Hartree−Fock and Density Functional Theory ab Initio Calculation of Optical Rotation Using GIAOs:  Basis Set Dependence

Cheeseman, James R.; Frisch, Michael J.; Devlin, F. J.; Stephens, Philip J.

doi:10.1021/jp993424s

Cited by 275 publications

(272 citation statements)

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“…It was found that the TD-DFT treatment offers greatly enhanced accuracy as compared to some of the more frequently used ab initio methods ͑RPA, CIS͒ at comparable or less computational expense, in particular as far as low-lying excitations are concerned. 9 TD-DFT implementations regarding optical activity have been reported recently for the frequency-dependent optical rotation parameter 10,11 within the Gaussian code, and for optical rotations and CD spectra within TURBOMOLE 12,13 and a numerical code. 14 Prior code developments for polarizabilities and excitation energies have been carried out by van Gisbergen et al 15,16 for the spectra.…”

Section: Introductionmentioning

confidence: 99%

Chiroptical properties from time-dependent density functional theory. I. Circular dichroism spectra of organic molecules

Autschbach

Ziegler

Gisbergen³

et al. 2002

The Journal of Chemical Physics

413

330

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We report the implementation of the computation of rotatory strengths, based on time-dependent density functional theory, within the Amsterdam Density Functional program. The code is applied to the simulation of circular dichroism spectra of small and moderately sized organic molecules, such as oxiranes, aziridines, cyclohexanone derivatives, and helicenes. Results agree favorably with experimental data, and with theoretical results for molecules that have been previously investigated by other authors. The efficient algorithms allow for the simulation of CD spectra of rather large molecules at a reasonable accuracy based on first-principles theory. The choice of the Kohn-Sham potential is a critical issue. It is found that standard gradient corrected functionals often yield the correct shape of the spectrum, but the computed excitation energies are systematically underestimated for the samples being studied. The recently developed exchange-correlation potentials ''GRAC'' and ''SAOP'' often yield much better agreement here with experiments for the excitation energies. The rotatory strengths of individual transitions are usually improved by these potentials as well.

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Section: Introductionmentioning

confidence: 99%

Chiroptical properties from time-dependent density functional theory. I. Circular dichroism spectra of organic molecules

Autschbach

Ziegler

Gisbergen³

et al. 2002

The Journal of Chemical Physics

413

330

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“…The origin of the variation in basis-set dependence of calculated linear and nonlinear molecular properties involving external or internal sources of electric or magnetic fields remains unclear, 44,50,[72][73][74] and it appears that only numerical investigations will be able to reveal the basis-set improvements that can be expected from the use of London atomic orbitals in the calculation of properties involving static or frequencydependent magnetic field perturbations.…”

Section: Resultsmentioning

confidence: 99%

Gauge-origin independent calculations of Jones birefringence

Shcherbin

Thorvaldsen

Jonsson

et al. 2011

The Journal of Chemical Physics

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We present the first gauge-origin independent formulation of Jones birefringence at the Hartree–Fock level of theory. Gauge-origin independence is achieved through the use of London atomic orbitals. The implementation is based on a recently proposed atomic orbital-based response theory formulation that allows for the use of both time- and perturbation-dependent basis sets [Thorvaldsen, Ruud, Kristensen, Jørgensen, and Coriani, J. Chem. Phys. 129, 214108 (2008)]. We present the detailed expressions for the response functions entering the Jones birefringence when London atomic orbitals are used. The implementation is tested on a set of polar and dipolar molecules at the Hartree–Fock level of theory. It is demonstrated that London orbitals lead to much improved basis-set convergence, and that the use of small, conventional basis sets may lead to the wrong sign for the calculated birefringence. For large basis sets, London orbitals and conventional basis sets converge to the same results.

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“…16 Origin-independence of b = 1/3 Tr[b ab ] is ensured by the use of GIAOs. Calculations were carried out using the basis sets: aug-cc-pVTZ, 6-311G(2d,2p), aug-cc-pVDZ, DZP, 6-31G**, cc-pVDZ, 6-31G*, 4-31G*, and 6-31G 12 and, in the case of DFT calculations, the functionals B3LYP, B3PW91, B3P86, and PBE1PBE. where N A is Avogadro's number and M is the molecular weight.…”

Section: Methodsmentioning

confidence: 99%

“…3), substantial errors can be anticipated in calculations of b in the static limit. An additional problem associated with the use of FIAOs is that calculated b values, and hence optical rotations, are origin-dependent 12 and therefore nonphysical; in contrast, the use of GIAOs ensures origin-independent, physically meaningful optical rotations, irrespective of basis set size.…”

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confidence: 99%

Ab initio prediction of optical rotation: Comparison of density functional theory and Hartree‐Fock methods for three 2,7,8‐trioxabicyclo[3.2.1]octanes

Stephens

Devlin

Cheeseman³

et al. 2002

Chirality

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We report ab initio calculations of the frequency-dependent electric dipole-magnetic dipole polarizabilities, beta(nu), at the sodium D line frequency and, thence, of the specific rotations, [alpha](D), of 2,7,8-trioxabicyclo[3.2.1]octane, 1, and its 1-methyl derivative, 2, using the Density Functional Theory (DFT) and Hartree-Fock/Self-Consistent Field (HF/SCF) methodologies. Gauge-invariant (including) atomic orbitals (GIAOs) are used to ensure origin-independent [alpha](D) values. Using large basis sets which include diffuse functions DFT [alpha](D) values are in good agreement with experimental values (175.8 degrees and 139.2 degrees for (1S,5R)-1 and -2, respectively); errors are in the range 25-35 degrees. HF/SCF [alpha](D) values, in contrast, are much less accurate; errors are in the range 75-95 degrees. The use of small basis sets which do not include diffuse functions substantially lowers the accuracy of predicted [alpha](D) values, as does the use of the static limit approximation: beta(nu) approximately beta(o). The use of magnetic-field-independent atomic orbitals, FIAOs, instead of GIAOs, leads to origin-dependent, and therefore nonphysical, [alpha](D) values. We also report DFT calculations of [alpha](D) for the 1-phenyl derivative of 1, 3. DFT calculations find two stable conformations, differing in the orientation of the phenyl group, of very similar energy, and separated by low barriers. Values of [alpha](D) predicted using two different algorithms for averaging over phenyl group orientations are in good agreement with experiment. In principle, the absolute configuration (AC) of a chiral molecule can be assigned by comparison of the optical rotation predicted ab initio to the experimental value. Our results demonstrate the critical importance of the choice of ab initio methodology in obtaining reliable optical rotations and, hence, ACs, and show that, at the present time, DFT constitutes the method of choice.

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Hartree−Fock and Density Functional Theory ab Initio Calculation of Optical Rotation Using GIAOs: Basis Set Dependence

Cited by 275 publications

References 50 publications

Chiroptical properties from time-dependent density functional theory. I. Circular dichroism spectra of organic molecules

Chiroptical properties from time-dependent density functional theory. I. Circular dichroism spectra of organic molecules

Gauge-origin independent calculations of Jones birefringence

Ab initio prediction of optical rotation: Comparison of density functional theory and Hartree‐Fock methods for three 2,7,8‐trioxabicyclo[3.2.1]octanes

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