| 4:14:25 AM PDT - Fri, Aug 3rd 2018 |
|
Hello!
Let's start with a short summary (details are further down).
The vibrational analysis of an optimized geometry (DFT with cpbe96 xpbe96) returns two imaginary modes (i33cm-1 and i24 cm-1 after projection), but numerical differentiation characterize the same stationary point as a minimum. Moreover, IRC and ZTS calculations suggest positive curvature along the first of the imaginary modes identified by the analytical vibrational analysis.
Now, I'm puzzled: the analytical vibrational analysis says "it's a second order saddle point", but all the rest screams "it's a minimum".
So, should we trust the analytical Hessian and the resulting negative curvatures? Or are those imaginary modes some kind of artifact?
Any comment or suggestion on how to get rid of those imaginary modes is very welcome.
Cheers,
Marco
Here are the details... and if you want more, just ask.
Searching for the global minimum of a Ru complex (NWChem-6.6, cpbe96+xpbe96 LANL2DZ basis set and polarization on selected atoms), I got a second order saddle point. Attempts to re-optimize after manual modification of the geometry could not get rid of the imaginary modes. Instead, numerical calculation of the Hessian characterizes the same stationary point as a minimum.
So, I tried to improve the accuracy of the DFT method both in the geometry optimizations and Hessian calculations.
Here is what I tried:
- tight convergence criteria in the SCF procedure (up to
CONVERGENCE density 1e-10 energy 1e-11 gradient 1e-9 with TOLERANCES accCoul 12 tight tol_rho 1e-14)
- extremely fine integration grid (up to
GRID nodisk lebedev 300 29 Ru 950 29)
- tight geometry optimization (up to
TIGHT for the DRIVER module).
These settings were used in various combinations, but in all cases the re-optimized geometry is roughly the same (RMSD lower than 0.01Å) and the vibrational analysis shows the same frequencies including the two imaginary modes (i.e., deviations below 0.1 cm-1). The input of the most demanding of these calculations is attached at the end of the post.
Next, as a further attempt to escape the saddle point or at least probe the curvature empirically, I tried IRC and ZTS calculations in the surroundings of the saddle point.
The IRC calculations along the first imaginary mode (MEPGS module, CONVERGENCE density 1e-10 energy 1e-11 gradient 1e-9, TOLERANCES accCoul 12 tight tol_rho 1e-14, and GRID nodisk lebedev 300 29 Ru 950 29) could only find points with energy higher than the initial geometry. I used EVIB=0.00000002 and larger EVIBs, but the energy of the first point found by MEPGS grows monotonously in both forward and backwards directions. These results suggest positive curvature.
Next, I run ZTS calculation between two points along the first imaginary mode with the same setting of the IRC described above. As initial and final geometries for the ZTS path I used two geometries generated by IRC calculations in opposite directions. The curvature of the optimized ZTS path is positive, with the lowest energy (-1760.72112386655) practically corresponding to the initial geometry (-1760.721123884277).
Below is an example of input files:
START
BASIS
Cl S
2.2310000E+00 -4.900589E-01
4.720000E-01 1.2542684E+00
Cl S
1.631000E-01 1.0000000E+00
Cl P
6.2960000E+00 -6.35641E-02
6.333000E-01 1.0141355E+00
Cl P
1.819000E-01 1.0000000E+00
Ru S
2.5650000E+00 -1.0431056E+00
1.5080000E+00 1.3314786E+00
5.129000E-01 5.613065E-01
Ru S
2.5650000E+00 8.770128E-01
1.5080000E+00 -1.2634660E+00
5.129000E-01 -8.384987E-01
1.362000E-01 1.0637773E+00
Ru S
4.17000E-02 1.0000000E+00
Ru P
4.8590000E+00 -9.45755E-02
1.2190000E+00 7.434798E-01
4.413000E-01 3.668144E-01
Ru P
5.725000E-01 -8.80864E-02
8.30000E-02 1.0283970E+00
Ru P
2.50000E-02 1.0000000E+00
Ru D
4.1950000E+00 4.85729E-02
1.3770000E+00 5.105223E-01
4.828000E-01 5.730028E-01
Ru D
1.501000E-01 1.0000000E+00
O S
7.8170000000E+03 1.1760E-03
1.1760000000E+03 8.9680E-03
2.732000000E+02 4.28680E-02
8.11700000E+01 1.439300E-01
2.71800000E+01 3.556300E-01
9.5320000E+00 4.612480E-01
3.4140000E+00 1.402060E-01
O S
9.5320000E+00 -1.541530E-01
9.398000E-01 1.0569140E+00
O S
2.846000E-01 1.0000000E+00
O P
3.51800000E+01 1.95800E-02
7.9040000E+00 1.242000E-01
2.3050000E+00 3.947140E-01
7.171000E-01 6.273760E-01
O P
2.137000E-01 1.0000000E+00
C S
4.2330000000E+03 1.2200E-03
6.349000000E+02 9.3420E-03
1.461000000E+02 4.54520E-02
4.25000000E+01 1.546570E-01
1.41900000E+01 3.588660E-01
5.1480000E+00 4.386320E-01
1.9670000E+00 1.459180E-01
C S
5.1480000E+00 -1.683670E-01
4.962000E-01 1.0600910E+00
C S
1.533000E-01 1.0000000E+00
C P
1.81600000E+01 1.85390E-02
3.9860000E+00 1.154360E-01
1.1430000E+00 3.861880E-01
3.594000E-01 6.401140E-01
C P
1.146000E-01 1.0000000E+00
H S
1.92384000E+01 3.28280E-02
2.8987000E+00 2.312040E-01
6.535000E-01 8.172260E-01
H S
1.776000E-01 1.0000000E+00
S4 S
1.8500000E+00 -5.324335E-01
4.035000E-01 1.2763801E+00
S4 S
1.438000E-01 1.0000000E+00
S4 P
4.9450000E+00 -6.08116E-02
4.870000E-01 1.0132686E+00
S4 P
1.379000E-01 1.0000000E+00
S4 D
4.960000E-01 1.0000000E+00
S5 S
1.8500000E+00 -5.324335E-01
4.035000E-01 1.2763801E+00
S5 S
1.438000E-01 1.0000000E+00
S5 P
4.9450000E+00 -6.08116E-02
4.870000E-01 1.0132686E+00
S5 P
1.379000E-01 1.0000000E+00
S5 D
4.960000E-01 1.0000000E+00
N7 S
5.9090000000E+03 1.1900E-03
8.875000000E+02 9.0990E-03
2.047000000E+02 4.41450E-02
5.98400000E+01 1.504640E-01
2.00000000E+01 3.567410E-01
7.1930000E+00 4.465330E-01
2.6860000E+00 1.456030E-01
N7 S
7.1930000E+00 -1.604050E-01
7.000000E-01 1.0582150E+00
N7 S
2.133000E-01 1.0000000E+00
N7 P
2.67900000E+01 1.82540E-02
5.9560000E+00 1.164610E-01
1.7070000E+00 3.901780E-01
5.314000E-01 6.371020E-01
N7 P
1.654000E-01 1.0000000E+00
N7 D
7.360000E-01 1.0000000E+00
N8 S
5.9090000000E+03 1.1900E-03
8.875000000E+02 9.0990E-03
2.047000000E+02 4.41450E-02
5.98400000E+01 1.504640E-01
2.00000000E+01 3.567410E-01
7.1930000E+00 4.465330E-01
2.6860000E+00 1.456030E-01
N8 S
7.1930000E+00 -1.604050E-01
7.000000E-01 1.0582150E+00
N8 S
2.133000E-01 1.0000000E+00
N8 P
2.67900000E+01 1.82540E-02
5.9560000E+00 1.164610E-01
1.7070000E+00 3.901780E-01
5.314000E-01 6.371020E-01
N8 P
1.654000E-01 1.0000000E+00
N8 D
7.360000E-01 1.0000000E+00
C9 S
4.2330000000E+03 1.2200E-03
6.349000000E+02 9.3420E-03
1.461000000E+02 4.54520E-02
4.25000000E+01 1.546570E-01
1.41900000E+01 3.588660E-01
5.1480000E+00 4.386320E-01
1.9670000E+00 1.459180E-01
C9 S
5.1480000E+00 -1.683670E-01
4.962000E-01 1.0600910E+00
C9 S
1.533000E-01 1.0000000E+00
C9 P
1.81600000E+01 1.85390E-02
3.9860000E+00 1.154360E-01
1.1430000E+00 3.861880E-01
3.594000E-01 6.401140E-01
C9 P
1.146000E-01 1.0000000E+00
C9 D
5.870000E-01 1.0000000E+00
C56 S
4.2330000000E+03 1.2200E-03
6.349000000E+02 9.3420E-03
1.461000000E+02 4.54520E-02
4.25000000E+01 1.546570E-01
1.41900000E+01 3.588660E-01
5.1480000E+00 4.386320E-01
1.9670000E+00 1.459180E-01
C56 S
5.1480000E+00 -1.683670E-01
4.962000E-01 1.0600910E+00
C56 S
1.533000E-01 1.0000000E+00
C56 P
1.81600000E+01 1.85390E-02
3.9860000E+00 1.154360E-01
1.1430000E+00 3.861880E-01
3.594000E-01 6.401140E-01
C56 P
1.146000E-01 1.0000000E+00
C56 D
5.870000E-01 1.0000000E+00
H57 S
1.92384000E+01 3.28280E-02
2.8987000E+00 2.312040E-01
6.535000E-01 8.172260E-01
H57 S
1.776000E-01 1.0000000E+00
H57 P
3.560000E-01 1.0000000E+00
END
CHARGE 0
ECP
Cl nelec 10
Cl ul
1 9.48130000E+01 -1.00000000E+01
2 1.656440000E+02 6.62729170E+01
2 3.08317000E+01 -2.89685950E+01
2 1.05841000E+01 -1.28663370E+01
2 3.7704000E+00 -1.7102170E+00
Cl s
0 1.288391000E+02 3.0000000E+00
1 1.203786000E+02 1.28528510E+01
2 6.35622000E+01 2.756723980E+02
2 1.80695000E+01 1.156777120E+02
2 3.8142000E+00 3.50606090E+01
Cl p
0 2.165263000E+02 5.0000000E+00
1 4.65723000E+01 7.4794860E+00
2 1.474685000E+02 6.130320000E+02
2 4.89869000E+01 2.808006850E+02
2 1.32096000E+01 1.078788240E+02
2 3.1831000E+00 1.53439560E+01
Ru nelec 28
Ru ul
0 5.543796303E+02 -5.15270E-02
1 1.551066871E+02 -2.01816536E+01
2 4.84976263E+01 -1.059966915E+02
2 1.47701594E+01 -4.22166788E+01
2 5.2077363E+00 -3.7675024E+00
Ru s
0 6.67118060E+01 2.9578344E+00
1 7.73503632E+01 2.53748707E+01
2 1.83571445E+01 5.361262372E+02
2 1.18404727E+01 -6.512057221E+02
2 8.1179479E+00 3.813816943E+02
Ru p
0 5.49937915E+01 4.9651557E+00
1 1.39399212E+01 2.38861501E+01
2 1.52118246E+01 4.644631344E+02
2 1.05460691E+01 -7.144451788E+02
2 7.5539486E+00 3.775503594E+02
Ru d
0 6.03444595E+01 3.0352988E+00
1 4.52100305E+01 2.32901723E+01
2 1.91190074E+01 1.460926620E+02
2 4.2712090E+00 2.89129770E+01
S4 nelec 10
S4 ul
1 5.326685222E+02 -1.00000000E+01
2 1.081342248E+02 -8.53593846E+01
2 2.45697664E+01 -3.04513290E+01
2 7.3702438E+00 -1.03745886E+01
2 2.3712569E+00 -9.899295E-01
S4 s
0 1.063176781E+02 3.0000000E+00
1 1.008245833E+02 1.06284036E+01
2 5.35858472E+01 2.236360469E+02
2 1.53706332E+01 9.36460845E+01
2 3.1778402E+00 2.87609065E+01
S4 p
0 1.019709185E+02 5.0000000E+00
1 9.32808973E+01 6.0969842E+00
2 6.51431772E+01 2.854425500E+02
2 2.46347440E+01 1.471448413E+02
2 7.8120535E+00 5.36569778E+01
2 2.3112730E+00 8.9249559E+00
S5 nelec 10
S5 ul
1 5.326685222E+02 -1.00000000E+01
2 1.081342248E+02 -8.53593846E+01
2 2.45697664E+01 -3.04513290E+01
2 7.3702438E+00 -1.03745886E+01
2 2.3712569E+00 -9.899295E-01
S5 s
0 1.063176781E+02 3.0000000E+00
1 1.008245833E+02 1.06284036E+01
2 5.35858472E+01 2.236360469E+02
2 1.53706332E+01 9.36460845E+01
2 3.1778402E+00 2.87609065E+01
S5 p
0 1.019709185E+02 5.0000000E+00
1 9.32808973E+01 6.0969842E+00
2 6.51431772E+01 2.854425500E+02
2 2.46347440E+01 1.471448413E+02
2 7.8120535E+00 5.36569778E+01
2 2.3112730E+00 8.9249559E+00
END
geometry units angstrom
Ru1 0.09290000 0.34820000 -0.05890000
Cl2 -2.55840000 4.85900000 -1.86160000
Cl3 -4.45010000 1.05160000 2.96630000
S4 -1.74170000 0.34360000 1.34610000
S5 -0.80050000 2.21350000 -1.10900000
O6 2.11520000 0.73100000 -1.21480000
N7 -0.71570000 -2.47900000 -0.74360000
N8 0.20270000 -2.43950000 1.26610000
C9 -0.03470000 -1.68520000 0.14450000
C10 -1.11610000 -3.78660000 -0.15480000
H11 -0.93330000 -4.61450000 -0.85960000
H12 -2.19540000 -3.76880000 0.09100000
C13 -0.23140000 -3.85630000 1.11080000
H14 -0.79070000 -4.19160000 2.00010000
H15 0.65170000 -4.51420000 0.98320000
C16 -0.91340000 -2.21070000 -2.14670000
C17 0.01490000 -2.79050000 -3.06750000
C18 -0.15340000 -2.54340000 -4.44740000
H19 0.56380000 -2.97520000 -5.15700000
C20 -1.21630000 -1.74220000 -4.93430000
C21 -2.14250000 -1.22360000 -4.00290000
H22 -2.98430000 -0.61780000 -4.36140000
C23 -2.02660000 -1.45390000 -2.60880000
C24 1.15200000 -3.67480000 -2.58650000
H25 1.62000000 -3.27730000 -1.66990000
H26 1.93050000 -3.77560000 -3.36190000
H27 0.79610000 -4.69750000 -2.35260000
C28 -1.34120000 -1.42960000 -6.41410000
H29 -2.39770000 -1.34050000 -6.72230000
H30 -0.86510000 -2.20640000 -7.03770000
H31 -0.85020000 -0.46570000 -6.65280000
C32 -3.08700000 -0.90350000 -1.67870000
H33 -2.98690000 0.19350000 -1.58340000
H34 -3.00730000 -1.30880000 -0.65860000
H35 -4.09630000 -1.11490000 -2.07630000
C36 1.08180000 -2.09350000 2.35330000
C37 2.48640000 -2.01930000 2.11540000
C38 3.33330000 -1.67090000 3.18790000
H39 4.41130000 -1.58200000 3.00400000
C40 2.82460000 -1.40660000 4.48410000
C41 1.43250000 -1.52840000 4.69540000
H42 1.02110000 -1.33670000 5.69430000
C43 0.54160000 -1.87990000 3.65020000
C44 3.06010000 -2.28660000 0.73850000
H45 2.82180000 -3.31100000 0.39170000
H46 4.15710000 -2.17350000 0.73860000
H47 2.64170000 -1.58410000 -0.00380000
C48 3.75930000 -0.98880000 5.60510000
H49 4.56010000 -1.73550000 5.76240000
H50 3.22040000 -0.86320000 6.55960000
H51 4.25630000 -0.02800000 5.36900000
C52 -0.94160000 -2.02620000 3.93160000
H53 -1.55530000 -1.69940000 3.07620000
H54 -1.23860000 -1.42150000 4.80480000
H55 -1.20090000 -3.08030000 4.15780000
C56 1.23780000 0.81320000 1.32770000
H57 0.89520000 0.91990000 2.37430000
C58 2.60970000 1.20930000 1.05570000
C59 3.50890000 1.62580000 2.07720000
H60 3.14050000 1.66120000 3.10890000
C61 4.83790000 1.98000000 1.77220000
H62 5.51940000 2.30140000 2.56680000
C63 5.28650000 1.92760000 0.43070000
H64 6.31650000 2.20770000 0.18380000
C65 4.41740000 1.51690000 -0.60910000
H66 4.79300000 1.48370000 -1.63480000
C67 3.09220000 1.16280000 -0.28740000
C68 2.48780000 0.68150000 -2.68120000
H69 3.10780000 1.57940000 -2.86750000
C70 1.19310000 0.77730000 -3.48270000
H71 0.47810000 0.00140000 -3.16570000
H72 1.41760000 0.62040000 -4.55390000
H73 0.71200000 1.76040000 -3.35940000
C74 3.27760000 -0.60800000 -2.94810000
H75 4.14560000 -0.70780000 -2.27450000
H76 3.64420000 -0.61200000 -3.99070000
H77 2.62100000 -1.48000000 -2.80940000
C78 -2.68650000 1.77990000 0.90350000
C79 -3.87830000 2.12370000 1.59410000
C80 -4.65010000 3.25150000 1.27630000
H81 -5.55860000 3.47750000 1.84080000
C82 -4.23180000 4.08940000 0.21420000
H83 -4.80910000 4.97650000 -0.05840000
C84 -3.05840000 3.76010000 -0.48580000
C85 -2.26560000 2.62600000 -0.17730000
SYMMETRY c1
END
SCF
SINGLET
END
TITLE "Step1: SP with HF"
TASK scf energy
CHARGE 0
dft mult 1
DISP vdw 3
TOLERANCES accCoul 12 tight tol_rho 1e-14
GRID nodisk lebedev 300 25 Ru1 950 29
CONVERGENCE density 1e-10 energy 1e-11 gradient 1e-9 ncyds 500
MAXITER 1500
XC cpbe96 xpbe96
DIRECT
END
TITLE "Step2: SP with DFT"
TASK dft energy
TITLE "Step3: initial Hessian and frequencies"
TASK dft frequencies
DRIVER
MAXITER 50
INHESS 2
CLEAR
TIGHT
END
TITLE "Step4: geom. opt. "
TASK dft optimize
TITLE "Step5: final Hessian and frequencies"
TASK dft frequencies
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