This calculation type keyword computes force constants and the resulting vibrational frequencies. Intensities are also computed. By default, the force constants are determined analytically if possible (for AM1, PM3, PM3MM, PM6, PDDG, RHF, UHF, MP2, CIS, all DFT methods and CASSCF), by single numerical differentiation for methods for which only first derivatives are available (MP3, MP4(SDQ), CID, CISD, CCD, CCSD, BD and QCISD), and by double numerical differentiation for those methods for which only energies are available.
Vibrational frequencies are computed by determining the second derivatives of the energy with respect to the Cartesian nuclear coordinates and then transforming to mass-weighted coordinates. This transformation is only valid at a stationary point! Thus, it is meaningless to compute frequencies at any geometry other than a stationary point for the method used for frequency determination.
For example, computing 6-311G(d) frequencies at a 6-31G(d) optimized geometry produces meaningless results. It is also incorrect to compute frequencies for a correlated method using frozen core at a structure optimized with all electrons correlated, or vice-versa. The recommended practice is to compute frequencies following a previous geometry optimization using the same method. This may be accomplished automatically by specifying both Opt and Freq within the route section for a job.
Note also that the CPHF (coupled perturbed SCF) method used in determining analytic frequencies is not physically meaningful if a lower energy wavefunction of the same spin multiplicity exists. Use the Stable keyword to test the stability of Hartree-Fock and DFT wavefunctions.
FREQUENCY CALCULATION VARIATIONS
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, Cheeseman09].
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, Barone03]. Numerical differentiation can also be performed along modes to compute zero-point energies, anharmonic frequencies [Califano76, Miller80, Papousek82, Clabo88, Page88, Miller90, Page90, Barone04, Barone05], and anharmonic vibrational-rotational couplings if Anharmonic is also specified [Adamo90, Barone94, Minichino94, Barone95, Barone03]. This option is only available for methods with analytic second derivatives: Hartree-Fock, DFT, CIS and MP2. Full anharmonic IR intensities are computed [Bloino12]. The DCPT2 and HDCPT2 methods support resonance-free computations of anharmonic frequencies and partition functions [Bloino12a]. Vibronic computations include ECD [Barone12].
There are several options for performing an analysis for an electronic excitation using the Franck-Condon and/or Herzberg-Teller methods (see below).
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.
INPUT FOR SELECTING NORMAL MODES
These sections specify the format of the input sections for the SelectNormalModes, SelectAnharmonicModes and SelectFranckCondonModes options. 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, although the [not]mode keywords may be used. 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:
2-5 Includes modes 2 through 5.
atoms=O Includes modes involving oxygen atoms.
1-20 atoms=Fe Includes modes 1 through 20 and any modes involving iron atoms.
layer=real notatoms=H Includes modes for heavy atoms in low layer (subject to default threshold).
OPTIONS REQUESTING SPECIFIC PROPERTIES/ANALYSES
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 (equivalent to NRaman).
Compute polarizability derivatives by numerically differentiating the analytic dipole derivatives with respect to an electric field. This is the default for MP2=Raman.
Compute polarizability derivatives by numerically differentiating the analytic polarizability with respect to nuclear coordinates.
Skips the extra steps required to compute the Raman intensities during Hartree-Fock analytic frequency calculations, saving 10-30% in CPU time.
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).
Compute dynamic analytic Raman optical activity intensities using GIAOs. 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. NNROA says to use the numerical ROA method from Gaussian 03; this is useful only for reproducing the results of prior calculations.
Analyze vibrational-rotational coupling.
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. This output includes IR intensities.
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 documented below following the examples.
Read an input section selecting which modes are used for differentiation in anharmonic analysis. The format of this input section is discussed above. SelAnharmonicModes is a synonym for this option.
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.
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.
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:
Atom1 Atom2 periodicity symmetry spin Repeated as necessary.
ELECTRONIC EXCITATION ANALYSIS OPTIONS
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 below), 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.
If CIS frequencies are to be used with the Herzberg-Teller or Franck-Condon-Herzberg-Teller analysis, the CIS frequencies must be done numerically (Freq=Numer rather than Freq). This is because the transition dipole derivatives are not computed during the analytic force constant evaluation. The corresponding HF frequency calculation on the ground state, which is also required, can be done analytically as usual.
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.
Use the Herzberg-Teller method [Herzberg33, Sharp64, Small71, Orlandi73, Lin74, Santoro08] (the implementation is described in [Santoro08]). HT is a synonym for this option.
Use the Franck-Condon-Herzberg-Teller method [Santoro08].
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 (although the sources of frequency data for the ground and excited state are as described above: current job=ground state, second checkpoint file=excited state).
Read an input section containing parameters for the calculation. Available input options are documented below following the examples. This input section precedes that for ReadAnharmon if both are present.
Read an input section selecting which modes are used for differentiation in Franck-Condon analysis. The format of this input section is discussed above. This input section precedes that for SelectAnharmonicModes if both are present, and the modes are specified in the usual Gaussian order (increasing), not the order displayed in the anharmonic output. SelFCModes is a synonym for this option.
NORMAL MODE RELATED OPTIONS
Include the high precision format (to five figures) vibrational frequency eigenvectors in the frequency output in addition to the normal three-figure output.
Print modes as displacements in redundant internal coordinates. IntModes is a synonym for this option.
Save all modes in the checkpoint file. SaveNM is a synonym for this option. NoSaveNormalModes, or NoSaveNM, is the default.
Read saved modes from the checkpoint file. ReadNM is a synonym for this option. NoReadNormalModes, or NoReadNM, is the default.
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 above. Note that this option does not affect the functioning of SaveNormalModes, which always saves all modes in the checkpoint file.
Sort modes by ONIOM layer in the output.
Display only modes involving the smallest model system in an ONIOM calculation.
Display only modes involving the two model systems in a 3-layer ONIOM.
By default, the zero displacements for frozen atoms are not printed in the mode output. This option requests that all atoms be listed.
Used to suppress printing of the normal mode components during a frequency calculation. The frequencies and intensities are still reported for each mode.
MOLECULE SPECIFICATION MODIFICATION OPTIONS
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.
This option allows you to specify alternatives to the default temperature, pressure, frequency scale factor and/or isotopes—298.15 K, 1 atmosphere, no scaling, and the most abundant isotopes (respectively). It is useful when you want to rerun an analysis using different parameters from the data in a checkpoint file.
Be aware, however, that all of these can be specified in the route section (Temperature, Pressure and Scale keywords) and molecule specification (Iso= parameter), as in this example:
#T Method/6-31G(d) JobType Temperature=300.0 …
ReadIsotopes input has the following format:
temp pressure [scale] Values must be real numbers.
isotope mass for atom 1
isotope mass for atom 2
isotope mass for atom n
where temp, pressure, and scale are the desired temperature, pressure, and an optional scale factor for frequency data when used for thermochemical analysis (the default is unscaled). The remaining lines hold the isotope masses for the various atoms in the molecule, arranged in the same order as they appeared in the molecule specification section. If integers are used to specify the atomic masses, the program will automatically use the corresponding actual exact isotopic mass (e.g., 18 specifies 18O, and Gaussian uses the value 17.99916).
ALGORITHM AND PROCEDURE RELATED OPTIONS
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.
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.
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.
Requests numerical differentiation of analytic second derivatives to produce third derivatives. Applicable only to methods having analytic frequencies but no analytic third derivatives.
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.
This option restarts a numerical frequency calculation after the last completed geometry. A failed numerical 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.
Diagonalize the full (3Natoms)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 section below for the output from this option.
DiagFull is the default; NoDiagFull says to skip this analysis.
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.
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.
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.
Analytic frequencies are available for the AM1, PM3, PM3MM, PM6, PDDG, DFTB, DFTBA, HF, DFT, MP2, CIS and CASSCF methods. Numerical frequencies are available for MP3, MP4(SDQ), CID, CISD, CCD, 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 now 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 [Foresman96b].
New Gaussian users are often surprised to see that the final part frequency calculation output that looks that of a geometry optimization at the beginning of a frequency job:
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 (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., αxx, αxy, αyy, αxz, αyz, αzz and βxxx, βxxy, βxyy, βyyy, βxxz, βxyz, βyyz, βxzz, βyzz, βzzz), 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
#P also produces a bar-graph of the simulated spectra for small cases.
Thermochemistry analysis follows the frequency and normal mode data:
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:
E (Thermal) Contributions to the thermal energy correction
CV Constant volume molar heat capacity
Q Partition function
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 Raman spectrum and the incident light used in the 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:
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:
Vibro-Rotational Analysis at the Harmonic level
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:
2nd 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)
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
O2-C1-H3=122.5294 O2-C1-H4=122.5294 H3-C1-H4=114.9412
Internal coordinates for the vibr.aver. structure at 0K (Sz)
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
O2-C1-H3=122.57 O2-C1-H4=122.57 H3-C1-H4=114.8601
Note that the bond lengths are slightly longer in the latter structure. The anharmonic zero point energy is given shortly thereafter in the output, preceded by its component terms:
ZPEharm = 6359.86859 cm-1 = 18.184 Kcal/mol = 76.081 Kj/mol
ZPEfund = 6135.92666 cm-1 = 17.543 Kcal/mol = 73.402 KJ/mol
ZPEaver = 6247.89762 cm-1 = 17.864 Kcal/mol = 74.741 KJ/mol
-1/4sumXii = 22.67024 cm-1 = 0.065 Kcal/mol = 0.271 KJ/mol
x0 = -6.63071 cm-1 = -0.019 Kcal/mol = -0.079 KJ/mol
ZPEtot = 6263.93715 cm-1 = 17.909 Kcal/mol = 74.933 KJ/mol
ZPEtot/ZPEharm = 0.98492 ZPEfund/ZPEharm= 0.96479
The anharmonic frequencies themselves appear just a bit later in this table, in the column labeled E(anharm):
Vibrational Energies and Rotational Constants (cm-1)
Mode(Quanta) E(harm) E(anharm) Aa(z) Ba(x) Ca(y)
Equilibrium Geometry 10.026637 1.293823 1.145922
Ground State 6359.869 6263.937 9.905085 1.288586 1.136128
Fundamental Bands (DE w.r.t. Ground State)
1(1) 3162.302 2990.777 9.727534 1.287879 1.133639
2(1) 1915.637 1884.683 9.913583 1.284564 1.128397
3(1) 1692.660 1657.100 9.955741 1.294044 1.133257
4(1) 1337.296 1315.965 6.861429 1.277085 1.137163
5(1) 3233.358 3068.112 9.809451 1.286693 1.134405
6(1) 1378.483 1355.216 12.919667 1.290780 1.130316
The harmonic frequencies are also listed for convenience.
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 25.6133
Low frequencies --- 385.4672 988.9028 1083.0692
This output is from an Opt Freq calculation on methanol. Following that are essentially 0, the lowest modes (ignoring sign) are located at around 14, 19 and 25 wavenumbers. If we rerun the calculation using tight optimization criteria and a larger integration grid (Opt=Tight Int=UltraFine), the lowest modes become:
Low frequencies --- -7.4956 -5.4813 -2.6908 0.0003 0.0007 0.0011
Low frequencies --- 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:
# HF/6-31G(d,p) Freq Test
Frequencies at STP
# HF/6-31G(d,p) Freq(ReadIso,ReadFC) Geom=Check Test
Repeat at 300 K
Note also that the freqchk utility may be used to rerun the thermochemical analysis from the frequency data stored in a Gaussian checkpoint file.
ADDITIONAL INPUT FOR FREQ=READANHARM
This input is read in a separate section. Its format changed with revision D.01. The following table gives the equivalents for the older keyword forms:
Control the printing of data. Items can include:
- Verbosity=n: Select the level of verbosity (default=0).
- NMOrder=keyword: Selects the order in which normal modes are printed. Keyword is one of: DescByIrrep (group by symmetry irreducible representation and use descending order within each group, i.e. spectroscopic order. This is the default with symmetry), DescNoIrrep (do not group by symmetry and use descending order; this is the default if symmetry is deactivated); AscByIrrep (group by symmetry irreducible representation and use ascending order within each group); AscNoIrrep (do not group by symmetry and use ascending order). Desc is synonymous with DescByIrrep, and Asc is synonymous with AscByIrrep.
- ITop=keyword: Selects the representation used for the vibro-rotational terms. By default, it is defined automatically by Gaussian from the principal moments of inertia. Available keywords are:
- Ir: Representation Ir: Iz < Ix < Iy
- IIr: Representation IIr: Iy < Iz < Ix
- IIIr: Representation IIIr: Ix < Iy < Iz
- IIIl: Representation IIIl: Iy < Ix < Iz
Select the main source of data, via one of the following keywords:
- Calc: Use data from the current job. This is the default.
- Chk[=Rebuild]: Use anharmonic data from the checkpoint file. If the Rebuild option is specified, then rebuild anharmonic data from various RWF of the checkpoint file.
- 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: Use data from the input stream in reduced form
- InDerGau: Use data from the input stream with the layout of the Gaussian output
- InGauDer: Use data from the input stream with the layout of the Gaussian output
- NMOrder=keyword: Selects the order in which normal modes are stored. Keyword is one of: Print (use the same order than that selected for printing see Print=NMOrder=keyword); DescByIrrep (group by symmetry irreducible representation and use descending order within each group, i.e. spectroscopic order; this is the default with symmetry); DescNoIrrep (do not group by symmetry and use descending order; this is the default if symmetry is deactivated); AscByIrrep (group by symmetry irreducible representation and use ascending order within each group); AscNoIrrep (do not group by symmetry and use ascending order). Desc is synonymous with DescByIrrep, and Asc is synonymous with AscByIrrep.
Replace harmonic frequencies with values given in input stream (in cm−1).
Modify input data with an automatic or semi-automatic procedure. Items can include:
- ScHarm=f: Scales harmonic frequencies with a constant scaling factor. The default is 1.0.
- NoCor: Discards Coriolis couplings in calculations
- DerOrder=n: Selects the derivative orders to keep. For example, DerOrder=123 discards all quartic force constants. The default is 1234.
- DerIndex=n: Sets the maximum number of independent indexes in a derivative. For example, DerIndex=2 keeps kiij but discards kijk. The default is 4
- SkipPT2=keyword: Selectively removes some derivatives. The keyword is one of Modes (cancels the derivatives with respect to at least one of the normal modes given in the input stream), OptModes (sames as Modes but forces Gaussian to read an option line before the list of normal modes) or Constants (cancels the derivatives based on the indexes given in the input stream. E.g., 4 5 6 makes Gaussian reset k456).
A single option line in the input is available with DataMod=SkipPT2=OptModes (see below for placement in the Gaussian input file). The available options are:
- MinInd=n: Controls the minimum number of times a selected normal mode must appear to discard the derivative. E.g., MinInd=2 means that kijk is kept, but kiij and kiii are removed. The default is 1.
- EnOrd=n: Controls the energy derivative orders to discard. By default, the reset is done on all energy derivatives. E.g., EnOrd=14 says to only remove the first and fourth energy derivatives and to keep the second and third energy derivatives. The default is 1234.
Modify the tolerance threshold to include/discard constants. Items are:
- Gradient=f: Threshold for the energy first derivatives (default: 3.7074 × 10−3).
- Hessian=f: Threshold for the energy second derivatives (default: 3.7074 × 10−5).
- Cubic=f: Threshold for the energy third derivatives (default: 3.7074 × 10−5).
- Quartic=f: Threshold for the energy fourth derivatives (default: 3.7074 × 10−5).
- Coriolis=f: Threshold for the Coriolis couplings (default: 1.0 × 10−3).
- Inertia=f: Threshold for the principal moments of inertia (default: 1.0 × 10−4 amu·Å2).
Controls the selective treatment of a part of the complete system. Items are:
- Inactive=n: Read modes in the input stream and sets them to be inactive.
- MinFreqIn=f: Sets the normal modes with a frequency above MinFreqIn to be inactive (default: infinity). Only valid if MaxFreqIn > MinFreqIn. If MaxFreqIn is not set by the user, then MinFreqIn automatically sets MaxFreqIn to infinity.
- MaxFreqIn=f: Sets the normal modes with a frequency lower than MinFreqIn to be inactive (default: 0.0). Only valid if MaxFreqIn > MinFreqIn. If MinFreqIn is not set by the user, then MaxFreqIn automatically sets MinFreqIn to 0.0.
Second-order Vibrational Perturbation Theory (VPT2)
Sets the VPT2 model to use:
- GVPT2: Use the Generalized 2nd-order Vibrational Perturbation Theory (default). Vibrational spectroscopy intensities are available for GVPT2.
- DCPT2: Use the Degeneracy-Corrected 2nd-order Perturbation Theory. Vibrational spectroscopy intensities are available for DCPT2.
- HDCPT2: Use the Hybrid Degeneracy-Corrected 2nd-order Perturbation Theory. Vibrational spectroscopy intensities are not available for HDCPT2.
Sets the parameters for the HDCPT2 model:
- Alpha=f: Sets the α parameter in Λ (default=1.0).
- Beta=f: Sets the β parameter in Λ (default: 5.0 × 105).
Sets resonance thresholds and parameters for GVPT2 calculations:
- DFreqFrm=f: Sets the maximum frequency for Fermi resonances (ωi − (ωj + ωk)) (default: 10 cm-1).
- DPT2Var=f: Sets the maximum difference between VPT2 and variational models (Martin test) (default: 1 cm-1).
- DaDeMin=f: Sets the minimum value for Darling-Dennison term (default: 10 cm-1).
- HDCPT2=f: Sets the minimum value for the HDCPT2/VPT2 difference test (default: 0.1).
- NoFermi: Deactivates the search for Fermi resonances
- NoDarDe: Deactivates the search for Darling-Dennison resonances
- List[=type]: Forces Gaussian to read resonance cases in input stream. Note: This information is specified as a list of indexes, one resonance per line, with 2 (i j) or 4 (i i j j) indexes for Darling-Dennison resonances and 3 indexes (i j k or i j j) for Fermi resonances. The type is one of Replace (discard automatic analysis and only use resonances given by the user) or Add (complements results from the automatic analysis with data from the user); the default is Replace.
Freq=ReadAnharm Input Section Structure
The following indicates the ordering of input within this section of the Gaussian input file
Freq=ReadAnharm keywords and options
DataSrc=option (other than Calc or Chk) data
DataMod=SkipPT2=OptModes options (separated by spaces)
DataMod=SkipPT2 normal modes
If one or more of these options are not used, then the blank line ending its subsection would be omitted.
Example Input Files
Example 1: Frequency data calculated in the current job:
#p B3LYP/6-311+G(d,p) Integral=Ultrafine Freq=(Anharmonic,ReadAnharm)
Anharmonic frequencies example
C 0.0000000000 0.0000000000 0.0283020404
O 0.0000000000 0.0000000000 1.2300226532
H 0.9396636401 0.0000000000 -0.5591623468
H -0.9396636401 0.0000000000 -0.5591623468
Print=NMOrder=AscNoIrrep ! Freq=ReadAnharm keywords and options
! blank line
6 ! RedDim=Inactive (list of normal modes)
! blank line
4 5 ! DataMod=SkipPT2=Modes (list of normal modes)
! blank line
2 3 3 ! Resonances=List (list of resonances)
! blank line
Example 2: Frequency data read from input file. It uses the checkpoint file from Example 1 to retrieve the molecular geometry and Hessian:
#p B3LYP/6-311+G(d,p) Integral=Ultrafine Freq=(ReadFC,Anharmonic,ReadAnharm) Geom=Check
Anharmonic frequencies example
Print=NMOrder=AscNoIrrep ! Freq=ReadAnharm keywords and options
! blank line
6 ! RedDim=Inactive (list of normal modes)
! blank line
1198.351 ! DataAdd=Freq (list of harmonic frequencies)
! blank line
1 1 0.054345 ! DataSrc=InDerAU (list of force constants)
2 2 0.060012
3 3 0.088662
6 6 0.327451
3 1 1 -0.010063
3 2 2 0.018871
3 3 3 -0.011382
6 3 2 0.049417
6 6 3 0.052014
1 1 1 1 0.058497
2 2 1 1 0.013491
2 2 2 2 0.048526
3 3 1 1 0.007299
3 3 2 2 0.026738
3 3 3 3 0.012838
6 6 1 1 -0.353903
6 6 2 2 -0.257164
6 6 3 3 -0.277332
x 1 3 -0.645574
x 1 4 0.567634
x 1 5 0.510907
y 2 3 -0.212852
y 2 4 -0.352650
y 2 5 -0.911225
y 3 6 -0.892797
y 4 6 0.449118
y 5 6 0.034736
z 1 2 0.528315
z 1 6 0.849048
! blank line
4 5 ! DataMod=SkipPT2=Modes (list of normal modes)
! blank line
2 3 3 ! Resonances=List (list of resonances)
! blank line
ADDITIONAL INPUT FOR FREQ=READFCHT
This input is read in a separate section which can contain the following keywords:
Sets the maximum overtone to reach when calculating the Franck-Condon factors corresponding to transitions to single excited vibrational state. The default value is 20.
Sets the maximum overtones reached by both states involved in two-state combinations of the final state. The default value is 13.
Sets the maximum number of integrals (in millions) computed for each class of transitions. The default value is 100.
Deactivates the use of the Sharp and Rosenstock analytic formulae to compute transition integrals to single overtones and two-state combinations.
By default, spectra bounds are given with respect to the energy of the I00 transition. This keyword must be given if absolute energies are given as spectrum bounds by the user.
Sets the lower bound (in cm-1) of the final photoelectron spectrum. Must be a real number. The default value is -1000.
Sets the upper bound (in cm-1) of the final photoelectron spectrum. Must be a real number. The default value is +8000.
Sets the gap (in cm-1) between two points of the discretized spectrum. This value can greatly influence the times of computations, very low values slowing greatly the calculation, especially if HWHM is set high. Must be a real number. The default value is 8.
Sets the Half-Width at Half-Maximum (in cm-1) of the spectral bands expressed with a Gaussian function. Must be a real number. The default value is 135.
Sets a threshold for terminating the calculation due to poor convergence. This value should be less than 1.0 (which corresponds to perfect convergence). The default is 0.0 (don’t terminate the calculation).
Prints in the Gaussian output the resulting spectra for each set of combinations (class) in addition to the final spectrum. This printing is deactivated by default
A succession of figures to print different matrices used as a basis for integrals calculations: 1 for the Duschinsky matrix J, 2 for the shift vector K, 3 for A, 4 for B, 5 for C, 6 for D and 7 for E, where A, B, C, D, E are the Sharp and Rosenstock matrices. The order of the figures is not important. The default value is 0.
Sets which integrals should be printed in output. The threshold is a fraction of the I00 intensity. Must be a real number. The default value is 0.01.
Enables the inclusion of temperature for the spectrum computation. By default, spectrum computation is performed at 0 K.
Sets the minimum population of a vibrational state to be taken into account as the starting point of a transition. The default value is 0.1.
Forces the program to use frequencies given by the user for the initial state. These frequencies are specified in the input after the Freq=ReadFCHT options line.
Forces the program to use frequencies given by the user for the final state. These frequencies are specified in the input after the Freq=ReadFCHT options line.
Forces the program to use the normal Duschinsky matrix (JDusch, the default) or an identity matrix as the Duschinsky matrix (JIdent). In the latter case, rotation of the modes is not taken into account. The default value is 0.
Enables computation of a scaling vector to modify frequencies of the final states using the scaling vector of the frequencies of the initial state and the Duschinsky matrix. When this keyword, is given, user frequencies are asked for the initial state in the same way as InFrS0.
Replaces the computed ΔE between initial and final states by a user-given one. Must be a real number. The default value is 0.
Last update: 14 May 2013