. Semiempirical GGAType Density Functional Constructed with a LongRange Dispersion Correction. Journal of Computational Chemistry 2006, 27 (15), 1787–1799. https://doi.org/10.1002/jcc.20495. ↩

Schmider, H. L.; Becke, A. D. Optimized Density Functionals from the Extended G2 Test Set. The Journal of Chemical Physics 1998, 108 (23), 9624–9631. https://doi.org/10.1063/1.476438. ↩

Adamo, C.; Barone, V. Toward Reliable Density Functional Methods Without Adjustable Parameters: The PBE0 Model. The Journal of Chemical Physics 1999, 110 (13), 6158–6170. https://doi.org/10.1063/1.478522. ↩

Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. Adiabatic Connection for Kinetics. The Journal of Physical Chemistry A 2000, 104 (21), 4811–4815. https://doi.org/10.1021/jp000497z. ↩

Sun, J.; Perdew, J. P.; Ruzsinszky, A. Semilocal Density Functional Obeying a Strongly Tightened Bound for Exchange. Proceedings of the National Academy of Sciences 2015, 112 (3), 685–689. https://doi.org/10.1073/pnas.1423145112. ↩

Verma, P.; Truhlar, D. G. HLE16: A Local KohnSham Gradient Approximation with Good Performance for Semiconductor Band Gaps and Molecular Excitation Energies. The Journal of Physical Chemistry Letters 2017, 8 (2), 380–387. https://doi.org/10.1021/acs.jpclett.6b02757. ↩

Yang, Z.; Peng, H.; Sun, J.; Perdew, J. P. More Realistic Band Gaps from MetaGeneralized Gradient Approximations: Only in a Generalized KohnSham Scheme. Physical Review B 2016, 93 (20), 205205. https://doi.org/10.1103/physrevb.93.205205. ↩

MejiaRodriguez, D.; Trickey, S. B. Deorbitalization Strategies for MetaGeneralizedGradientApproximation ExchangeCorrelation Functionals. Physical Review A 2017, 96 (5), 052512. https://doi.org/10.1103/physreva.96.052512. ↩

Wang, Y.; Jin, X.; Yu, H. S.; Truhlar, D. G.; He, X. Revised M06l Functional for Improved Accuracy on Chemical Reaction Barrier Heights, Noncovalent Interactions, and SolidState Physics. Proceedings of the National Academy of Sciences 2017, 114 (32), 8487–8492. https://doi.org/10.1073/pnas.1705670114. ↩

Wang, Y.; Verma, P.; Jin, X.; Truhlar, D. G.; He, X. Revised M06 Density Functional for MainGroup and TransitionMetal Chemistry. Proceedings of the National Academy of Sciences 2018, 115 (41), 10257–10262. https://doi.org/10.1073/pnas.1810421115. ↩

Chai, J.D.; HeadGordon, M. Systematic Optimization of LongRange Corrected Hybrid Density Functionals. The Journal of Chemical Physics 2008, 128 (8), 084106. https://doi.org/10.1063/1.2834918. ↩

Lin, Y.S.; Li, G.D.; Mao, S.P.; Chai, J.D. LongRange Corrected Hybrid Density Functionals with Improved Dispersion Corrections. Journal of Chemical Theory and Computation 2012, 9 (1), 263–272. https://doi.org/10.1021/ct300715s. ↩

Bartók, A. P.; Yates, J. R. Regularized SCAN Functional. The Journal of Chemical Physics 2019, 150 (16), 161101. https://doi.org/10.1063/1.5094646. ↩

Furness, J. W.; Kaplan, A. D.; Ning, J.; Perdew, J. P.; Sun, J. Accurate and Numerically Efficient r2SCAN MetaGeneralized Gradient Approximation. The Journal of Physical Chemistry Letters 2020, 11 (19), 8208–8215. https://doi.org/10.1021/acs.jpclett.0c02405. ↩

Bursch, M.; Neugebauer, H.; Ehlert, S.; Grimme, S. Dispersion Corrected r2SCAN Based Global Hybrid Functionals: r2SCANh, r2SCAN0, and r2SCAN50. The Journal of Chemical Physics 2022, 156 (13), 134105. https://doi.org/10.1063/5.0086040. ↩

MejíaRodríguez, D.; Trickey, S. B. MetaGGA Performance in Solids at Almost GGA Cost. Physical Review B 2020, 102 (12), 121109. https://doi.org/10.1103/physrevb.102.121109. ↩

MejíaRodríguez, D.; Trickey, S. B. SpinCrossover from a WellBehaved, LowCost MetaGGA Density Functional. The Journal of Physical Chemistry A 2020, 124 (47), 9889–9894. https://doi.org/10.1021/acs.jpca.0c08883. ↩

CarmonaEspíndola, J.; Gázquez, J. L.; Vela, A.; Trickey, S. B. Generalized Gradient Approximation Exchange Energy Functional with NearBest Semilocal Performance. Journal of Chemical Theory and Computation 2018, 15 (1), 303–310. https://doi.org/10.1021/acs.jctc.8b00998. ↩

Kurth, S.; Perdew, J. P.; Blaha, P. Molecular and SolidState Tests of Density Functional Approximations: LSD, GGAs, and MetaGGAs. International Journal of Quantum Chemistry 1999, 75 (45), 889–909. https://doi.org/10.1002/(sici)1097461x(1999)75:4/5<889::aidqua54>3.0.co;28. ↩

Savin, A. Beyond the KohnSham Determinant. In Recent advances in density functional methods; WORLD SCIENTIFIC, 1995; pp 129–153. https://doi.org/10.1142/9789812830586\_0004. ↩

Iikura, H.; Tsuneda, T.; Yanai, T.; Hirao, K. A LongRange Correction Scheme for GeneralizedGradientApproximation Exchange Functionals. The Journal of Chemical Physics 2001, 115 (8), 3540–3544. https://doi.org/10.1063/1.1383587. ↩

Tawada, Y.; Tsuneda, T.; Yanagisawa, S.; Yanai, T.; Hirao, K. A LongRangeCorrected TimeDependent Density Functional Theory. The Journal of Chemical Physics 2004, 120 (18), 8425–8433. https://doi.org/10.1063/1.1688752. ↩

Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid ExchangeCorrelation Functional Using the CoulombAttenuating Method (CAMB3LYP). Chemical Physics Letters 2004, 393 (13), 51–57. https://doi.org/10.1016/j.cplett.2004.06.011. ↩

Peach, M. J. G.; Cohen, A. J.; Tozer, D. J. Influence of CoulombAttenuation on ExchangeCorrelation Functional Quality. Phys. Chem. Chem. Phys. 2006, 8 (39), 4543–4549. https://doi.org/10.1039/b608553a. ↩

Song, J.W.; Hirosawa, T.; Tsuneda, T.; Hirao, K. LongRange Corrected Density Functional Calculations of Chemical Reactions: Redetermination of Parameter. The Journal of Chemical Physics 2007, 126 (15), 154105. https://doi.org/10.1063/1.2721532. ↩

Livshits, E.; Baer, R. A WellTempered Density Functional Theory of Electrons in Molecules. Physical Chemistry Chemical Physics 2007, 9 (23), 2932. https://doi.org/10.1039/b617919c. ↩

Cohen, A. J.; MoriSánchez, P.; Yang, W. Development of ExchangeCorrelation Functionals with Minimal ManyElectron SelfInteraction Error. The Journal of Chemical Physics 2007, 126 (19), 191109. https://doi.org/10.1063/1.2741248. ↩

Rohrdanz, M. A.; Herbert, J. M. Simultaneous Benchmarking of Ground and ExcitedState Properties with LongRangeCorrected Density Functional Theory. The Journal of Chemical Physics 2008, 129 (3), 034107. https://doi.org/10.1063/1.2954017. ↩

Govind, N.; Valiev, M.; Jensen, L.; Kowalski, K. Excitation Energies of Zinc Porphyrin in Aqueous Solution Using LongRange Corrected TimeDependent Density Functional Theory. The Journal of Physical Chemistry A 2009, 113 (21), 6041–6043. https://doi.org/10.1021/jp902118k. ↩

Baer, R.; Livshits, E.; Salzner, U. Tuned RangeSeparated Hybrids in Density Functional Theory. Annual Review of Physical Chemistry 2010, 61 (1), 85–109. https://doi.org/10.1146/annurev.physchem.012809.103321. ↩

Autschbach, J.; Srebro, M. Delocalization Error and Functional Tuning in KohnSham Calculations of Molecular Properties. Accounts of Chemical Research 2014, 47 (8), 2592–2602. https://doi.org/10.1021/ar500171t. ↩

Verma, P.; Bartlett, R. J. Increasing the Applicability of Density Functional Theory. IV. Consequences of IonizationPotential Improved ExchangeCorrelation Potentials. The Journal of Chemical Physics 2014, 140 (18), 18A534. https://doi.org/10.1063/1.4871409. ↩

Swart, M.; Solà, M.; Bickelhaupt, F. M. A New AllRound Density Functional Based on Spin States and SN2 Barriers. The Journal of Chemical Physics 2009, 131 (9), 094103. https://doi.org/10.1063/1.3213193. ↩

Swart, M.; Solà, M.; Bickelhaupt, F. M. Switching Between OPTX and PBE Exchange Functionals. Journal of Computational Methods in Sciences and Engineering 2009, 9 (12), 69–77. https://doi.org/10.3233/jcm20090230. ↩

Grimme, S. Semiempirical Hybrid Density Functional with Perturbative SecondOrder Correlation. The Journal of Chemical Physics 2006, 124 (3), 034108. https://doi.org/10.1063/1.2148954. ↩↩

Rabuck, A. D.; Scuseria, G. E. Improving SelfConsistent Field Convergence by Varying Occupation Numbers. The Journal of Chemical Physics 1999, 110 (2), 695–700. https://doi.org/10.1063/1.478177. ↩

Wu, Q.; Voorhis, T. V. Direct Optimization Method to Study Constrained Systems Within DensityFunctional Theory. Physical Review A 2005, 72 (2), 024502. https://doi.org/10.1103/physreva.72.024502. ↩

Warren, R. W.; Dunlap, B. I. Fractional Occupation Numbers and Density Functional Energy Gradients Within the Linear Combination of GaussianType Orbitals Approach. Chemical Physics Letters 1996, 262 (34), 384–392. https://doi.org/10.1016/00092614(96)011074. ↩

Becke, A. D. A Multicenter Numerical Integration Scheme for Polyatomic Molecules. The Journal of Chemical Physics 1988, 88 (4), 2547–2553. https://doi.org/10.1063/1.454033. ↩

Stratmann, R. E.; Scuseria, G. E.; Frisch, M. J. Achieving Linear Scaling in ExchangeCorrelation Density Functional Quadratures. Chemical Physics Letters 1996, 257 (34), 213–223. https://doi.org/10.1016/00092614(96)006008. ↩

Murray, C. W.; Handy, N. C.; Laming, G. J. Quadrature Schemes for Integrals of Density Functional Theory. Molecular Physics 1993, 78 (4), 997–1014. https://doi.org/10.1080/00268979300100651. ↩

Mura, M. E.; Knowles, P. J. Improved Radial Grids for Quadrature in Molecular DensityFunctional Calculations. The Journal of Chemical Physics 1996, 104 (24), 9848–9858. https://doi.org/10.1063/1.471749. ↩

Treutler, O.; Ahlrichs, R. Efficient Molecular Numerical Integration Schemes. The Journal of Chemical Physics 1995, 102 (1), 346–354. https://doi.org/10.1063/1.469408. ↩

Sharp, R. T.; Horton, G. K. A Variational Approach to the Unipotential ManyElectron Problem. Physical Review 1953, 90 (2), 317–317. https://doi.org/10.1103/physrev.90.317. ↩

Talman, J. D.; Shadwick, W. F. Optimized Effective Atomic Central Potential. Physical Review A 1976, 14 (1), 36–40. https://doi.org/10.1103/physreva.14.36. ↩

Krieger, J. B.; Li, Y.; Iafrate, G. J. Construction and Application of an Accurate Local SpinPolarized KohnSham Potential with Integer Discontinuity: ExchangeOnly Theory. Physical Review A 1992, 45 (1), 101–126. https://doi.org/10.1103/physreva.45.101. ↩

Krieger, J. B.; Li, Y.; Iafrate, G. J. Systematic Approximations to the Optimized Effective Potential: Application to OrbitalDensityFunctional Theory. Physical Review A 1992, 46 (9), 5453–5458. https://doi.org/10.1103/physreva.46.5453. ↩

Li, Y.; Krieger, J. B.; Iafrate, G. J. SelfConsistent Calculations of Atomic Properties Using SelfInteractionFree ExchangeOnly KohnSham Potentials. Physical Review A 1993, 47 (1), 165–181. https://doi.org/10.1103/physreva.47.165. ↩

Garza, J.; Nichols, J. A.; Dixon, D. A. The Optimized Effective Potential and the SelfInteraction Correction in Density Functional Theory: Application to Molecules. The Journal of Chemical Physics 2000, 112 (18), 7880–7890. https://doi.org/10.1063/1.481421. ↩

Galvan, M.; Vela, A.; Gazquez, J. L. Chemical Reactivity in SpinPolarized Density Functional Theory. The Journal of Physical Chemistry 1988, 92 (22), 6470–6474. https://doi.org/10.1021/j100333a056. ↩

Chamorro, E.; Pérez, P. CondensedtoAtoms Electronic Fukui Functions Within the Framework of SpinPolarized DensityFunctional Theory. The Journal of Chemical Physics 2005, 123 (11), 114107. https://doi.org/10.1063/1.2033689. ↩

Wu, Q.; Yang, W. Empirical Correction to Density Functional Theory for van Der Waals Interactions. The Journal of Chemical Physics 2002, 116 (2), 515–524. https://doi.org/10.1063/1.1424928. ↩

Zimmerli, U.; Parrinello, M.; Koumoutsakos, P. Dispersion Corrections to Density Functionals for Water Aromatic Interactions. The Journal of Chemical Physics 2004, 120 (6), 2693–2699. https://doi.org/10.1063/1.1637034. ↩

Grimme, S. Accurate Description of van Der Waals Complexes by Density Functional Theory Including Empirical Corrections. Journal of Computational Chemistry 2004, 25 (12), 1463–1473. https://doi.org/10.1002/jcc.20078. ↩

Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFTd) for the 94 Elements hPu. The Journal of Chemical Physics 2010, 132 (15), 154104. https://doi.org/10.1063/1.3382344. ↩