Gaussian 03 Online Manual
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 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, QCISD, and all semi-empirical methods), 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 3-21G frequencies at a STO-3G 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 coupled perturbed Hartree-Fock (CPHF) 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
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., QCISD 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 .
Pre-resonance Raman intensities may be computed by specifying a Raman option, 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 similarly be computed by including CPHF=RdFreq within the route (subject to their usual availability restrictions).
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.
You should specify alternative isotopes for frequency jobs using the standard method. However, the ReadIsotopes option is retained for rerunning completed calculations under different conditions (see the examples).
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.
temp pressure [scale] 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 O18, and Gaussian uses the value 17.99916).
Analytic frequencies are available for the HF, DFT, MP2, CIS and CASSCF methods. Numerical frequencies are available for MP3, MP4(SDQ), CID, CISD, CCD, CCSD and QCISD. ROA is available for HF and DFT methods.
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 .
You may be surprised to see output that looks like it belongs to a geometry optimization at the beginning of a frequency job:
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 (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 -1.10991697D+01
#P also produces a
bar-graph of the simulated spectra for small cases.
Thermochemistry analysis follows the frequency and normal mode data. The zero-point energy output in Gaussian has been expanded over that produced by older versions:
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  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 S Entropy 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 if they are group rotations and high accuracy is needed, their harmonic contributions can be subtracted from the totals, and their correctly computed contributions included. Expressions for hindered rotational contributions to these terms can be found in Benson . 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:
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 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 product additional output following the normal frequency output. (It follows the vibration-rotation coupling output if this was specified as well.) We will briefly consider the most important items within it here.
This 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 1.220000 0.000000 3 H 1.080000 1.993088 0.000000 4 H 1.080000 1.993088 1.870615 0.000000 Interatomic angles: O2-C1-H3=120. O2-C1-H4=120. H3-C1-H4=120. O2-H3-H4= 62.0127 Dihedral angles: H4-C1-H3-O2= 180. Internal coordinates for the vibr.aver. structure at 0K (Sz) Interatomic distances: 1 2 3 4 1 C 0.000000 2 O 1.223954 0.000000 3 H 1.093363 2.007355 0.000000 4 H 1.093363 2.007355 1.894824 0.000000 Interatomic angles: O2-C1-H3=119.9442 O2-C1-H4=119.9442 H3-C1-H4=120.1116 O2-H3-H4= 61.8377 Dihedral angles: H4-C1-H3-O2= 180.
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:
Zero Point Terms Harmonic ZPE (cm-1) = 6339.70913 Sum(Xij) (cm-1) = -79.34418 3rd der.Anh.E0 (cm-1) = -24.91960 4th der.Anh.E0 (cm-1) = 23.36569 Vibr.Rot.E0 (cm-1) = -4.77806 Anharmonic ZPE (cm-1) = 6254.03298
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 9.560323 1.288616 1.135528 Ground State 6339.709 6254.033 9.425702 1.283838 1.125877 Fundamental Bands (DE w.r.t. Ground State) 1(1) 3180.793 3008.554 9.244416 1.283898 1.123734 2(1) 1839.248 1805.679 9.432233 1.280472 1.118196 3(1) 1661.905 1625.622 9.467760 1.288838 1.123277 4(1) 1315.801 1292.782 7.968990 1.271489 1.126802 5(1) 3292.300 3172.585 9.311674 1.282911 1.124406 6(1) 1389.371 1365.996 10.859898 1.285869 1.119543
The harmonic frequencies are also listed for convenience.
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 # HF/6-31G(d,p) Freq Test Frequencies at STP molecule specification --Link1-- %Chk=freq %NoSave # HF/6-31G(d,p) Freq(ReadIso,ReadFC) Geom=Check Test 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.
INPUT FOR FREQ=READANHARM
This input is read in a separate section which can contain the following keywords: