Multiple imaginary frequencies in vibrational analysis

[Jacob Jensen]

Dear All,

I'm doing vibrational analysis in order to validate some of the saddle points achieved from the NEB calculations. I have a system consist of impinging molecules on the metal surface, so for doing vib. analysis, I have fixed all the metal slab's atoms and only tried to do the calculation for the molecules adsorbed on the surface (I don't know how valid this is! Any thoughts?).

The problem is, even though the keyword FULLY_PERIODIC is set to False by default for removing the rotational frequencies, I still get three imaginary frequencies which I have no clue where they are coming from. Do you have any idea about the source of these "extra" imaginary frequencies? Or in another words, what is your best suggested strategy to get a single imaginary frequency for the validation of the results coming from NEB calculations?

I have attached my input, (a part of output) and the coordinate file of the TS. Your advice or suggestion would be much appreciated.

Kind regards,

Jacob

 VIB|                        NORMAL MODES - CARTESIAN DISPLACEMENTS

 VIB|

 VIB|                         1                    2                    3

 VIB|Frequency (cm^-1)  -627.437013          -370.258287           -12.385518

 VIB|Intensities           0.000000             0.000000             0.000000

 VIB|Red.Masses (a.u.)     2.780368             1.414776             3.913531

 VIB|Frc consts (a.u.)    -0.001103            -0.000068            -0.000000

  ATOM  EL             X     Y     Z        X     Y     Z        X     Y     Z

    65  N             0.07  0.13 -0.15     0.14 -0.05  0.07    -0.13  0.37  0.13

    66  C            -0.03 -0.24  0.22    -0.01  0.07 -0.05     0.01  0.24 -0.02

    67  H            -0.41  0.72 -0.16    -0.95  0.05 -0.03    -0.17  0.34 -0.06

    68  H             0.15  0.17 -0.15     0.14 -0.11  0.09     0.38  0.52  0.28

    69  H            -0.04 -0.19 -0.17     0.14 -0.05  0.03    -0.22 -0.16 -0.25

 VIB|                         4                    5                    6

 VIB|Frequency (cm^-1)    94.311628           142.307646           224.156404

 VIB|Intensities           0.000000             0.000000             0.000000

 VIB|Red.Masses (a.u.)     4.349457             2.189311             1.433603

 VIB|Frc consts (a.u.)     0.000001             0.000002             0.000009

  ATOM  EL             X     Y     Z        X     Y     Z        X     Y     Z

    65  N             0.14  0.08 -0.38     0.23  0.12  0.14     0.13 -0.02 -0.02

    66  C             0.02  0.31 -0.08     0.03 -0.06  0.02     0.13  0.02 -0.01

    67  H             0.10  0.18 -0.03     0.44  0.06 -0.02     0.37 -0.09  0.03

    68  H            -0.31 -0.15 -0.47    -0.12  0.20 -0.02     0.61 -0.02  0.17

    69  H             0.22  0.53 -0.10     0.32  0.59  0.45     0.09 -0.45 -0.45

 VIB|                         7                    8                    9

 VIB|Frequency (cm^-1)   421.227384           449.047513           749.374099

 VIB|Intensities           0.000000             0.000000             0.000000

 VIB|Red.Masses (a.u.)     3.868163             5.072223             1.257520

 VIB|Frc consts (a.u.)     0.000312             0.000528             0.001015

  ATOM  EL             X     Y     Z        X     Y     Z        X     Y     Z

    65  N             0.06 -0.05  0.04    -0.02 -0.10  0.08    -0.08 -0.09  0.01

    66  C            -0.45  0.12  0.17     0.24  0.25  0.48     0.07 -0.01  0.01

    67  H             0.39 -0.02  0.22    -0.02  0.15  0.52    -0.08  0.27 -0.11

    68  H             0.41 -0.21  0.24    -0.35 -0.30  0.03     0.37  0.25  0.08

    69  H             0.24  0.14 -0.44    -0.08 -0.08  0.34     0.27  0.72 -0.31

 VIB|                        10                   11                   12

 VIB|Frequency (cm^-1)   854.933502           940.779054          1487.032716

 VIB|Intensities           0.000000             0.000000             0.000000

 VIB|Red.Masses (a.u.)     1.261018             1.071511             1.088996

 VIB|Frc consts (a.u.)     0.001725             0.002149             0.013633

  ATOM  EL             X     Y     Z        X     Y     Z        X     Y     Z

    65  N            -0.02  0.11 -0.01    -0.01 -0.01  0.05     0.03 -0.02  0.07

    66  C             0.04 -0.07  0.03     0.01  0.01 -0.05     0.00  0.00  0.00

    67  H            -0.18 -0.49  0.23     0.18  0.63 -0.30    -0.01 -0.00 -0.00

    68  H            -0.10 -0.57  0.23    -0.21 -0.61  0.20    -0.55  0.29 -0.36

    69  H             0.12  0.31 -0.39     0.01 -0.05 -0.12     0.12 -0.11 -0.67

 VIB|                        13                   14                   15

 VIB|Frequency (cm^-1)  3078.134845          3178.790354          3420.829077

 VIB|Intensities           0.000000             0.000000             0.000000

 VIB|Red.Masses (a.u.)     1.083814             1.061101             1.079557

 VIB|Frc consts (a.u.)     0.249102             0.277381             0.378480

  ATOM  EL             X     Y     Z        X     Y     Z        X     Y     Z

    65  N            -0.00 -0.00 -0.00     0.01 -0.02 -0.06    -0.07  0.03  0.00

    66  C            -0.00 -0.03 -0.08    -0.00 -0.00  0.00     0.00 -0.00  0.00

    67  H             0.01  0.38  0.92     0.00 -0.00 -0.02    -0.00 -0.00 -0.01

    68  H            -0.00  0.02  0.01    -0.39  0.35  0.82     0.05 -0.07 -0.19

    69  H             0.02 -0.01  0.00     0.21 -0.09  0.00     0.91 -0.30  0.18

[Patrick Gono]

Dear Jacob,

Imaginary frequencies are a consequence of your geometry not being an energy minimum. By construction, you are trying to study saddle points, which are not energy minima, and hence negative eigenvalues of the dynamical matrix are to be expected. In general, negative frequencies indicate the studied structure is not stable at finite temperature (which is evidently true for saddle points / transition states).

In the case you are evaluating minimum energy geometries (such as the initial and final configuration in your simulations), the existence of negative frequencies points to an insufficient geometry optimization. You may try to reduce EPS_SCF even further to achieve better wave function optimization, and at the same time reduce the geometry optimization convergence parameters. If you use the BFGS algorithm, reduce TRUST_RADIUS to make the convergence more stable. If your configuration really corresponds to an energy minimum, then no negative frequencies should be present in the spectrum at all.

If you need to assess the energy profile of some reaction at finite temperatures, you may want to resort to the so-called Blue Moon sampling technique, which is an analog to NEB but uses ab-initio molecular dynamics at finite temperature instead of static 0K calculations. See, for instance, https://www.cp2k.org/exercises:2015_ethz_mmm:nacl_free_energy.

To answer your question about the validity of "freezing" the substrate -- this is conventionally done and generally accepted to be okay, especially if you only care about the differences between e.g. zero point energies or vibrational entropies of different adsorbed configurations.

Yours sincerely,

Patrick Gono

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[Patrick Gono]

Dear Jacob,

I apologize, I didn't read your original email careful enough -- you are trying to validate the NEB results and instead of one you observe multiple negative frequencies.

In this case, try to make sure the calculations are well converged. You may also try to reduce the finite difference displacement for the vibrational calculations.

Sorry once again for the misunderstanding.

Yours sincerely,

Patrick Gono

[Jacob Jensen]

Dear Patrick,

Thank you for your input. The point is, in some cases (e.g. unstable initial gas phase reactants like radicals) I can't get convergence for CI-NEB with the criteria tighter than:

RMS_DR : 0.0002
MAX_DR : 0.002
RMS_FORCE: 0.0003
MAX_FORCE: 0.004

Even with this level of accuracy convergence is not possible if I use line search (which again I have no clue what I'm loosing by deactivating it). The main goal is to get a reaction barrier that makes sense. As long as I somehow reach this goal and get a "reliable" barrier for a difficult reaction containing/ending to gas phase reactants/products, I'm happy.

One may suggest using DIMER method for transition state optimization, and then doing the vibrational analysis to see whether I can get an imaginary frequency or not, but still some points are not clear to me.
If I use DIMER method for a TS corresponding to a BAND which is very hard to converge, how can I get the "correct" reaction barrier considering that the minimas achieved from NEB are not at the same accuracy level of the DIMER method? specially considering that the GEO_OPT gives different total energies than the BAND calculation does for the two minima.

Kind regards,

Jacob

On Tuesday, March 3, 2020 at 1:31:09 PM UTC+1, Patrick Gono wrote:

Dear Jacob,

I apologize, I didn't read your original email careful enough -- you are trying to validate the NEB results and instead of one you observe multiple negative frequencies.

In this case, try to make sure the calculations are well converged. You may also try to reduce the finite difference displacement for the vibrational calculations.

Sorry once again for the misunderstanding.

Yours sincerely,

Patrick Gono

On Tue, 3 Mar 2020 at 13:24, Patrick Gono <patri...@gmail.com> wrote:

Dear Jacob,

Imaginary frequencies are a consequence of your geometry not being an energy minimum. By construction, you are trying to study saddle points, which are not energy minima, and hence negative eigenvalues of the dynamical matrix are to be expected. In general, negative frequencies indicate the studied structure is not stable at finite temperature (which is evidently true for saddle points / transition states).

In the case you are evaluating minimum energy geometries (such as the initial and final configuration in your simulations), the existence of negative frequencies points to an insufficient geometry optimization. You may try to reduce EPS_SCF even further to achieve better wave function optimization, and at the same time reduce the geometry optimization convergence parameters. If you use the BFGS algorithm, reduce TRUST_RADIUS to make the convergence more stable. If your configuration really corresponds to an energy minimum, then no negative frequencies should be present in the spectrum at all.

If you need to assess the energy profile of some reaction at finite temperatures, you may want to resort to the so-called Blue Moon sampling technique, which is an analog to NEB but uses ab-initio molecular dynamics at finite temperature instead of static 0K calculations. See, for instance, https://www.cp2k.org/exercises:2015_ethz_mmm:nacl_free_energy.

To answer your question about the validity of "freezing" the substrate -- this is conventionally done and generally accepted to be okay, especially if you only care about the differences between e.g. zero point energies or vibrational entropies of different adsorbed configurations.

Yours sincerely,

Patrick Gono

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