Bernard Kirtman

Assessment of conventional density functional schemes for computing the polarizabilities and hyperpolarizabilities of conjugated oligomers: An ab initio investigation of polyacetylene chains

DFT schemes based on conventional and less conventional exchange-correlation (XC) functionals have been employed to determine the polarizability and second hyperpolarizability of π-conjugated polyacetylene chains. These functionals fail in one or more of several ways: (i) the correlation correction to α is either much too small or in the wrong direction, leading to an overestimate; (ii) γ is significantly overestimated; (iii) the chain length dependence is excessively large, particularly for γ and for the more alternant system; and (iv) the bond length alternation effects on γ are either underestimated or qualitatively incorrect. The poor results with the asymptotically correct van Leeuwen–Baerends XC potential show that the overestimations are not related to the asymptotic behavior of the potential. These failures are described in terms of the separate effects of the exchange and the correlation parts of the XC functionals. They are related to the short-sightedness of the XC potentials which are relatively insensitive to the polarization charge induced by the external electric field at the chain ends.

A perturbation method for calculating vibrational dynamic dipole polarizabilities and hyperpolarizabilities

Perturbation formulas are derived for calculating the vibrational dynamic polarizability (αv) and hyperpolarizabilities (βv and γv ) of polyatomic molecules. These formulas, based on an initial harmonic oscillator approximation, include corrections for mechanical anharmonicity (cubic) terms in the vibrational potential and electrical anharmonicity (quadratic) terms in the dependence of the electrical field polarization potential on nuclear coordinates. Results are presented for FH and CO2. In the former case, comparison is made to ‘‘exact’’ numerical values. Fully documented computer programs for the perturbation treatment are available.

Compact formulas for vibrational dynamic dipole polarizabilities and hyperpolarizabilities

Compact, readily‐programmable formulas are given for the vibrational dynamic dipole polarizability (αv) and hyperpolarizabilities (β v and γv) for polyatomic molecules. They are based on perturbation theory and should replace those presented by us previously.

Nonlinear optical properties of quasilinear conjugated oligomers, polymers and organic molecules

Recent developments concerning the nonlinear optical (NLO) properties of quasilinear conjugated oligomers, polymers and organic molecules are reviewed. Although our approach is from a theoretical perspective, it is oriented towards the practical design of both second- and third-order NLO materials. Since the field is relatively new, we critically assess the current state of knowledge and indicate where further investigations are needed. Some of the topics covered, which have received limited attention in the past, are vibrational hyperpolarizabilities, the potential for enhancement of NLO response due to formation of charged structures, and the quantitative role of the solid-state medium. After the introduction there is a section on the theoretical background which presents the formal expressions that are needed, introduces the available computational methodology and points out its limitations especially when applied to large systems. Then we discuss the results that have been obtained, starting with some...

A simple method for determining approximate static and dynamic vibrational hyperpolarizabilities

A simple method is presented for calculating approximate static and dynamic vibrational hyperpolarizabilities. It involves determining electrical properties in the presence of a static field with and without geometry optimization. This method is readily applicable to all tensor components of a general polyatomic molecule.

Additional compact formulas for vibrational dynamic dipole polarizabilities and hyperpolarizabilities

Compact expressions, complete through second order in electrical and/or mechanical anharmonicity, are given for the dynamic dipole vibrational polarizability and dynamic first and second vibrational hyperpolarizabilities. Certain contributions not previously formulated are now included.

Calculation of electric dipole (hyper)polarizabilities by long-range-correction scheme in density functional theory: A systematic assessment for polydiacetylene and polybutatriene oligomers

The long-range correction (LC) for treating electron exchange in density functional theory, combined with the Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, was used to determine (hyper)polarizabilities of polydiacetylene/polybutatriene oligomers. In comparison with coupled-cluster calculations including single and double excitations as well as a perturbative treatment of triple excitations, our values indicate that the tendency of conventional functionals to result in a catastrophic overshoot for these properties is alleviated but not eliminated. No clear-cut preference for LC-BLYP over Hartree-Fock values is obtained. This analysis is consistent with the calculations of Sekino et al. [J. Chem. Phys. 126, 014107 (2007)] on polyacetylene and molecular hydrogen oligomers. Thus, the performance of LC-BLYP with regard to (hyper)polarizabilities of quasilinear conjugated systems is now well characterized.

Calculation of first and second static hyperpolarizabilities of one- to three-dimensional periodic compounds. Implementation in the CRYSTAL code.

A computational scheme for the evaluation of the static first (beta) and second (gamma) hyperpolarizability tensors of systems periodic in 1D (polymers), 2D (slabs), 3D (crystals), and, as a limiting case, 0D (molecules) has been implemented, within the coupled perturbed Hartree-Fock framework (CPHF), in the CRYSTAL code, which uses a Gaussian type basis set. This generalizes to 2D and 3D the work by Bishop et al. (J. Chem. Phys. 114, 7633 (2001)). CPHF is applied for beta and gamma (the polarizability tensor alpha is also reported for completeness) of LiF in different aggregation states: finite and infinite chains, slabs, and cubic crystal. Correctness of the computational scheme and its numerical efficiency are documented by the trend of beta and gamma for increasing dimensionality: for a finite linear chain containing N LiF units, the hyperpolarizability tends to the infinite chain value at large N, N parallel chains give the slab value when N is sufficiently large, and N superimposed slabs tend to the bulk value. High numerical accuracy can be achieved at relatively low cost, with a dependence on the computational parameters similar to that observed for field-free self-consistent field (SCF) calculations.

Simultaneous calculation of several interacting electronic states by generalized Van Vleck perturbation theory

We present an accurate many‐body perturbation theory for the simultaneous calculation of an arbitrary set of interacting electronic states based on the generalized Van Vleck method. This treatment yields an effective Hamiltonian for the interacting states (or model space) which is Hermitian and energy‐independent. A special provision is made for external states that are energetically adjacent to the model space. The perturbation formulas for the effective Hamiltonian matrix contain ordinary Rayleigh–Schrodinger type energy denominators which include zeroth‐order splitting between the various interacting states. These energy denominators factor in all orders just as they do in the nondegenerate problem. A convenient diagrammatic representation of the perturbation expansion is developed. In carrying out the expansion there is some freedom associated with the orthonormality condition for states in the model space. We make the simplest possible choice with regard to evaluation of the perturbation formulas. Th...

Calculation of vibrational dynamic hyperpolarizabilities for H2O, CO2, and NH3

Dynamic vibrational first and second hyperpolarizabilities, applicable to a number of nonlinear optical processes, have been calculated for H2O, CO2, and NH3 at a typical laser frequency. As a percentage of their electronic counterparts, they range from being very small to being on the order of 20–30 %. The static values have also been calculated and are much larger. The calculations were based on perturbation theory and required knowledge of (a) first and second derivatives of the electrical properties (dipole moment, polarizability, and first hyperpolarizability functions) with respect to the normal coordinates, and (b) the harmonic and first anharmonic force constants. These were found at both the SCF and MP2 levels of approximation. In most cases electron correlation has a marked effect on the vibrational hyperpolarizabilities. Anharmonicity contributions are relatively small except for the static case and for the dc‐Kerr effect.