Description
This method keyword requests that the dipole electric field polarizabilities (and hyperpolarizabilities, if possible) be computed. No geometry change or derivatives are implied, but this keyword may be combined in the same job with numerical differentiation of forces by specifying both Freq and Polar in the route section. Freq and Polar may not be combined for methods lacking analytic gradients (MP4(SDTQ), QCISD(T), CCSD(T), and so on). Note that Polar is done by default when second derivatives are computed analytically.
The polarizability and hyperpolarizability are presented in the output in the standard orientation in lower triangular and lower tetrahedral order, respectively: αxx, αxy, αyy, αxz, αyz, αzz and βxxx, βxxy, βxyy, βyyy, βxxz, βxyz, βyyz, βxzz, βyzz, βzzz.
Normally, polarizabilities and hyperpolarizabilities are computed using static frequencies. However, frequency-dependent polarizabilities and hyperpolarizabilities [ Olsen85 J. Olsen and P. Jørgensen, “Linear and Nonlinear Response Functions for an Exact State and for an MCSCF State,” J. Chem. Phys., 82 (1985) 3235-64. DOI: , Sekino86 H. Sekino and R. J. Bartlett, “Frequency-Dependent Nonlinear Optical-Properties of Molecules,” J. Chem. Phys., 85 (1986) 976-89. DOI: , Rice90 J. E. Rice, R. D. Amos, S. M. Colwell, N. C. Handy, and J. Sanz, “Frequency-Dependent Hyperpolarizabilities with Application to Formaldehyde and Methyl-Fluoride,” J. Chem. Phys., 93 (1990) 8828-39. DOI: , Rice91 J. E. Rice and N. C. Handy, “The Calculation of Frequency-Dependent Polarizabilities as Pseudo-Energy Derivatives,” J. Chem. Phys., 94 (1991) 4959-71. DOI: , Rice92 J. E. Rice and N. C. Handy, “The Calculation of Frequency-Dependent Hyperpolarizabilities Including Electron Correlation-Effects,” Int. J. Quantum Chem., 43 (1992) 91-118. DOI: ] may be computed by including CPHF=RdFreq in the route section and specifying the desired frequency in the input file.
Optical rotations [Rosenfeld28, Condon37 E. U. Condon, “Theories of optical rotatory power,” Rev. Mod. Phys., 9 (1937) 432-57. DOI: , Eyring44, Buckingham67 A. D. Buckingham, in Advances in Chemical Physics, Ed. I. Prigogine, Vol. 12 (Wiley Interscience, New York, 1967) 107. DOI: , Buckingham68 A. D. Buckingham and G. C. Longuet-Higgins, “Quadrupole Moments of Dipolar Molecules,” Mol. Phys., 14 (1968) 63. DOI: , Atkins69 P. W. Atkins and L. D. Barron, “Rayleigh Scattering of Polarized Photons by Molecules,” Mol. Phys., 16 (1969) 453. DOI: , Barron71 L. D. Barron and A. D. Buckingham, “Rayleigh and Raman Scattering from Optically Active Molecules,” Mol. Phys., 20 (1971) 1111. DOI: , Charney79, Amos82 R. D. Amos, “Electric and Magnetic Properties of CO, HF, HCl and CH3F,” Chem. Phys. Lett., 87 (1982) 23-26. DOI: , Jorgensen88 P. Jørgensen, H. J. A. Jensen, and J. Olsen, “Linear Response Calculations for Large-Scale Multiconfiguration Self-Consistent Field Wave-Functions,” J. Chem. Phys., 89 (1988) 3654-61. DOI: ] may also be predicted via the OptRot option [ Karna91 S. P. Karna and M. Dupuis, “Frequency-Dependent Nonlinear Optical-Properties of Molecules - Formulation and Implementation in the Hondo Program,” J. Comp. Chem., 12 (1991) 487-504. DOI: , Helgaker94 T. Helgaker, K. Ruud, K. L. Bak, P. Jørgensen, and J. Olsen, “Vibrational Raman Optical-Activity Calculations Using London Atomic Orbitals,” Faraday Discuss., 99 (1994) 165-80. DOI: , Pedersen95 T. B. Pedersen and A. E. Hansen, “Ab initio calculation and display of the rotatory strength tensor in the random phase approximation. Method and model studies,” Chem. Phys. Lett., 246 (1995) 1-8. DOI: , Kondru98 R. K. Kondru, P. Wipf, and D. N. Beratan, “Theory-assisted determination of absolute stereochemistry for complex natural products via computation of molar rotation angles,” J. Am. Chem. Soc., 120 (1998) 2204-05. DOI: , Stephens01 P. J. Stephens, F. J. Devlin, J. R. Cheeseman, and M. J. Frisch, “Calculation of optical rotation using density functional theory,” J. Phys. Chem. A, 105 (2001) 5356-71. DOI: , Mennucci02 B. Mennucci, J. Tomasi, R. Cammi, J. R. Cheeseman, M. J. Frisch, F. J. Devlin, S. Gabriel, and P. J. Stephens, “Polarizable continuum model (PCM) calculations of solvent effects on optical rotations of chiral molecules,” J. Phys. Chem. A, 106 (2002) 6102-13. DOI: , Ruud02 K. Ruud and T. Helgaker, “Optical rotation studied by density-functional and coupled-cluster methods,” Chem. Phys. Lett., 352 (2002) 533-39. DOI: , Stephens02a P. J. Stephens, F. J. Devlin, J. R. Cheeseman, M. J. Frisch, and C. Rosini, “Determination of Absolute Configuration Using Optical Rotation Calculated Using Density Functional Theory,” Org. Lett., 4 (2002) 4595-98. DOI: , Stephens03 P. J. Stephens, F. J. Devlin, J. R. Cheeseman, M. J. Frisch, O. Bortolini, and P. Besse, “Determination of Absolute Configuration Using Ab Initio Calculation of Optical Rotation,” Chirality, 15 (2003) S57-S64. DOI: ]. See [ Stephens05 P. J. Stephens, D. M. McCann, J. R. Cheeseman, and M. J. Frisch, “Determination of absolute configurations of chiral molecules using ab initio time-dependent density functional theory calculations of optical rotation: How reliable are absolute configurations obtained for molecules with small rotations?,” Chirality, 17 (2005) S52-S64. DOI: , Wilson05 S. M. Wilson, K. B. Wiberg, J. R. Cheeseman, M. J. Frisch, and P. H. Vaccaro, “Nonresonant optical activity of isolated organic molecules,” J. Phys. Chem. A, 109 (2005) 11752-64. DOI: , Stephens08 J. P. Stephens, J. J. Pan, F. J. Devlin, and J. R. Cheeseman, “Determination of the Absolute Configurations of Natural Products Using TDDFT Optical Rotation Calculations: The Iridoid Oruwacin,” J. Natural Prod., 71 (2008) 285-88. DOI: ] for example applications.
Predicting ROA and Raman Spectra
Raman and ROA intensities can be calculated separately from calculation of the force constants and normal modes, to facilitate using a larger basis for these properties as recommended in [ Cheeseman11a J. R. Cheeseman, M. J. Frisch, “Basis Set Dependence of Vibrational Raman and Raman Optical Activity Intensities,” J. Chem. Theory and Comput., 7, (2011), 3323-3334. DOI: ]. The options Polar=Raman and Polar=ROA request that the force constants be picked up from the checkpoint file (i.e., from a previous Freq calculation) and new polarizability derivatives (and the other two tensor derivatives for ROA) be computed and combined with the force constants in predicting intensities and spectra. Test job 931 provides an example of a two-step ROA calculation. For these jobs, be aware that the energy reported in the log file archive entry and in the final checkpoint file/formatted checkpoint file is the one computed in the frequency job—i.e., the value read from the checkpoint file at the start of the job—and not the energy computed with the model chemistry of the Raman/ROA calculation and reported in the final SCF Done output line.
オプション
Options
ROA
Compute dynamic analytic Raman optical activity intensities using GIAOs [
Cheeseman11a
J. R. Cheeseman, M. J. Frisch, “Basis Set Dependence of Vibrational Raman and Raman Optical Activity Intensities,” J. Chem. Theory and Comput., 7, (2011), 3323-3334. DOI:
]. 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 Polar=ROA). See the Examples for a sample input file.
This option is valid for Hartree-Fock and DFT methods.
Raman
Calculate Raman spectrum from force constants read-in from the checkpoint file.
OptRot
Perform optical rotation calculation. Use CPHF=RdFreq to specify the desired frequencies. Available for HF and DFT only. This option cannot be combined with NMR. Include IOp(10/46=7) in the route section to include the dipole-quadrupole contribution to the dipole-magnetic dipole polarizability in order to compute the full optical rotation tensor [ Pedersen95 T. B. Pedersen and A. E. Hansen, “Ab initio calculation and display of the rotatory strength tensor in the random phase approximation. Method and model studies,” Chem. Phys. Lett., 246 (1995) 1-8. DOI: ,Barron04]; the latter will be labeled as Optical Rotation G’ tensor in the output. Note that doing so does not change the optical rotation.
DCSHG
Do extra frequency-dependent CPHF for dc-SHG (direct current second harmonic generation) hyperpolarizabilities. This option implies CPHF=RdFreq as well.
Gamma
Equivalent to Polar=(DCSHG,Cubic) to do 2nd hyperpolarizabilities.
Analytic
Analytically compute the polarizability and the hyperpolarizability when analytic third derivatives are available. This option is the default for method with analytic second derivatives: RHF and UHF, CASSCF, CIS, MP2 and DFT methods. Note that the polarizability is always computed during analytic frequency calculations.
WorkerPerturbations
During numerical frequencies using Linda parallelism, run separate displacements on each worker instead of parallelizing each energy+derivative evaluation across the cluster. More efficient, but requires specifying an extra worker on the master node. This is the default if at least 3 Linda workers were specified. NoWorkerPerturbations suppresses this behavior.
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
Computes hyperpolarizabilities in addition to polarizabilities for methods with analytic gradients (first derivatives). Computes polarizabilities by double numerical differentiation of the energy for methods without analytic derivatives. EnOnly is a synonym for DoubleNumer.
Cubic
Numerically differentiate analytic polarizabilities to produce hyperpolarizabilities. Applicable only to methods having analytic frequencies but no analytic third derivatives.
Numerical
Computes the polarizability as a numerical derivative of the dipole moment (it is the analytic derivative of the energy, of course, not the expectation value in the case of MP2 or CI energies). The default for methods for which only analytic first derivative gradients are available.
Step=N
Specifies the step size in the electric field to be 0.0001N atomic units (applies to numerical differentiation).
Restart
Restarts a numerical calculation from the checkpoint file. A failed Polar calculation may be restarted from its checkpoint file by simply repeating the route section of the original job, adding the Restart option to the Polar keyword. No other input is required.
Susceptibility
Compute magnetic susceptibility as well as other properties (see NMR). Available for HF and DFT only.
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 (Polar=Numer). Not valid with Polar=DoubleNumer.
Dipole
Compute the dipole polarizabilities (the default).
適用範囲
Availability
The following table summarizes the options to Polar that are required to compute polarizabilities and hyperpolarizabilities for the available methods.
| Method Capabilities | Polarizability | Hyperpolarizability | ||
| Analytic 3rd derivatives (HF, most DFT) | Polar (default=Analytic) | Polar (default=Analytic) | ||
| Analytic frequencies (MP2, CIS, …) | Polar (default=Analytic) | Polar=Cubic | ||
| Only analytic gradients (CCSD, BD, …) | Polar (default=Numeric) | Polar=DoubleNumer | ||
| No analytic derivatives (CCSD(T), …) | Polar (default=DoubleNumer) | N/A |
Frequency-dependent polarizabilities and hyperpolarizabilities (i.e., Polar CPHF=RdFreq) are available only for HF and DFT methods.
関連キーワード
Related Keywords
実例
Examples
Frequency-Dependent Properties. The following job will compute frequency-dependent polarizabilities and hyperpolarizabilities using ω=0.1 Hartrees:
# Polar CPHF=RdFreq HF/6-31G(d)
Frequency-dependent calculation: w=0.1
molecule specification
0.1
Performing a frequency-dependent Polar calculation produces the results for the specified frequency following those for the static case within the output. For example, here are the polarizability values for a frequency-dependent job (ω=0.1 Hartree):
SCF Polarizability for W= 0.000000:
1 2 3
1 0.482729D+01
2 0.000000D+00 0.112001D+02
3 0.000000D+00 0.000000D+00 0.165696D+02
Isotropic polarizability for W= 0.000000 10.87 Bohr**3.
SCF Polarizability for W= 0.100000:
1 2 3
1 0.491893D+01
2 0.000000D+00 0.115663D+02
3 0.000000D+00 0.000000D+00 0.171826D+02
Isotropic polarizability for W= 0.100000 11.22 Bohr**3.
A static polarizability calculation would include only the first section. Similar output follows for hyperpolarizabilities and additional properties.
Optical Rotations. Here is the key part of the output for optical rotation jobs (OptRot option). In this case, we have performed a frequency-dependent calculation by including CPHF=RdFreq in the route section and specified a frequency of 589.3 nm:
Dipole-magnetic dipole polarizability for W= 0.077318:
1 2 3
1 -0.428755D+01 -0.175571D+01 0.000000D+00
2 -0.552645D+01 0.987070D+01 0.000000D+00
3 0.000000D+00 0.000000D+00 -0.676292D+00
w= 0.077318 a.u., Optical Rotation Beta= -1.6356 au.
Molar Mass = 172.2694 grams/mole, [Alpha] ( 5893.0 A) = -366.99 deg.
The specific rotation value is highlighted in the example output.
Recommended Model Chemistries for ROA. The following two-step job illustrates the recommended models for predicting ROA spectra from [ Cheeseman11a J. R. Cheeseman, M. J. Frisch, “Basis Set Dependence of Vibrational Raman and Raman Optical Activity Intensities,” J. Chem. Theory and Comput., 7, (2011), 3323-3334. DOI: ]:
%chk=freq.chk
# APFD/6-311+g(2d,2p) Opt Freq …
Freq + ROA: optimization+frequency
0 1
molecule specification
--Link1--
%Oldchk=freq.chk
%Chk=roa.chk
# APFD/spAug-cc-pVTZ Polar=ROA Guess=Read Geom=Check …
Freq + ROA: ROA calculation with larger basis set
0 1
532nm