A generalized Romberg differentiation procedure for calculation of hyperpolarizabilities

Medveď, Miroslav; Stachová, Mária; Jacquemin, Denis; André, Jean‐Marie; Perpète, Éric A.

doi:10.1016/j.theochem.2007.08.028

Cited by 63 publications

(45 citation statements)

References 11 publications

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“…Most of the reported dipole moment and polarizability values have been determined by the standard FF method using the Romberg procedure [43,44]. The minimum external electric field (F 0 ) was set to 2 × 10 −4 a.u.…”

Section: Computational Detailsmentioning

confidence: 99%

Electric properties of the low-lying excited states of benzonitrile: geometry relaxation and solvent effects

2015

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Section: Computational Detailsmentioning

confidence: 99%

Electric properties of the low-lying excited states of benzonitrile: geometry relaxation and solvent effects

2015

Self Cite

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“…Mean dipole polarizability, polarizability anisotropy, and the axial polarizability of the Be-TCNE complex constituents have also been calculated analytically. The corresponding quantities of the complex have been obtained by the finite-field differentiation method from the field dependent total energies employing the Romberg iterative procedure [28,29].…”

Section: Theoretical and Computational Aspectsmentioning

confidence: 99%

MP2 and DFT study of IR spectra of TCNE‐methylsubstituted benzene complexes: Is charge transfer important?

Kyseľ

Budzák

Mach

et al. 2009

Int J of Quantum Chemistry

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ABSTRACT:The second-order Møller-Plesset (MP2) and density functional theory (DFT; B3LYP, B3LYP-D) approaches show that the CN (and also CAC) stretching IR vibrations are relatively small but reproducibly shifted to lower frequencies in a series of methylbenzenes-tetracyanoethylene (NMB-TCNE, N ϭ mono-, di-, …, hexa-) complexes with increasing number of methyl groups (N). These CN stretching IR frequency shifts, ranging from 8 to 12 cm Ϫ1 , are linearly dependent on number N but still 2-4 times greater than recently published experimental data [Stires et al., Chem Commun, 2005, 28, 3532; Pawlukojc et al., Chem Phys, 2006, 327, 311]. An explanation of the shifts toward lower frequencies is in literature [Stires et al., Chem Commun, 2005, 28, 3532; Pawlukojc et al., Chem Phys, 2006, 327, 311] usually attributed to the magnitude of transferred electron charge ⌬Q from a donor molecule to TCNE (mainly to its LUMO [lowest unoccupied molecular orbital]). The LUMO has antibonding character on CN and CAC bonds, and thus the respective CN and CAC bond orders are, due to partial occupation in the complex, decreased. However, the difference by a factor of 2-4 between our MP2 (and also B3LYP) calculations and experiment is probably also due to the effect of environment, i.e., intermolecular forces between complex and solvent molecules or crystal lattice. The calculated interplanar distance R, dipole moment , and transferred charge ⌬Q are approximately linearly dependent on number of methyl groups N. However, between N ϭ 2 and 3, the abrupt changes in the dependencies were observed. This is caused by the change of mutual (perpendicular) orientations between respective methyl benzenes and TCNE in the complexes as a consequence of preferred interaction between one of two degenerated or near degenerated highest occupied molecular orbitals (being orthogonal) on NMB with LUMO located mainly on TCNE. This fact is important for many properties (especially for electron excited states) of these complexes. A strong dependence of polarizability, namely of its ␣ zz part, of the benzene-TCNE (Be-TCNE) complex on soft vibrations was found. The vibrational contribution to ␣ zz value is almost as large as the electronic ␣ zz contribution. Finally, MP2 and B3LYP studies indicate that inclusion of anharmonicity has small, if any, effect on calculated vibrational frequencies of Be-TCNE. This theoretical finding is quite important especially because it holds also for soft vibrational modes, which are always present at weak intermolecular complexes.

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“…lead to non‐negligible contributions to the overall energy with increasing field strength. This effect is systematic and can be cancelled out by linear combination of properties obtained at different field strengths, which is usually applied in literature …”

Section: Introductionmentioning

confidence: 99%

Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

2013

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The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude.

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A generalized Romberg differentiation procedure for calculation of hyperpolarizabilities

Cited by 63 publications

References 11 publications

Electric properties of the low-lying excited states of benzonitrile: geometry relaxation and solvent effects

Electric properties of the low-lying excited states of benzonitrile: geometry relaxation and solvent effects

MP2 and DFT study of IR spectra of TCNE‐methylsubstituted benzene complexes: Is charge transfer important?

Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

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