Freq

Additional related properties may also be computed during frequency calculations, including the following:

• When frequencies are done analytically, polarizabilities are also computed automatically; when numerical differentiation is required (or requested with Freq=Numer), polarizabilities must be explicitly requested using the Polar keyword (e.g., CCSD Freq Polar).
• The VCD option may be used to compute the vibrational circular dichroism (VCD) intensities in addition to the normal frequency analysis at the Hartree-Fock and DFT levels [Cheeseman96a].
• The ROA option computes analytic Raman optical activity intensities [Helgaker94, Dukor00, Ruud02a, Barron04, Thorvaldsen08, Cheeseman11a]. However, see Polar=ROA for the recommended method and model chemistries for predicting ROA spectra.
• Pre-resonance Raman intensities may be computed by specifying one of the Raman options, and also including CPHF=RdFreq within the route and specifying the desired frequency in the input file (see the examples for additional information).
• Frequency-dependent polarizabilities and hyperpolarizabilities may be computed by including CPHF=RdFreq within the route (subject to their usual availability restrictions).
• Vibrational-rotational coupling can be computed using Freq=VibRot [Califano76, Miller80, Papousek82, Clabo88, Page88, Adamo90, Miller90, Page90, Cossi03].
• The Anharmonic option performs numerical differentiation to compute anharmonic frequencies and zero-point energies [Califano76, Miller80, Papousek82, Clabo88, Page88, Miller90, Page90, Barone04, Barone05] and anharmonic vibrational-rotational couplings [Adamo90, Barone94, Minichino94, Barone95, Cossi03, Bloino12] (as requested). This option is only available for methods with analytic second derivatives: Hartree-Fock, DFT, CIS and MP2. Full anharmonic IR intensities are computed [Bloino12, Bloino15a]. The DCPT2 [Kuhler96, Bloino12a] and HDCPT2 [Bloino12a] methods support resonance-free computations of anharmonic frequencies and partition functions. Anharmonic VCD and ROA spectra can also be predicted [Bloino15]. Calculations in solution are supported [Cappelli11].
• There are several options for performing an analysis for an electronic excitation using the Franck-Condon [Sharp64, Doktorov77, Kupka86, Zhixing89, Berger97, Peluso97, Berger98, Borrelli03, Weber03, Coutsias04, Dierksen04, Lami04, Dierksen04a, Dierksen05, Liang05, Jankowiak07, Santoro07, Santoro07a, Santoro08, Barone09, Bloino10, Baiardi13], Herzberg-Teller method [Herzberg33, Sharp64, Small71, Orlandi73, Lin74, Santoro08, Barone09, Bloino10, Baiardi13] or combined Franck-Condon/Herzberg-Teller [Santoro08, Barone09, Bloino10, Baiardi13] methods (see the Options and additional input sections). They can be used to predict vibronic spectra and intensities, as well as resonance Raman spectra [Egidi14, Baiardi14]. Vibronic computations support chiral spectroscopies as well (ECD and CPL) [Barone12, Barone14]. For a tutorial review, see [Bloino16].

The keyword Opt=CalcAll requests that analytic second derivatives be done at every point in a geometry optimization. Once the requested optimization has completed all the information necessary for a frequency analysis is available. Therefore, the frequency analysis is performed and the results of the calculation are archived as a frequency job.

The SelectNormalModes and SelectAnharmonicModes options require additional input. The modes to select are specified in a separate blank-line terminated input section. The initial mode list is always empty.

Integers and integer ranges without a keyword are interpreted as mode numbers (e.g., 1 5-9); these can also be preceded by not in order to exclude rather than include the specified atoms (e.g., not 10-20).

The keywords atoms and notatoms can be used to define an atom list whose modes should be included/excluded (respectively). Atoms can also be specified by ONIOM layer via the [not]layer keywords, which accept these values: real for the real system, model for the model system in a 2-layer ONIOM, middle for the middle layer in a 3-layer ONIOM, and small for the model layer of a 3-layer ONIOM. Atoms may be similarly included/excluded by residue with residue and notresidue, which accept lists of residue names or numbers. Both keyword sets function as shorthand forms for atom lists.

Here are some examples:

Retrieving Force Constants

ReadFC

Requests that the force constants from a previous frequency calculation be read from the checkpoint file, and the mode and thermochemical analysis be repeated, presumably using a different temperature, pressure, or isotopes, at minimal computational cost. Note that since the basis set is read from the checkpoint file, no general basis should be input. If the Raman option was specified in the previous job, then do not specify it again when using this option.

Requesting Specific Spectra

Raman

Compute Raman intensities in addition to IR intensities. This is the default for Hartree-Fock. It may be specified for DFT and MP2 calculations. For MP2, Raman intensities are produced by numerical differentiation of dipole derivatives with respect to the electric field. (Raman is equivalent to NRaman for this method.)

NRaman

Compute polarizability derivatives by numerically differentiating the analytic dipole derivatives with respect to an electric field. This is the default for MP2 if Freq=Raman.

NNRaman

Compute polarizability derivatives by numerically differentiating the analytic polarizability with respect to nuclear coordinates.

NoRaman

Skips the extra steps required to compute the Raman intensities during Hartree-Fock analytic frequency calculations, saving 10-30% in CPU time.

VCD

Compute the vibrational circular dichroism (VCD) intensities in addition to the normal frequency analysis. This option is valid for Hartree-Fock and DFT methods. This option also computes optical rotations (see Polar=OptRot).

ROA

Compute dynamic analytic Raman optical activity intensities using GIAOs [Cheeseman11a]. This procedure requires one or more incident light frequencies to be supplied in the input to be used in the electromagnetic perturbations (CPHF=RdFreq is the default with Freq=ROA). This option is valid for Hartree-Fock and DFT methods. Note that the Polar=ROA keyword is often a better choice. NNROA says to use the numerical ROA method from Gaussian 03; this is useful only for reproducing the results of prior calculations.

Anharmonic Frequency Analysis

Anharmonic

Do numerical differentiation along modes to compute zero-point energies, anharmonic frequencies, and anharmonic vibrational-rotational couplings if VibRot is also specified. This option is only available for methods with analytic second derivatives: Hartree-Fock, DFT, CIS, and MP2.

ReadAnharm

Read an input section with additional parameters for the vibrational-rotational coupling and/or anharmonic vibrational analysis (VibRot or Anharmonic options). Available input options are listed in the "Availability" tab.

ReadHarmonic

Read the central point force constants and normal modes from a previous harmonic frequency calculation and avoid repeating the calculation at the central point.

ReadDifferentharmonic

Read the central point energy, forces, and force constants from a previous calculation and then compute 3^rd and 4^th derivatives at the current (presumably lower) level of theory for anharmonic spectra.

SelectAnharmonicModes

Read an input section selecting which modes are used for differentiation in anharmonic analysis. The format of this input section is discussed in the "Input" tab. SelAnharmonicModes is a synonym for this option.

Vibronic Spectra: Franck-Condon, Herzberg-Teller and FCHT

The following options perform an analysis for an electronic excitation using the corresponding method; these jobs use vibrational analysis calculations for the ground state and the excited state to compute the amplitudes for electronic transitions between the two states. The vibrational information for the ground state is taken from the current job (Freq or Freq=ReadFC), and the vibrational information for the excited state is taken from a checkpoint file, whose name is provided in a separate input section (enclose the path in quotes if it contains internal spaces). The latter will be from a CI-Singles or TD-DFT Freq=SaveNormalModes calculation.

The ReadFCHT option can be added to cause additional input to be read to control these calculations (see the "Availability" tab), and the SelFCModes option can be used to select the modes involved. In the latter case, the excited state checkpoint file would typically have been generated with Freq=(SelectNormalModes, SaveNormalModes) with the same modes selected.

FranckCondon

Use the Franck-Condon method [Sharp64, Doktorov77, Kupka86, Zhixing89, Berger97, Peluso97, Berger98, Borrelli03, Weber03, Coutsias04, Dierksen04, Lami04, Dierksen04a, Dierksen05, Liang05, Jankowiak07, Santoro07, Santoro07a, Barone09] (the implementation is described in [Santoro07, Santoro07a, Santoro08, Barone09]). FC is a synonym for this option. Transitions for ionizations can be analyzed instead of excitations. In this case, the molecule specification corresponds to the neutral form, and the additional checkpoint file named in the input section corresponds to the cation.

HerzbergTeller

Use the Herzberg-Teller method [Herzberg33, Sharp64, Small71, Orlandi73, Lin74, Santoro08] (the implementation is described in [Santoro08]). HT is a synonym for this option.

FCHT

Use the Franck-Condon-Herzberg-Teller method [Santoro08].

Emission

Indicates that emission rather than absorption should be simulated for a Franck-Condon and/or Herzberg-Teller analysis. In this case, within the computation, the initial state is the excited state, and the final state is the ground state (current job=ground state, second checkpoint file=excited state). This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor the sources of frequency data for the ground and excited state are as described previously.

ReadFCHT

Read an input section containing parameters for the calculation. Available input options are documented in the "Availability" tab. This input section precedes that for ReadAnharmon if both are present.

Other Calculation Variations and Properties

VibRot

Analyze vibrational-rotational coupling.

Projected

For a point on a mass-weighted reaction path (IRC), compute the projected frequencies for vibrations perpendicular to the path. For the projection, the gradient is used to compute the tangent to the path. Note that this computation is very sensitive to the accuracy of the structure and the path [Baboul97]. Accordingly, the geometry should be specified to at least 5 significant digits. This computation is not meaningful at a minimum.

TProjected

Perform a projected harmonic frequency analysis if the RMS force is ≥ 1.d-3 Hartree/Bohr and perform regular harmonic analysis if the RMS force is smaller.

HinderedRotor

Requests the identification of internal rotation modes during the harmonic vibrational analysis [McClurg97, Ayala98, McClurg99]. If any modes are identified as internal rotation, hindered or free, the thermodynamic functions are corrected. The identification of the rotating groups is made possible by the use of redundant internal coordinates. Because some structures, such as transition states, may have a specific bonding pattern not automatically recognized, the set of redundant internal coordinates may need to be altered via the Geom=Modify keyword. Rotations involving metals require additional input via the ReadHinderedRotor option (see below).

If the force constants are available on a previously generated checkpoint file, additional vibrational/internal rotation analyses may be performed by specifying Freq=(ReadFC, HinderedRotor). Since Opt=CalcAll automatically performs a vibrational analysis on the optimized structure, Opt=(CalcAll, HinderedRotor) may also be used.

ReadHinderedRotor

Causes an additional input section to be read containing the rotational barrier cutoff height (in kcal/mol) and optionally the periodicity, symmetry number and multiplicity for rotational modes. Rotations with barrier heights larger than the cutoff value will be automatically frozen. If the periodicity value is negative, then the corresponding rotor is also frozen. You must provide the periodicity, symmetry and spin multiplicity for all rotatable bonds contain metals. The input section is terminated with a blank line, and has the following format:

Normal Modes

HPModes

Include the high precision format (to five figures) vibrational frequency eigenvectors in the frequency output in addition to the normal three-figure output.

InternalModes

Print modes as displacements in redundant internal coordinates. IntModes is a synonym for this option.

SaveNormalModes

Save all modes in the checkpoint file. SaveNM is a synonym for this option. It is the default.

ReadNormalModes

Read saved modes from the checkpoint file. ReadNM is a synonym for this option. NoReadNormalModes, or NoReadNM, is the default.

SelectNormalModes

Read input selecting the particular modes to display. SelectNM is a synonym for this option. NoSelectNormalModes, or NoSelectNM, is the default. AllModes says to include all modes in the output. The format of this input section is discussed in the "Input" tab. Note that this option does not affect the functioning of SaveNormalModes, which always saves all modes in the checkpoint file.

SortModes

Sort modes by ONIOM layer in the output.

ModelModes

Display only modes involving the smallest model system in an ONIOM calculation.

MiddleModes

Display only modes involving the two model systems in a 3-layer ONIOM.

PrintDerivatives

Print normal mode derivatives of the dipole moment, polarizability, and so on.

PrintFrozenAtoms

By default, the zero displacements for frozen atoms are not printed in the mode output. This option requests that all atoms be listed.

NoPrintNM

Used to suppress printing of the normal mode components during a frequency calculation. The frequencies and intensities are still reported for each mode.

Geometry-Related Options

ModRedundant

Read-in modifications to redundant internal coordinates (i.e., for use with InternalModes). Note that the same coordinates are used for both optimization and mode analysis in an Opt Freq, for which this is the same as Opt=ModRedundant. See the discussion of the Opt keyword for details on the input format.

Algorithm Variations and Execution Options

Analytic

This specifies that the second derivatives of the energy are to be computed analytically. This option is available only for RHF, UHF, CIS, CASSCF, MP2, and all DFT methods, and it is the default for those cases.

Numerical

This requests that the second derivatives of the energy are to be computed numerically using analytically calculated first derivatives. It can be used with any method for which gradients are available and is the default for those for which gradients but not second derivatives are available. Freq=Numer can be combined with Polar=Numer in one job step.

FourPoint

Do four displacements instead of two for each degree of freedom during numerical frequencies, polarizabilities, or Freq=Anharm. This gives better accuracy and less sensitivity to step size at the cost of doing twice as many calculations.

DoubleNumer

This requests double numerical differentiation of energies to produce force constants. It is the default and only choice for those methods for which no analytic derivatives are available. EnOnly is a synonym for DoubleNumer.

Cubic

Requests numerical differentiation of analytic second derivatives to produce third derivatives. Applicable only to methods having analytic frequencies but no analytic third derivatives.

Step=N

Specifies the step-size for numerical differentiation to be 0.0001*N (in Angstoms unless Units=Bohr has been specified). If Freq=Numer and Polar=Numer are combined, N also specifies the step-size in the electric field. The default is 0.001 Å for Hartree-Fock and correlated Freq=Numer, 0.005 Å for GVB and CASSCF Freq=Numer, and 0.01 Å for Freq=EnOnly. For Freq=Anharmonic or Freq=VibRot, the default is 0.025 Å.

Restart

This option restarts a frequency calculation after the last completed geometry. A failed frequency job may be restarted from its checkpoint file by simply repeating the route section of the original job, adding the Restart option to the Freq=Numer keyword/option. No other input is required.

Analytic frequencies can be restarted with the Restart keyword provided that the read-write file was named and saved from the failed job. See the description of that keyword for more information and an example.

DiagFull

Diagonalize the full (3N_atoms)² force constant matrix—including the translation and rotational degrees of freedom—and report the lowest frequencies to test the numerical stability of the frequency calculation. This precedes the normal frequency analysis where these modes are projected out. Its output reports the lowest 9 modes, the upper 3 of which correspond to the 3 smallest modes in the regular frequency analysis. Under ideal conditions, the lowest 6 modes reported by this analysis will be very small in magnitude. When they are significantly non-zero, it indicates that the calculation is not perfectly converged/numerically stable. This may indicate that translations and rotations are important modes for this system, that a better integration grid is needed, that the geometry is not converged, etc. The system should be studied further in order to obtain accurate frequencies. See the "Examples" tab for the output from this option. DiagFull is the default; NoDiagFull says to skip this analysis.

TwoPoint

When computing numerical derivatives, make two displacements in each coordinate. This is the default. FourPoint will make four displacements but only works with Link 106 (Freq=Numer). Not valid with Freq=DoubleNumer.

NFreq=N

Requests that the lowest N frequencies be solved for using Davidson diagonalization. At present, this option is only available for ONIOM(QM:MM) model chemistries.

WorkerPerturbations

During numerical frequencies using Linda parallelism, run separate displacements on each worker instead of parallelizing each energy+derivative evaluation across the cluster. This strategy is more efficient, but it requires specifying an extra worker on the master node. It is the default if at least 3 Linda workers were specified. NoWorkerPerturbations suppresses this behavior.

Analytic frequencies are available for the AM1, PM3, PM3MM, PM6, PDDG, DFTB, DFTBA, HF, DFT, MP2, CIS, TD and CASSCF methods.

Numerical frequencies are available for MP3, MP4(SDQ), CID, CISD, CCD, CCSD, EOM-CCSD and QCISD.

Raman is available for the HF, DFT and MP2 methods.

VCD and ROA are available for HF and DFT methods.

Anharmonic is available for HF, DFT, MP2 and CIS methods.

Freq and NMR can both be on the same route for HF and DFT.

Polar, Opt, Stable, NMR.

Frequency Output. The basic components of the output from a frequency calculation are discussed in detail in chapter 4 of Exploring Chemistry with Electronic Structure Methods [Foresman15].

New Gaussian users are often surprised to see frequency calculation output that looks like that of a geometry optimization:

GradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
Berny optimization.
Initialization pass.

Link 103, which performs geometry optimizations, is executed at the beginning and end of all frequency calculations. This is done so that the quadratic optimization step can be computed using the correct second derivatives. Occasionally an optimization will complete according to the normal criterion using the approximate Hessian matrix, but the step size is actually larger than the convergence criterion when the correct second derivatives are used. The next step is printed at the end of a frequency calculation so that such problems can be identified. If you think this concern is applicable, use Opt=CalcAll instead of Freq in the route section of the job, which will complete the optimization if the geometry is determined not to have fully converged (usually, given the full second derivative matrix near a stationary point, only one additional optimization step is needed), and will automatically perform a frequency analysis at the final structure.

Specifying #P in the route section produces some additional output for frequency calculations. Of most importance are the polarizability and hyperpolarizability tensors (the latter in Raman calculations only); although, they still may be found in the archive entry in normal print-level jobs. They are presented in lower triangular and lower tetrahedral order, respectively (i.e., α_xx, α_xy, α_yy, α_xz, α_yz, α_zz and β_xxx, β_xxy, β_xyy, β_yyy, β_xxz, β_xyz, β_yyz, β_xzz, β_yzz, β_zzz), in the standard orientation:

Dipole        = 2.37312183D-16 -6.66133815D-16 -9.39281319D-01
Polarizability= 7.83427191D-01  1.60008472D-15  6.80285860D+00
               -3.11369582D-17  2.72397709D-16  3.62729494D+00
HyperPolar    = 3.08796953D-16 -6.27350412D-14  4.17080415D-16
                5.55019858D-14 -7.26773439D-01 -1.09052038D-14
               -2.07727337D+01  4.49920497D-16 -1.40402516D-13
               -1.10991697D+01

#P also produces a bar-graph of the simulated spectra for small cases.

Zero-point correction=                   .023261 (Hartree/Particle)	 
Thermal correction to Energy=            .026094	 
Thermal correction to Enthalpy=          .027038	 
Thermal correction to Gibbs Free Energy= .052698	 
Sum of electronic and zero-point Energies=   -527.492585   E0=Eelec+ZPE
Sum of electronic and thermal Energies=      -527.489751   E= E0+ Evib+ Erot+Etrans
Sum of electronic and thermal Enthalpies=    -527.488807   H=E+RT
Sum of electronic and thermal Free Energies= -527.463147   G=H-TS

The raw zero-point energy correction and the thermal corrections to the total energy, enthalpy, and Gibbs free energy (all of which include the zero-point energy) are listed, followed by the corresponding corrected energy. The analysis uses the standard expressions for an ideal gas in the canonical ensemble. Details can be found in McQuarrie [McQuarrie73] and other standard statistical mechanics texts. In the output, the various quantities are labeled as follows:

The thermochemistry analysis treats all modes other than the free rotations and translations as harmonic vibrations. For molecules having hindered internal rotations, this can produce slight errors in the energy and heat capacity at room temperatures and can have a significant effect on the entropy. The contributions of any very low frequency vibrational modes are listed separately so that their harmonic contributions can be subtracted from the totals and their correctly computed contributions included should they be group rotations and high accuracy is required. Expressions for hindered rotational contributions to these terms can be found in Benson [Benson68]. The partition functions are also computed, with both the bottom of the vibrational well and the lowest (zero-point) vibrational state as reference.

Pre-resonance Raman. This calculation type is requested with one of the Raman options in combination with CPHF=RdFreq. The frequency specified for the latter should be chosen as follows:

• Determine the difference in frequency between the peak of interest in the UV/visible absorption spectrum and the incident light used in the Raman experiment.
• Perform a TD calculation using a DFT method in order to determine the predicted location of the same peak.
• Specify a frequency for CPHF=RdFreq which is shifted from the predicted peak by the same amount as the incident light differs from the observed peak.

Pre-resonance Raman results are reported as additional rows within the normal frequency tables:

 Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman 
 scattering activities (A**4/AMU), depolarization ratios for plane 
 and unpolarized incident light, reduced masses (AMU), force constants 
 (mDyne/A), and normal coordinates:
                     1
                    B1
 Frequencies --  1315.8011
 Red. masses --     1.3435
 Frc consts  --     1.3704
 IR Inten    --     7.6649
 Raman Activ --     0.0260
 Depolar (P) --     0.7500
 Depolar (U) --     0.8571
 RamAct Fr= 1--     0.0260  Additional output lines begin here.
  Dep-P Fr= 1--     0.7500
  Dep-U Fr= 1--     0.8571
 RamAct Fr= 2--     0.0023
  Dep-P Fr= 2--     0.7500
  Dep-U Fr= 2--     0.8571

Vibration-Rotation Coupling Output. If the VibRot option is specified, then the harmonic vibrational-rotational analysis appears immediately after the normal thermochemistry analysis in the output, introduced by this header:

 Harmonic Vibro-Rotational Analysis

If anharmonic analysis is requested as well (i.e., VibRot and Anharmonic are both specified), then the anharmonic vibrational-rotational analysis results follow the harmonic ones, introduced by the following header:

 Second-order Perturbative Anharmonic Analysis

Anharmonic Frequency Calculations. Freq=Anharmonic jobs produce additional output following the normal frequency output. (It follows the vibrational-rotational coupling output if this was specified as well.) We will briefly consider the most important items.

The output displays the equilibrium geometry (i.e., the minimum on the potential energy surface), followed by the anharmonic vibrationally averaged structure at 0 K:

 Internal coordinates for the Equilibrium structure (Se)

                          Interatomic distances:
                   1          2         3         4
     1  C    0.000000
     2  O    1.206908   0.000000
     3  H    1.083243   2.008999   0.000000
     4  H    1.083243   2.008999   1.826598   0.000000
                          Interatomic angles:
      O2-C1-H3=122.5294      O2-C1-H4=122.5294      H3-C1-H4=114.9412
      O2-H3-H4= 62.9605
                             Dihedral angles:
      H4-C1-H3-O2= 180.  

 Internal coordinates for the vibrationally average structure at 0K (Sz)

                          Interatomic distances:
                   1          2         3         4
     1  C    0.000000
     2  O    1.210431   0.000000
     3  H    1.097064   2.024452   0.000000
     4  H    1.097064   2.024452   1.849067   0.000000
                          Interatomic angles:
      O2-C1-H3=122.57        O2-C1-H4=122.57        H3-C1-H4=114.8601
      O2-H4-H3= 62.8267
                             Dihedral angles:
      H4-C1-H3-O2= 180.  

Note that the bond lengths are slightly longer in the latter structure. The predicted coordinates at STP follow in the output.

The anharmonic zero point energy is given shortly thereafter in the output:

 Anharmonic Zero Point Energy
 ----------------------------
 Harmonic       : cm-1 =  5008.40626 ; Kcal/mol =  14.320 ; KJ/mol =  59.914
 Anharmonic Pot.: cm-1 =   -53.31902 ; Kcal/mol =  -0.152 ; KJ/mol =  -0.638
 Watson+Coriolis: cm-1 =   -12.83227 ; Kcal/mol =  -0.037 ; KJ/mol =  -0.154
 Total Anharm   : cm-1 =  4942.25496 ; Kcal/mol =  14.131 ; KJ/mol =  59.122

The anharmonic frequencies themselves appear just a bit later in this table, in the column labeled E(anharm):

     ==================================================
              Anharmonic Infrared Spectroscopy
     ==================================================

 Units: Transition energies (E) in cm^-1
        Integrated intensity (I) in km.mol^-1

 Fundamental Bands
 -----------------
   Mode(n)                  E(harm)   E(anharm)        I(harm)       I(anharm)
      1(1)                  2938.531   2788.983     55.17567187     55.41312200
      2(1)                  1888.862   1864.231    101.42877427    104.63741421
      ...

 Overtones
 ---------
   Mode(n)                  E(harm)   E(anharm)                      I(anharm)
      1(2)                  5877.061   5517.149                      0.00211652
      2(2)                  3777.724   3710.383                      3.68324904
      ...

 Combination Bands
 -----------------
   Mode(n)     Mode(n)      E(harm)   E(anharm)                      I(anharm)
      2(1)        1(1)      4827.393   4654.114                      1.74785224
      3(1)        1(1)      4490.139   4271.343                      0.04557003
      ...

The harmonic frequencies are also listed for convenience.

Vibronic Analysis. The following input file predicts the vibronic spectrum:

%OldChk=excited                      Excited state calculation.
%Chk=fcht
# Freq=(ReadFC,FCHT,ReadFCHT) Geom=AllCheck …

TimeIndependent                      ReadFCHT additional input.
Output=Matrix=JK                     Output Duschinsky matrix and shift vector.
     final blank line

The molecule specification is taken from the checkpoint file from the excited state, as are the force constants for the excited states.

FCHT analysis produces many results. The final Duschinsky (state overlap) matrix appears as follows:

Final Duschinsky matrix
-----------------------
Note: The normal coordinates of the final state (columns) are expressed
      in the basis set of the normal coordinates of the initial state (rows)
           1             2             3             4             5
1  -0.539484D+00  0.839747D+00  0.139916D-01 -0.147815D-01  0.167387D-02
2  -0.594185D+00 -0.373849D+00 -0.647845D+00  0.757424D-01 -0.627709D-02
3   0.303582D-01  0.276954D-01  0.572527D-02  0.354162D+00 -0.933518D+00
…

Note that this output reports the value of J_ij for each pair of states. Generally, what is plotted is J².

The locations and intensities of the predicted bands are reported as follows:

     ==================================================
                 Information on Transitions
     ==================================================

 Energy of the 0-0 transition:  31327.1976 cm^(-1)

 NOTE: The energy (transition energy) refers to the relative energy,
       with respect to the 0-0 transition energy.
       The intensity is the line intensity.
       DipStr is the dipole strength.

 Energy =      0.0000 cm^-1: |0> -> |0>              Frequency and transition (states).
   -> Intensity =  7003.     (DipStr = 0.9135E-01)

 Energy =    457.9310 cm^-1: |0> -> |9^1>            Location is ~31875 cm-1.
   -> Intensity =  650.2     (DipStr = 0.8360E-02)   Intensity in dm3cm-1mol-1;
 …                                                  Dipole strength in au.

The final predicted spectrum follows in a form suitable for plotting:

    ==================================================
                       Final Spectrum
     ==================================================

 Band broadening simulated by mean of Gaussian functions with
 Half-Widths at Half-Maximum of  135.00 cm^(-1)

 Legend:
 -------
 1st col.: Energy (in cm^-1)
 2nd col.: Intensity at T=0K
 Intensity: Molar absorption coefficient (in dm^3.mol^-1.cm^-1)
 -----------------------------
    30327.1976    0.000000D+00
    …
    31319.1976    0.699549D+04
    31327.1976    0.701428D+04
    31335.1976    0.699927D+04
    …

Resonance Raman Spectra. The following input file computes the resonance Raman intensities from two previously run frequency calculations.

%Chk=S0_freq                                         Ground state checkpoint file.
# Freq=(FC,ReadFC,ReadFCHT) Geom=AllCheck …

TimeIndependent                                      ReadFCHT additional input.
Spectroscopy=ResonanceRaman                          Predict resonance Raman spectrum.
Spectrum=(Lower=800.,Upper=2800.,Broadening=Stick)   Spectrum specifications.
Intermediate=Source=Chk                              Get second state data from checkpoint file (named below).
RR=(OmegaMin=55000,OmegaMax=56000,OmegaStep=100)     RR analysis parameters: ω range and step size.

S2_freq.chk                                          Excited state checkpoint file.

See the section on Freq=ReadFCHT for details about the additional input. For each of the Raman modes, the following output appears for each point in the specified range of incident energies (omega):

     ==================================================
                 Information on Transitions
     ==================================================

 Energy of the 0-0 transition:  54854.2397 cm^(-1)

 Alp2: alpha^2, BsAl: beta_s(alpha)^2, BaAl: beta_a(alpha)^2

 Energy =      0.0000 cm^-1: |0> -> |0>            Relative energy and involved states. 
   -> Omega =  55000.0 cm^-1, Sigma =   1.1332
      Alp2 =  0.33009E+02, BsAl =  0.29859E+03, BaAl =  0.00000E+00

Following this output, the same data is presented in a tabular form:

     ==================================================
                       Final Spectrum
     ==================================================

 No band broadening applied (stick spectrum)

 Legend:
 -------
 1st col.: Raman shift (in cm^-1)
 2nd col.: Intensity at T=0K for incident energy:  55000.00 cm^-1
 3rd col.: Intensity at T=0K for incident energy:  55100.00 cm^-1
 4th col.: Intensity at T=0K for incident energy:  55200.00 cm^-1
 5th col.: Intensity at T=0K for incident energy:  55300.00 cm^-1
 Raman scattering intensity in cm^3.mol^-1.sr^-1
 -----------------------------------------------------------------------------
 … 
 1188.0000    0.000000D+00    0.000000D+00    0.000000D+00    0.000000D+00
 1190.0000    0.134622D-21    0.213038D-21    0.358179D-21    0.644832D-21
 1192.0000    0.000000D+00    0.000000D+00    0.000000D+00    0.000000D+00
 …

Since no spectral broadening was requested here (Spectrum=Broadening=Stick), the only rows with non-zero intensities correspond to the Raman active frequencies.

Examining Low-Lying Frequencies. The output from the full force constant matrix diagonalization (the default Freq=DiagFull), in which the rotational and translational degrees of freedom are retained, appears as following in the output:

 Low frequencies ---  -19.9673   -0.0011   -0.0010    0.0010   14.2959 
 Low frequencies ---   25.6133  385.4672  988.9028 1083.0692

This output is from an Opt Freq calculation on methanol. Ignoring sign, there are 3 low-lying modes, located at around 14, 19, and 25 wavenumbers (in addition to the three that are ~0). However, if we rerun the calculation using tight optimization criteria (Opt=Tight) and a larger integration grid, the lowest modes become:

 Low frequencies ---   -7.4956   -5.4813   -2.6908    0.0003    0.0007 
 Low frequencies ---    0.0011  380.1699  988.1436 1081.9083

The low-lying modes are now quite small, and the lowest frequencies have moved slightly as a result.

This analysis is especially important for molecular systems having frequencies at small wavenumbers. For example, if the lowest reported frequency is around 30 and there is a low-lying mode around 25 as above, then the former value is in considerable doubt (as is whether the molecular structure is even a minimum).

Rerunning a Frequency Calculation with Different Thermochemistry Parameters. The following two-step job contains an initial frequency calculation followed by a second thermochemistry analysis using a different temperature, pressure, and selection of isotopes:

%Chk=freq
# B3LYP/6-311+G(2d,p) Freq
 
Frequencies at STP
 
molecule specification
 
-Link1-
%Chk=freq
%NoSave
# B3LYP/6-311+G(2d,p) Freq(ReadIso,ReadFC) Geom=Check

Repeat at 300 K

0,1
 
300.0 1.0
16
 2
 3
…

Note also that the freqchk utility may be used to rerun the thermochemical analysis from the frequency data stored in a Gaussian checkpoint file.

Keywords available in the L717 section

The following keywords for specifying various aspects of Freq=Anharm calculations are included as additional input within the Gaussian input file. They control various aspects of anharmonic frequency analyses. Note that these keywords are completely different from those supported in Gaussian 09 (a few of these changes were introduced in Gaussian 09 revision D.01).

Data Sources and Format

The DataSrc, DataAdd and DataMod input items locate the various data required by the anharmonic frequency analysis. They each take a list of parameters and associated values which specify locations from which to retrieve different data items. In general, parameters specify what data is to be read and their values specify the location of that data. The available options for the latter are listed below. Generally, they may be optionally followed by a format suffix.

Source keywords are used to specify where the data is located:

• Src: Use data from the RWF file for the current job. RWF is a synonym.
• Chk: Retrieve data from the current checkpoint file (as defined with %Chk or %OldChk).
• In: Read data from the input stream.
• InChkn: Retrieve data from the nth file in the file list (see the discussion of additional input sections below). Valid values of n run from 1 to 6.

Format Suffixes are appended directly to the source item, and they specify a non-default format for various read-in data. For example, InQMW says to read derivative data from the input stream in mass-weighted normal coordinates. The following suffixes are available:

• QMW: Derivatives are with respect to normal modes in mass-weighted normal coordinates. Q is a synonym for this format suffix.
• QMWX: Harmonic derivatives are with respect to normal modes in Cartesian coordinates, and anharmonic derivatives are with respect to normal modes in mass-weighted normal coordinates. X is a synonym for this format suffix.
• QRedX: Harmonic derivatives are with respect to normal modes in Cartesian coordinates, and anharmonic derivatives are with respect to normal modes in dimensionless normal coordinates.

By default, QMWX is tried first, followed by QMW.

DataSrc=param: Specify the source(s) of various read-in data. The parameter consists of a keyword indicating the data to which it applies and a source keyword indicating its location (and possibly its format). The available parameters are:

• source: Sets the data source for all data.
• Harm=source: Sets the data source for harmonic data. The default is taken from the source file.
• Anharm=source: Sets the data source for harmonic data. The default is taken from the source file.
• Coriolis=source: Sets the data source for the Coriolis couplings. At present, the only supported items are Src and In, and format suffixes may not be used.
• NMOrder=ordering: Specifies the order normal modes are stored in the input source, selected from the following list. This item may be specified in addition to a source item.
  • AscNoIrrep: Ascending order. Do not sort by irreducible representation. This is the default.
  • Asc: Ascending order. Sort by irreducible representation if possible.
  • Desc: Descending order. Sort by irreducible representation if possible.
  • DescNoIrrep: Descending order. Do not sort by irreducible representation.
  • Print: Use same order as for printing.

The following DataSrc items are deprecated, and are included only for backward similarity to Gaussian 09 (where they functioned as top-level additional input items).

• InDerAU: Use data from the input stream in atomic units.
• InDerAJ: Use data from the input stream in attoJoules
• InDerRed: Use data from the input stream in reduced form. Reduced is an alternate name for this item.
• InDerGau: Use data from the input stream with the layout of the Gaussian output. InGauDer is an alternate name for this item.

DataAdd=params: Read alternate data to replace or complete the original data. Using this option will replace the already existing information in the original data with the data specified here.

• Freq: Replace harmonic frequencies with values given in the input stream (in cm^-1). A data source may also be specified as a parameter: Freq=source, but format suffixes are not allowed.
• PESFull=sources: Read force constraints from specified specified source.
• PESHarm=sources: Read harmonic force constants from specified specified source.
• PESAnh=sources: Read anharmonic force constants from specified specified source.
• EDipFull=sources: Read the electric dipole from the specified specified source.
• EDipHarm=sources: Read the harmonic components of the electric dipole from the specified specified source.
• EDipAnh=sources: Read the anharmonic components of the electric dipole from the specified specified source.
• MDipFull=sources: Read the magnetic dipole from the specified source.
• MDipHarm=sources: Read the harmonic components of the magnetic dipole from the specified source.
• MDipAnh=sources: Read the anharmonic components of the magnetic dipole from the specified source.
• PolFull=sources: Read the polarizability tensor from the specified source.
• PolHarm=sources: Read the harmonic components of the polarizability tensor from the specified source.
• PolAnh=sources: Read the anharmonic components of the polarizability tensor from the specified source.
• MagFFull=sources: Read the magnetic-field properties from the specified source.
• MagFHarm=sources: Read the harmonic components of the magnetic-field properties from the specified source.
• MagFAnh=sources: Read the anharmonic components of the magnetic-field properties from the specified source.
• FreqDepPFull=sources: Read the frequency-dependent properties from the specified source.
• FreqDepPHarm=sources: Read the harmonic components of the frequency-dependent properties from the specified source.
• FreqDepPAnh=sources: Read the anharmonic components of the frequency-dependent properties from the specified source.

DataMod=params: Modify the data in various manners.

• ScHarm=value: Scales harmonic frequencies with a constant scaling factor (default is 1.0).
• NoCor: Discards Coriolis couplings in calculations. By default, all couplings will be retained.
• DerOrder=N: Selects the derivatives order to keep. E.g. DerOrder=123 discards all quartic force constants.
• DerIndex=N: Sets the maximum number of independent indexes for a derivative. E.g. DerIndex=2 keeps k_iij but discards k_ijk.
• SkipPT2=what: Selectively removes derivatives based on the parameter, whose possible values are listed below:
  • No: Do not remove the data. This is the default option.
  • Modes: Removes the derivatives with respect to any of the normal modes given in the input stream.
  • Constants: Removes the derivatives based on the indexes given in the input stream. The input explicitly specifies the force constants (energy derivatives) to be removed. Each line specifies the involved normal modes, with the derivative order implied by the number of indexes. For example, to remove the third derivatives with respect to normal coordinates Q₁ Q₂ Q₅, the input line would be:

    1 2 5

  • OptModes: Modify derivatives based on additional instructions in the input stream (see input ordering section below).

Tolerances=data: Modify the tolerance threshold to include/discard derivative data.

• Gradient=value: Threshold for the energy first derivatives (default is 3.7074×10⁻³).
• Hessian=value: Threshold for the energy second derivatives (default is 3.7074×10⁻⁵).
• Cubic=value: Threshold for the energy third derivatives (default is 3.7074×10⁻⁵).
• Quartic=value: Threshold for the energy fourth derivatives (default is 3.7074×10⁻⁵).
• Coriolis=value: Threshold for the Coriolis couplings (default is 1.0×10⁻³).
• Inertia=value: Threshold for the principal moments of inertia (default is 1.0×10⁻⁴Ų).
• Symm=value: Tolerance for anharmonic data with respect to symmetry rules (default is 2%).

Output Control

This section specifies the contents and destination of the calculation output.

Print=items: Include items in the output file. Available items are the following:

• InDataX: Include data compatible with DataSrc=InQMWX. The form Print=InDataX=Ext writes the data to the external file input_data.dat.
• InDataNM: Include data compatible with DataSrc=InQMW. The form Print=InDataNM=Ext writes the data to the external file input_data.dat
• YMatrix: Include the Y matrix (a variant of the χ matrix).
• Verbosity=n: Specify the verbosity level. The default is 0.
• ITop=rep: Selects the representation used for rotational spectroscopy. By default, it is defined automatically by Gaussian from the principal moments of inertia. Available representations are:
  • Ir: Ir Representation: I_z < I_x < I_y
  • IIr: IIr Representation: I_y < I_z < I_x
  • IIIr: IIIr Representation: I_x < I_y < I_z
  • Il: Il Representation: I_z < I_y < I_x
  • IIl: IIl Representation: I_x < I_z < I_y
  • IIIl: IIIl Representation: I_y < I_x < I_z
• ZAxisSymm=axis: Sets the Eckart axis to be used as Z for the definition of the reduced Hamiltonians for the vibrorotational analysis. Available choices are:
  • X: Z collinear with X.
  • Y: Z collinear with Y.
  • Z: Z collinear with Z.
• NMOrder=ordering: Specifies the order in which normal modes are listed:
  • Asc: Ascending order. Sort by irreducible representation if possible.
  • Desc: Descending order. Sort by irreducible representation if possible. This is the default.
  • AscNoIrrep: Ascending order. Do not sort by irreducible representation.
  • DescNoIrrep: Descending order. Do not sort by irreducible representation.
• PT2VarEVec: Include the eigenvector matrix from the diagonalization of the variational matrix.
• PT2VarStates: Include the projection of the variational states on the deperturbed ones.
• PT2VarProj: Include the projection of the DVPT2 states on the new variational states.
• InDataAU: Write data compatible with DataSrc=InDerAU (deprecated).
• Polymode: Write data to use in the Polymode program.

Reduced-Dimensionality Schemes

RedDim=items: Specifies which normal modes are active in the analysis. Items are:

• Active=n: Activate the n modes specified in the input stream. By default, all modes are active.
• Inactive=n: Read list of n inactive modes from the input stream.
• Frozen=n: Read n modes to be frozen from the input stream.
• MinFreqAc=freq: Sets the normal modes with a frequency above the specified value to be active (default is 0). Only valid if MaxFreqAc>MinFreqAc.
• MaxFreqAc=freq: Sets the normal modes with a frequency below the specified value to be active (default is infinity). Only valid if MaxFreqAc>MinFreqAc.
• MinFreqIn=freq: Sets the normal modes with a frequency above the specified value to be inactive (default is 0). Only valid if MaxFreqIn>MinFreqIn.
• MaxFreqIn=freq: Sets the normal modes with a frequency below the specified value to be active (default is infinity). Only valid if MaxFreqIn>MinFreqIn.
• MinFreqFr=freq: Sets the normal modes with a frequency above the specified value to be frozen (default is 0). Only valid if MaxFreqFr>MinFreqFr.
• MaxFreqFr=freq: Sets the normal modes with a frequency below the specified value to be frozen (default is infinity).Only valid if MaxFreqFr>MinFreqFr.

Second-Order Vibrational Perturbation Theory (VPT2)

PT2Model=data: Sets the VPT2 model to use. The default is GVPT2.

• HDCPT2: Use the Hybrid Degeneracy-Corrected 2nd-order Perturbation Theory.
• VPT2: Use the original 2nd-order Vibrational Perturbation Theory. Vibrational spectroscopy intensities are available for this model.
• DVPT2: Use the Deperturbed 2nd-order Vibrational Perturbation Theory. Vibrational spectroscopy intensities are available for this model. The form DVPT2=all selects all possibly resonant terms as Fermi resonances, and it is equivalent to Resonances=(DFreqFrm=∞,DPT2Var=0.)
• GVPT2: Use the Generalized 2nd-order Vibrational Perturbation Theory. This is the default. It is similar to DVPT2, but the removed terms are treated variationally in a second step. Vibrational spectroscopy intensities are available for this model. The form GVPT2=all selects all possibly resonant terms as Fermi resonances, and it is equivalent to Resonances=(DFreq12=∞,K12Min=0.)
• DCPT2: Use the Degeneracy-Corrected 2nd-order Perturbation Theory.

HDCPT2=params: Set the parameters for the model with the Alpha and Beta options (i.e., HDCPT2=Alpha=value), which specify values for the corresponding variables in the expression for Λ:

Spectroscopy

Spectro=MaxQuanta=quanta: Compute transition integrals to states with up to the specified quanta. The default is 2.

ROA=params: Options related to Raman optical activity. If the keyword is specified, then only those scatterings explicitly requested will be computed. If the ROA is not specified, then intensities are computed for all supported scatterings.

• ICP0: Compute ROA intensity for ICP forward scattering.
• ICP90x: Compute ROA intensity for incident circular polarization (ICP) right-angle scattering (polarized).
• ICP90z: Compute ROA intensity for ICP right-angle scattering (depolarized).
• ICP90*: Compute ROA intensity for ICP right-angle scattering (magic angle).
• ICP180: Compute ROA intensity for ICP backward scattering.
• SCP0: Compute ROA intensity for scattered circular polarization(SCP) forward scattering.
• SCP90x: Compute ROA intensity for SCP right-angle scattering (polarized).
• SCP90z: Compute ROA intensity for SCP right-angle scattering (depolarized).
• SCP90*: Compute ROA intensity for SCP right-angle scattering (magic angle).
• SCP180: Compute ROA intensity for SCP backward scattering.
• DCP180: Compute ROA intensity for double circular polarization (DCP) backward scattering.
• All: Compute the ROA intensity for all supported scatterings.

Freq=ReadAnharm Additional Input Ordering

The potential input sections for the various Freq=ReadAnharm additional input items should follow the keyword list section in the following order. Blank lines separate input sections, but each section and its terminating blank line should be included only when the corresponding keyword is specified.

Freq=ReadAnharm input keywords

blank line

checkpoint file list for DataSrc=InChkn or DataAdd=…=InChkn

blank line

data for DataSrc=In or DataAdd=…=In (harmonic followed immediately by anharmonic)

blank line

data for DataAdd=Freq

blank line

n modes for RedDim=Active

blank line

n modes for RedDim=Inactive

blank line

n modes for RedDim=Frozen

blank line

keyword for DataMod=SkipPT2=OptModes (see below)

modes for DataMod=SkipPT2=Modes or Constants or DataMod=SkipPT2=OptModes

blank line

data for Resonances=List

blank line

DataMod=SkipPT2=OptModes Keywords: Removal of Contributions from Selected Normal Modes

One or more options are specified on a single line with no blank line following. The options available are:

• MinInd=n: Controls the minimum number of times a selected normal mode must appear to discard the derivative. The default is 1. For example, a value of 2 means that k_ijk is kept, but k_iij and k_iii are removed.
• EnOrd=mask: Controls the energy derivative orders to consider. The default is 1234 which says to include all energy derivatives. The value 14 says to only treat the first and fourth energy derivatives and to ignore the second and third energy derivatives.

Here is an example calculation using DataMod=SkipPT2=OptModes:

# Freq=(Anharm,ReadAnharm) …

Formaldehyde

0 1
  C      -0.6067825443565   -0.0000000216230    0.0000000000000
  O       0.6033290944914    0.0000000215000    0.0000000000000
  H      -1.1752074085613    0.9201232113261    0.0000000000000
  H      -1.1752073429832   -0.9201232950844    0.0000000000000

PT2Model=GVPT2 Resonances=(NoDarDen,NoFermi)
DataMod=SkipPT2=OptModes 

MinInd=2 EnOrd=34        Control keywords: keep only kijk for third and fourth derivatives 
5 6                      Modes for which to remove derivatives
                         terminating blank line

Specifying Resonances

For Resonances=Add, Resonances=List=Replace and Resonances=Delete, each line contains the type of resonance and the indexes of the normal modes involved in the resonances. Supported types are:

• 1-2 or 12: 1-2 Fermi resonance. 3 indexes needed, given in the order: ω₁ ≈ ω₂ + ω₃
• 1-1 or 11: 1-1 Darling-Dennison resonance. 2 indexes needed, given in the order: ω₁ ≈ ω₂
• 1-3 or 13: 1-3 Darling-Dennison resonance. 4 indexes needed, given in the order: ω₁ ≈ ω₂ + ω₃ + ω₄
• 2-2 or 22: 2-2 Darling-Dennison resonance. 4 indexes needed, given in the order: ω₁ + ω₂ ≈ ω₃ + ω₄

For Resonances=List=Modify, an action must be specified at the beginning of the line, before the resonance type and the normal modes. The available actions are ADD (add resonance) and DEL (remove resonance if previously identified).

%Chk=example1
# B3LYP/6-311+G(d,p) Freq=(Anharmonic,ReadAnharm)

Anharmonic frequencies example 1

molecule specification

DataMod=SkipPT2=Modes            Freq=ReadAnharm additional input
RedDim=Inactive=1                # modes to make inactive
PT2Model=GVPT2
Resonances=Add
Print=InDataX=Ext                Write data to an external file
                                 blank line
6                                Modes to make inactive: RedDim=Inactive
                                 blank line
4 5                              Modes for which to discard derivatives: DataMod=SkipPT2=Modes
                                 blank line
1-2 2 3 3                        List of additional resonances: Resonances=Add
                                 blank line

Example 2: Frequency data read from input stream. It uses the checkpoint file from Example 1 to retrieve the molecular geometry and Hessian:

%OldChk=example1
%Chk=example2
# B3LYP/6-311+G(d,p) Freq=(ReadFC,Anharmonic,ReadAnharm) Geom=Check

Anharmonic frequencies example 2

0 1

PT2Model=GVPT2                    Freq=ReadAnharm additional input
DataSrc=(InQMWX,NMOrder=Desc)     Read harmonic/anharmonic data from input
DataAdd=Freq                      Replace harmonic frequencies with input values
RedDim=Inactive=1
                                  blank line
@input_data.dat                   Data file from previous job with Print=InDataX=Ext
                                  blank line
1198.351                          List of harmonic frequencies: DataAdd=Freq
1259.285                         
1530.636
1814.590
2884.164
2941.556
                                  blank line
6
                                  blank line

Example 3: The following example specifies alternate values for several parameters:

#  B3LYP/6-31G(d) Freq=(Anharm,ReadAnharm) 

Anharmonic frequencies example 3

molecule specification

Tolerances=Coriolis=0.25                Freq=ReadAnharm additional input
Resonances=(DFreq12=220.0,K12Min=1.1) 
DataMod=SCHarm=0.98
                                        blank line

%Chk=project4
# Freq=(ROA,VCD,Anharm,ReadAnharm) CPHF=RdFreq …

Anharmonic VCD and ROA spectrum

0 1
molecule specification

589.3nm                           incident light frequency

PT2Model=GVPT2                    ReadAnharm input section
Spectro=MaxQuanta=3
                                  blank line