Frequency-dependent hyperpolarizabilities in the coupled-cluster method: the Kerr effect for molecules
TL;DR: In this paper, the frequency dependence in the equation-of-motion coupled-cluster method was introduced to evaluate the optical Kerr effect for butadiene and ammonia, and a critical evaluation of dispersion estimates via the uncorrelated time-dependent Hartree-Fock theory was performed.
About: This article is published in Chemical Physics Letters.The article was published on 1995-03-03. It has received 65 citations till now. The article focuses on the topics: Kerr effect & Coupled cluster.
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201 citations
TL;DR: In this paper, an atomic-integral direct algorithm for calculating singlet excitation energies in the coupled cluster singles and doubles (CCSD) model is presented. But this algorithm does not consider the effect of triple excitations.
Abstract: Algorithms for calculating singlet excitation energies in the coupled cluster singles and doubles (CCSD) model are discussed and an implementation of an atomic‐integral direct algorithm is presented. Each excitation energy is calculated at a cost comparable to that of the CCSD ground‐state energy. Singlet excitation energies are calculated for benzene using up to 432 basis functions. Basis‐set effects of the order of 0.2 eV are observed when the basis is increased from augmented polarized valence double‐zeta (aug‐cc‐pVDZ) to augmented polarized valence triple‐zeta (aug‐cc‐pVTZ) quality. The correlation problem is examined by performing calculations in the hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3, as well as by using the CCSDR(3) perturbative triples corrections. The effect of triple excitations are less than 0.2 eV for all excitations except for the 2 1E2g state. The calculated excitation energies are compared with experiment and other theoretical results.
191 citations
TL;DR: In this article, the frequency-dependent first (β) and second (γ) hyperpolarizabilities for the set of small molecules, N2, CO2, CS2, C2H4, NH3, CO, HF, H2O, and CH4, were compared to Hartree-Fock and correlated ab initio calculations, as well as to experimental results.
Abstract: In this paper we present time-dependent density functional calculations on frequency-dependent first (β) and second (γ) hyperpolarizabilities for the set of small molecules, N2, CO2, CS2, C2H4, NH3, CO, HF, H2O, and CH4, and compare them to Hartree–Fock and correlated ab initio calculations, as well as to experimental results. Both the static hyperpolarizabilities and the frequency dispersion are studied. Three approximations to the exchange-correlation (xc) potential are used: the widely used Local Density Approximation (LDA), the Becke–Lee–Yang–Parr (BLYP) Generalized Gradient Approximation (GGA), as well as the asymptotically correct Van Leeuwen–Baerends (LB94) potential. For the functional derivatives of the xc potential the Adiabatic Local Density Approximation (ALDA) is used. We have attempted to estimate the intrinsic quality of these methods by using large basis sets, augmented with several diffuse functions, yielding good agreement with recent numerical static LDA results. Contrary to claims which have appeared in the literature on the basis of smaller studies involving basis sets of lesser quality, we find that the static LDA results for β and γ are severely overestimated, and do not improve upon the (underestimated) Hartree–Fock results. No improvement is provided by the BLYP potential which suffers from the same incorrect asymptotic behavior as the LDA potential. The results are however clearly improved upon by the LB94 potential, which leads to underestimated results, slightly improving the Hartree–Fock results. The LDA and BLYP potentials overestimate the frequency dependence as well, which is once again improved by the LB94 potential. Future improvements are expected to come from improved models for asymptotically correct exchange-correlation potentials. Apart from the LB94 potential used in this work, several other asymptotically correct potentials have recently been suggested in the literature and can also be expected to improve considerably upon the relatively poor LDA and GGA results, for both the static properties and their frequency dependence.
165 citations
TL;DR: In this paper, an integral-direct implementation of first-order one-electron properties in the coupled cluster singles and doubles (CCSD!) model is presented, and the convergence towards the basis set limit is faster at the Hartree-Fock level than at the CCSD level.
Abstract: An integral-direct implementation of first-order one-electron properties in the coupled cluster singles and doubles ~CCSD! model is presented. The implementation increases the range of applicability of CCSD first-order one-electron property calculations significantly compared to nondirect approaches. As an application a thorough basis set investigation is performed on five diatomic molecules at the Hartree‐Fock and CCSD levels for the molecular electric dipole moment, the molecular electric quadrupole moment, and the electric field gradient at the nuclei. In general, basis sets of polarized triple-zeta quality are the smallest to be recommended, and the convergence towards the basis set limit is faster at the Hartree‐Fock level than at the CCSD level. Among the properties considered, the electric dipole moment is the easiest to converge. The electric dipole and especially the electric quadrupole moment require diffuse functions for high accuracy. With standard basis sets, it is not possible to calculate electric field gradients consistently within three thousandths of an atomic unit of the basis set limit—for this purpose, elaborate nonstandard basis sets are required. The electric field gradients at the nuclei in HCN and the electric dipole moment of the furan molecule are calculated at the CCSD level employing up to 417 basis functions, further demonstrating the large-scale applicability of the implementation. © 1997 American Institute of Physics. @S0021-9606~97!02927-9#
127 citations
TL;DR: Molecular switches: Highly efficient acido- and photoswitchable frequency doublers (see scheme) based on the indolinooxazolidine core are studied by means of hyper-Rayleigh experiments and quantum-chemical calculations.
Abstract: Molecular switches: Highly efficient acido- and photoswitchable frequency doublers (see scheme) based on the indolinooxazolidine core are studied by means of hyper-Rayleigh experiments and quantum-chemical calculations.
To optimize the nonlinear optical (NLO) contrast, a series of indolinooxazolidine derivatives with electron-withdrawing substituents in the para position on the indolinic residue have been synthesized. Their linear and nonlinear optical properties have been characterized by UV-visible absorption and hyper-Rayleigh scattering measurements, as well as by ab initio calculations. The two-way photo- or pH-triggered switching mechanism has been demonstrated by comparing the absorption spectra of the zwitterionic and protonated open forms (POF). Hyper-Rayleigh measurements have revealed that the second-order NLO contrast between the closed indolinooxazolidine and the open π-conjugated colored forms remain very large upon substitution. Theory and measurements show that for the POFs the amplitude of the first hyperpolarizability follows the Hammett parameters of the withdrawing groups. However, because the measurements are performed in resonance, to recover this behavior, elaborate procedures including homogeneous and inhomogeneous broadenings, as well as single-mode vibronic structures are necessary to extrapolate to the static limit.
127 citations
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TL;DR: In this article, an extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the first row atoms carbon to fluorine, where each inner shell is represented by a single basis function taken as a sum of four Gaussians and each valence orbital is split into inner and outer parts described by three and one Gaussian function, respectively.
Abstract: An extended basis set of atomic functions expressed as fixed linear combinations of Gaussian functions is presented for hydrogen and the first‐row atoms carbon to fluorine. In this set, described as 4–31 G, each inner shell is represented by a single basis function taken as a sum of four Gaussians and each valence orbital is split into inner and outer parts described by three and one Gaussian function, respectively. The expansion coefficients and Gaussian exponents are determined by minimizing the total calculated energy of the atomic ground state. This basis set is then used in single‐determinant molecular‐orbital studies of a group of small polyatomic molecules. Optimization of valence‐shell scaling factors shows that considerable rescaling of atomic functions occurs in molecules, the largest effects being observed for hydrogen and carbon. However, the range of optimum scale factors for each atom is small enough to allow the selection of a standard molecular set. The use of this standard basis gives theoretical equilibrium geometries in reasonable agreement with experiment.
8,551 citations
TL;DR: In this paper, a comprehensive overview of the equation of motion coupled-cluster (EOM•CC) method and its application to molecular systems is presented by exploiting the biorthogonal nature of the theory, it is shown that excited state properties and transition strengths can be evaluated via a generalized expectation value approach that incorporates both the bra and ket state wave functions.
Abstract: A comprehensive overview of the equation of motion coupled‐cluster (EOM‐CC) method and its application to molecular systems is presented. By exploiting the biorthogonal nature of the theory, it is shown that excited state properties and transition strengths can be evaluated via a generalized expectation value approach that incorporates both the bra and ket state wave functions. Reduced density matrices defined by this procedure are given by closed form expressions. For the root of the EOM‐CC effective Hamiltonian that corresponds to the ground state, the resulting equations are equivalent to the usual expressions for normal single‐reference CC density matrices. Thus, the method described in this paper provides a universal definition of coupled‐cluster density matrices, providing a link between EOM‐CC and traditional ground state CC theory.Excitation energy,oscillator strength, and property calculations are illustrated by means of several numerical examples, including comparisons with full configuration interaction calculations and a detailed study of the ten lowest electronically excited states of the cyclic isomer of C4.
2,171 citations
TL;DR: The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities.
Abstract: The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities. The excellent performance of the [13.10.4/7.5.2] GTO/CGTO polarized basis sets derived for Si through Cl is illustrated by the atomic polarizability results and SCF and MBPT data for dipole moments and polarizabilities of the second-row atom hydrides. The possible applications of the electric-property oriented polarized basis sets are discussed. The basis set data for Si through Cl are those for H and C through F append the paper.
690 citations
TL;DR: In this article, the static dipole polarizability and second hyperpolarizability tensors are calculated for polyene systems via ab initio coupled-perturbed Hartree-Fock theory.
Abstract: The static dipole polarizability and second hyperpolarizability tensors are calculated for polyene systems via ab initio coupled‐perturbed Hartree–Fock theory. The effect of basis set augmentation on the calculated properties is explored for C4H6 and example basis sets are used to calculate the polarizability and second hyperpolarizability for the longer polyenes: C6H8, C8H10, C10H12, C12H14, C14H16,C16H18, C18H20, C20H22, C22H24. Results for the finite polyenes are extrapolated to predict the unit‐cell polarizability and second hyperpolarizability of infinite polyacetylene. The working equations which take advantage of the 2n+1 theorem of perturbation theory for calculating up to the second hyperpolarizability are given, and their implementation is briefly discussed. In particular it is shown that the implementation is readily amenable to parallel processing.
440 citations
TL;DR: In this article, various nonlinear optical polarizabilities are derived and evaluated by time dependent Hartree-Fock theory (TDHF) and applied to evaluate dispersion effects for the series of molecules CH4, CH3F, CH2F2, CHF3, and CF4.
Abstract: Various nonlinear optical polarizabilities are derived and evaluated by time dependent Hartree–Fock theory (TDHF). The recursive nature of the TDHF theory is exploited to develop formulas that are applicable in any order. The theory is applied to evaluate dispersion effects for the series of molecules CH4, CH3F, CH2F2, CHF3, and CF4. Comparisons are made with results obtained from dc‐induced, second‐Harmonic generation, and third‐Harmonic generation experiments. Additional applications are reported for H2 and HF.
342 citations