Can this vibrational analysis be accepted as for a geometry optimization stationary point?
Forum Vet
7:08:37 AM PST - Tue, Feb 26th 2019
I used DFTB2 to optimize C2H5SH with GAMESS, but the following vibrational analysis told me it was not a stationary point on PES. Yestoday, Dr. Schmidt told me why here there was a warning like this. I used NWCHEM6.8 to do the vibrational analysis by DFT and RHF, the inputs were
echo
start molecule
memory total 12000 stack 4000 heap 500 global 7500 mb

title "Title"
charge 0

geometry units angstroms print xyz autosym
  ...
end

basis
 * library 6-31G
end

dft
 xc b3lyp

 mult 1
end

task dft freq
and
echo

start molecule
memory total 12000 stack 4000 heap 500 global 7500 mb

title "Title"
charge 0

geometry units angstroms print xyz autosym
  ...
end

basis
 * library 6-31G
end

SCF
RHF
END

task scf freq

I got in the DFT case:

Normal Eigenvalue ||    Projected Derivative Dipole Moments (debye/angs)

 Mode   [cm**-1]  ||      [d/dqX]             [d/dqY]           [d/dqZ]

------ ---------- || ------------------ ------------------ -----------------

   1       -0.000 ||       0.001              -0.000             0.211

   2       -0.000 ||      -0.089              -0.121             0.005

   3       -0.000 ||       0.070               0.094             0.001

   4       -0.000 ||      -0.001               0.000            -0.163

   5        0.000 ||      -0.020              -0.027             0.001

   6        0.000 ||       0.003               0.002             0.298

   7      251.813 ||      -0.001              -0.001            -0.036

   8      327.340 ||      -0.049               0.277            -0.000

   9      455.218 ||      -0.002              -0.001            -0.758

  10      717.307 ||      -0.034               0.188             0.000

  11      859.934 ||      -0.004               0.001             0.365

  12      904.596 ||      -0.333              -0.063            -0.005

  13     1070.980 ||       0.105              -0.371             0.000

  14     1109.831 ||       0.011              -0.014            -0.030

  15     1168.240 ||       0.203               0.203            -0.002

  16     1328.353 ||       0.015              -0.033            -0.170

  17     1392.799 ||       0.483              -0.868             0.011

  18     1481.538 ||       0.275               0.377            -0.002

  19     1542.006 ||      -0.002               0.010             0.490

  20     1552.169 ||      -0.173               0.287            -0.013

  21     1568.989 ||       0.200               0.247            -0.019

  22     2120.546 ||       0.906               0.775            -0.001

  23     2892.624 ||       0.738              -0.294             0.399

  24     2965.138 ||       0.438              -0.171            -0.595

  25     3033.997 ||      -0.354              -0.643            -0.003

  26     3104.707 ||       0.595              -0.449             0.002

  27     3116.689 ||       0.016              -0.009            -0.799

----------------------------------------------------------------------------





 

 

----------------------------------------------------------------------------

Normal Eigenvalue ||           Projected Infra Red Intensities

 Mode   [cm**-1]  || [atomic units] [(debye/angs)**2] [(KM/mol)] [arbitrary]

------ ---------- || -------------- ----------------- ---------- -----------

   1       -0.000 ||    0.001924           0.044         1.876       1.582

   2       -0.000 ||    0.000982           0.023         0.957       0.807

   3       -0.000 ||    0.000596           0.014         0.581       0.490

   4       -0.000 ||    0.001157           0.027         1.128       0.951

   5        0.000 ||    0.000049           0.001         0.048       0.041

   6        0.000 ||    0.003839           0.089         3.743       3.156

   7      251.813 ||    0.000057           0.001         0.055       0.046

   8      327.340 ||    0.003427           0.079         3.341       2.817

   9      455.218 ||    0.024917           0.575        24.291      20.480

  10      717.307 ||    0.001583           0.037         1.543       1.301

  11      859.934 ||    0.005771           0.133         5.626       4.743

  12      904.596 ||    0.004993           0.115         4.867       4.104

  13     1070.980 ||    0.006461           0.149         6.299       5.311

  14     1109.831 ||    0.000052           0.001         0.051       0.043

  15     1168.240 ||    0.003564           0.082         3.474       2.929

  16     1328.353 ||    0.001311           0.030         1.278       1.078

  17     1392.799 ||    0.042811           0.988        41.734      35.187

  18     1481.538 ||    0.009436           0.218         9.199       7.756

  19     1542.006 ||    0.010398           0.240        10.136       8.546

  20     1552.169 ||    0.004863           0.112         4.740       3.997

  21     1568.989 ||    0.004410           0.102         4.299       3.625

  22     2120.546 ||    0.061632           1.422        60.082      50.657

  23     2892.624 ||    0.034234           0.790        33.373      28.138

  24     2965.138 ||    0.024935           0.575        24.308      20.495

  25     3033.997 ||    0.023362           0.539        22.774      19.202

  26     3104.707 ||    0.024058           0.555        23.453      19.774

  27     3116.689 ||    0.027675           0.638        26.979      22.746

----------------------------------------------------------------------------

in the RHF case

Normal Eigenvalue ||    Projected Derivative Dipole Moments (debye/angs)

 Mode   [cm**-1]  ||      [d/dqX]             [d/dqY]           [d/dqZ]

------ ---------- || ------------------ ------------------ -----------------

   1       -0.000 ||       0.003               0.002             0.346

   2       -0.000 ||      -0.024              -0.032            -0.002

   3       -0.000 ||      -0.096              -0.126             0.005

   4       -0.000 ||       0.001               0.000             0.173

   5        0.000 ||       0.076               0.100            -0.001

   6        0.000 ||      -0.000              -0.001             0.166

   7      362.271 ||      -0.001               0.005            -0.008

   8      367.001 ||      -0.034               0.275             0.000

   9      568.596 ||      -0.001              -0.002            -0.782

  10      751.215 ||      -0.089               0.276            -0.000

  11      962.902 ||      -0.005              -0.001             0.291

  12      997.976 ||      -0.370              -0.179            -0.004

  13     1131.567 ||       0.225              -0.275            -0.001

  14     1219.019 ||       0.012              -0.007             0.008

  15     1265.285 ||       0.216               0.303            -0.002

  16     1440.273 ||       0.009              -0.022            -0.146

  17     1518.070 ||       0.525              -0.888             0.008

  18     1617.833 ||       0.271               0.336            -0.002

  19     1662.843 ||      -0.002               0.009             0.469

  20     1670.485 ||      -0.184               0.222            -0.011

  21     1689.357 ||       0.229               0.309            -0.018

  22     2127.666 ||       0.801               0.811            -0.002

  23     2932.493 ||       0.714              -0.325             0.414

  24     3002.990 ||       0.459              -0.202            -0.570

  25     3073.851 ||      -0.342              -0.759            -0.006

  26     3132.781 ||       0.649              -0.531             0.003

  27     3145.187 ||       0.018              -0.012            -0.877

----------------------------------------------------------------------------





 

 

----------------------------------------------------------------------------

Normal Eigenvalue ||           Projected Infra Red Intensities

 Mode   [cm**-1]  || [atomic units] [(debye/angs)**2] [(KM/mol)] [arbitrary]

------ ---------- || -------------- ----------------- ---------- -----------

   1       -0.000 ||    0.005175           0.119         5.045       3.999

   2       -0.000 ||    0.000068           0.002         0.066       0.053

   3       -0.000 ||    0.001090           0.025         1.063       0.842

   4       -0.000 ||    0.001305           0.030         1.272       1.008

   5        0.000 ||    0.000679           0.016         0.662       0.525

   6        0.000 ||    0.001194           0.028         1.164       0.923

   7      362.271 ||    0.000004           0.000         0.004       0.003

   8      367.001 ||    0.003334           0.077         3.250       2.576

   9      568.596 ||    0.026523           0.612        25.856      20.496

  10      751.215 ||    0.003640           0.084         3.549       2.813

  11      962.902 ||    0.003664           0.085         3.572       2.831

  12      997.976 ||    0.007306           0.169         7.123       5.646

  13     1131.567 ||    0.005482           0.126         5.344       4.236

  14     1219.019 ||    0.000011           0.000         0.011       0.008

  15     1265.285 ||    0.006003           0.139         5.852       4.639

  16     1440.273 ||    0.000952           0.022         0.928       0.736

  17     1518.070 ||    0.046084           1.063        44.925      35.612

  18     1617.833 ||    0.008057           0.186         7.854       6.226

  19     1662.843 ||    0.009525           0.220         9.286       7.361

  20     1670.485 ||    0.003608           0.083         3.517       2.788

  21     1689.357 ||    0.006425           0.148         6.263       4.965

  22     2127.666 ||    0.056353           1.300        54.936      43.547

  23     2932.493 ||    0.034098           0.787        33.240      26.349

  24     3002.990 ||    0.024977           0.576        24.349      19.301

  25     3073.851 ||    0.030016           0.692        29.261      23.195

  26     3132.781 ||    0.030497           0.704        29.730      23.567

  27     3145.187 ||    0.033326           0.769        32.488      25.753

----------------------------------------------------------------------------
Can this be accepted as a stationary point for geometry optimization.

I know this requires rich group knowledge, structural intuition and art, just as indicated in the GAMESS test for [Ni(NH3)6]2+, etc.

Very Best Regards!

Forum Vet
8:33:40 PM PST - Tue, Feb 26th 2019
The OPTTOL in GAMESS is set to 1.0D-10 for DFTB, and also to 1.0D-11, and the related RHF
frequency analysis is 
    1      22.790    A        4.789345    0.040791

    2       0.084    A        6.890251    0.000000

    3       0.023    A        6.885812    0.000000

    4       0.034    A        6.890374    0.000000

    5      37.846    A        3.929379    0.036886

    6     172.729    A        2.086567    0.022109

    7     363.748    A        3.410336    0.077421

    8     434.011    A        1.023444    0.000317

    9     615.593    A        1.038901    0.723858

   10     751.224    A        4.094947    0.087465

   11     979.847    A        1.089670    0.094492

   12    1038.404    A        1.197033    0.161830

   13    1134.356    A        1.978351    0.117989

   14    1237.757    A        1.203437    0.002447

   15    1264.022    A        1.567909    0.140356

   16    1456.219    A        1.189515    0.011190

   17    1530.772    A        1.269786    1.076701

   18    1617.789    A        1.219209    0.186595

   19    1662.150    A        1.039877    0.219738

   20    1669.327    A        1.045953    0.090570

   21    1686.310    A        1.098514    0.141698

   22    2126.253    A        1.037980    1.311076

   23    2985.475    A        1.057992    0.829015

   24    3016.134    A        1.106556    0.438324

   25    3073.863    A        1.036438    0.693348

   26    3132.885    A        1.099075    0.716761

   27    3145.120    A        1.101099    0.797947
No imaginary frequency existing in GAMESS.
According to an article published in JACS in 1995, the ab initio vibrational analysis of the minimum of D-H exchange of CD4 and Zeolite cluster had 5 imaginary frequencies -200.414, -127.723, -56.788, -22.541, -12,698cms-1, which was explained as a spurious consequence of the Cs symmetry of the cluster. The transition state also has 3 imaginary frequencies -1423.384, -155.086 and -42.834 cms-1.
 I think the optimized geometry at this level makes this intrisinc and only a very good first guess may eliminate it, thus the warnings from GAMESS perhaps can be ignored with an low enough OPTTOL.
Special, sincere thanks should be given to Dr. Schmidt for his clarification of the technical meaning of this warning in GAMESS and instructions for me to beigin with GAMESS, especially geometry optimization, etc., and long time lucid explanations as well as useful advices on my ceaseless questions; and all those on this forum and NWCHEM Github to teach me to compile NWCHEM.

Forum Vet
6:01:00 AM PST - Wed, Feb 27th 2019
It seems there is no obvious problem to identify the dftb2 optimized one is a minimum for some practical use, e.g., reorganization energy calculation for some molecules, and the first excited state parameters of TDDFT TPA calculation of thiol using a certain functional tried by me .
 I used MP2 and a large basis set to optimize it and RHF for frequency analysis, but still got the warning.
The MP2 semi-numerical HESSIAN calculations using the large basis set eliminate the warning of the geometry from MP2 with the same basis set but still get it for that from DFTB2.
Please note the thermochemical composite G3MP2 in GAMESS using the MP2 and DFTB2 optimized initial geometries, respectively, all gave gaseous heats of formation of -47.82 kJ/mol-1 at 298.15K, in good agreement with that of -46.15kJ/mol-1 in NIST Chemistry Webbook.

Forum Vet
9:18:19 PM PST - Mon, Mar 4th 2019
The following references are related to the imaginary frequencies of a geometry
1.In an article on BC3 honeycomb published in J. Phy.Chem.C in 2011
"Our fragment structure II is in fact a ninth-order saddle point. Geometry optimization following the imaginary frequencies led us to structure I, which is the most stable isomer found in our calculations. "
"However, the completely planar structure of the 1,2,3-C6H4(BH2)2 molecule has two imaginary frequencies. Thus, we proved that the repulsion between hydrogen atoms is responsible for the instability of isomer II in the C6(BH2)6 case. "
2.Prof. Gordon commented on an article published in JACS in 1991
"...The twisted group IVB carbenes (2b) have two imaginary frequencies-one which corresponds largely to rotation about the M-C bond leading to the planar structure (2a) and one which entails bending of the MH2 fragment such that the coordination about the metal goes from trigonal planar to pyramidal. ..."
3. J. H.Jessen said in Predicting binding free energies in solution :
"If all else(meaning the methods to eliminate the imaginary frequencies resulting from a flat PES and numerical errors) fails, it is probably better to pretend that the imaginary frequency is real and add the corresponding vibrational free energy contribution. However, this needs to be systematically tested".
4. In an article published in Journal of Organometallic Chemistry in 1995 on tetrafluorocyclodisilazanes on References and notes 18
"In the case of 8c a very small imaginary frequency ( ~ 7 cm- ’) corresponding to rotation of the exocyclic silyl groups was present. Because the effect of such a small imaginary frequency on the energy or the structure is neglegible, we have not reoptimized this structure."
5. In an article pubished in Chemical Physics in 1992
"However the C, keto form contains a planar secondary amine moiety, and it is therefore not surprising that it represents a transition state with an a” transition vector (imaginary frequency 96i cm- ’ )."(Singlet excited-state intramolecular proton transfer in 2- ( 2 ’ -hydroxyphenyl ) benzoxazole: spectroscopy at low temperatures, femtosecond transient absorption, and MNDO calculations)
6. In an article published on Computational Materials Science in 2015:
" The results, shown in Fig. 4, demonstrate that if the frequency is very low (<39.0 cm-1), a high-accuracy frequency calculation can remove up to 42% of the imaginary frequencies. However, high accuracy re-optimization is less helpful for larger imaginary frequencies. In contrast, the two molecular geometry perturbation strategies work extremely well: they remove at least 21 out of the 24 imaginary frequencies for the whole range of imaginary frequencies."
7. In an article published in J. Chem. Edu. in 2002
"Often, as in the case of (PH3)2Ir(H)2(H2)Cl discussed later in this paper, optimizations with a symmetry plane present (Cs in this example) result in a converged structure with one or more imaginary frequencies that correspond to motions that would break the symmetry plane. To converge a structure to an energy minimum (no imaginary frequencies), the computation must be carried out again in a lower symmetry group (here C1). "
8. In an article published in J, Phy. Chem. A in 2012
"the u-B3LYP/6-31G(d)-optimized 1B1 structure had one imaginary frequency, corresponding to rotation of the perpendicular CH2. "
9. In an article published in JACS in 1987 entitled A Theoretical Study of Thermal Reactions of Bicyclo[ 2.1.0 ]pent-2-ene.
 "A similar analysis for 4 gave one imaginary frequency (134i cm"1). This vibrational mode of a" symmetry is mainly a twist of the CH2 group showing that 4 is a transition state for the conversion of 3 into itself."
 10. In an article published on pyrimidine in JACS in 1992
"The coordinate associated with this imaginary frequency is an out-of-plane one of bl symmetry which lowers the symmetry of the molecule from C2v to Clh, the reflection plane being the zx plane. The subsequent optimization of the geometry within Clh symmetry leads to a minimum corresponding to a nonplanar geometry for pyrimidine in the 3Bl(n7r*) state at an energy 68 cm-I below that of the corresponding state in the C, geometry."
I think most of these comments are suitable.


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