Molecular response properties from explicitly time-dependent configuration interaction methods

In this paper we report the calculation of molecular electric response properties with the help of explicitly time-dependent configuration interaction (TD-CI) methods. These methods have the advantage of being applicable (within the limitations of the time-dependent Schrodinger equation) to time-dependent perturbations of arbitrary shape and strength. Three variants are used to solve the time-dependent electronic Schrodinger equation, namely, the TD-CIS (inclusion of single excitations only), TD-CISD (inclusion of single and double excitations), and TD-CIS(D) (single excitations and perturbative treatment of double excitations) methods and applied for illustration to small molecules, H(2) and H(2)O. In the calculation, slowly varying off-resonant electric fields are applied to the molecules and linear (polarizabilities) and nonlinear (hyperpolarizabilities, harmonic generation) response properties are determined from the time-dependent dipole moments.     

Density-functional theory study of electric and magnetic properties of hexafluorobenzene in the vapor phase

A series of electric and magnetic properties of hexafluorobenzene have been calculated, including the electric dipole polarizability, magnetizability, electric quadrupole moment, and nonlinear mixed electric dipole-magnetic dipole-electric quadrupole hyperpolarizabilities needed to obtain estimates of the Kerr, Cotton-Mouton, Buckingham, Jones, and magnetoelectric birefringences in the vapor phase. Time-dependent density-functional theory was employed for the calculation of linear-, quadratic, and cubic response functions. A number of density functionals have been considered, along with Sadlej's triple-zeta basis set and the augmented correlation-consistent polarized valence double zeta and augmented correlation-consistent polarized valence triple zeta basis sets. Comparisons have been made with experiment where possible. The analysis of results allows for an assessment of the capability of time-dependent density-functional theory for high-order electromagnetic properties of an electron-rich system such as hexafluorobenzene.     

A mixed numerical-analytical approach to the calculation of non-linear electric properties

Non-linear electric properties of atoms and molecules can be determined by computing the second-order polarizabilities from the analytic perturbation equations, numerically modified by the presence of an additional finite field. The scheme is applied in a test calculation of the He atom hyperpolarizabilities, γ( 0;0,0,0) and γ(-ω;ω,0, 0).     

Structures and static electric properties of novel alkalide anions F-Li+Li- and F-Li3+Li3-

Novel cluster anions Li2F- and Li6F- with alkalide character have been studied in the present paper. In contrast to a typical neutral alkalide, Li2F- contains a F- anion instead of the neutral ligand and forms an alkalide anion F-Li+Li-. In addition to a F- anion ligand, Li6F- contains a Li3+ superalkali cation instead of the alkali metal cation and a Li3- superalkali anion instead of the alkali metal anion, and this alkalide anion can be denoted by F-Li3+Li3-, which is supported by NBO charge results. The results indicate that the F- anion can polarize not only the Li atom but also the Li3 superalkali to form alkalide anions with excess electrons. For Li2F-, two linear structures (1Sigma+ and 3Sigma+ states) are obtained. For Li6F-, the structure of the 1A1 state is a trigonal antiprism capped by the F- anion with C3v symmetry, while the structure of the 7A' state is a slightly distorted trigonal antiprism with Cs symmetry. Due to the excess electrons on the alkali metal and superalkali anions (Li- and Li3-), the alkalide anions Li2F- and Li6F- have large first hyperpolarizabilities (beta0=1.116x10(4)-1.764x10(5) au). For the spin multiplicity effect on electric properties, in these two alkalide anions, the values of the static electric properties, especially the first hyperpolarizabilities, of the high spin states are larger than the corresponding values of the low spin states. For the substitution effect of superalkali atoms, in the two singlet states, as the Li3 superalkalis substitute the Li atoms, the value of the mean of polarizability increases, while the values of dipole moment and the first hyperpolarizability decrease.     

MNDO calculations of molecular electric polarizabilities,hyperpolarizabilities, and nonlinear optical coefficients

Molecular electric polarizabilities, hyperpolarizabilities, and nonlinear optical coefficients have been calculated by the MNDO SCF MO method with reasonably satisfactory results.     

Analytic calculations of vibrational hyperpolarizabilities in the atomic orbital basis

We present an analytic scheme for the calculation of pure vibrational contributions to linear and nonlinear optical properties such as the polarizability and the first and second hyperpolarizabilities. The formalism is fully expressed in terms of a perturbation- and time-dependent atomic orbital basis, using the elements of the density matrix in the atomic orbital basis as the basic variables. We calculate perturbed densities up to third order with respect to the electric field in accordance with the n + 1 rule, and the approach is therefore applicable for the calculation of pure vibrational contributions involving all vibrational coordinates in large molecular complexes. In the case of static electric fields, we therefore only need to calculate 19 response equations, independent of the size of the molecule. If we can determine the molecular energy and force field, the calculation of pure vibrational contributions to the nonlinear optical properties of the molecule is therefore a rather straightforward task. We illustrate the implementation by calculating pure vibrational contributions to the first and second hyperpolarizabilities of molecules containing up to 66 atoms using basis sets of good quality.     

Synthesis, molecular structure, spectroscopic studies and second-order nonlinear optical behaviour of N,N'-(2-hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II)

N,N'-(2-Hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II) has been synthesized. The crystal structure has been determined by X-ray diffraction analysis, and linear optical characterization has been determined by UV-vis spectroscopy. It was found that the molecule under investigation has solvatochromic behaviour in the UV region, implying non-zero microscopic first hyperpolarizability. To reveal the microscopic nonlinear optical (NLO) properties, the static first hyperpolarizabilities (beta) and the electric dipole moments (mu) were evaluated by using the ab initio finite field (FF) method. According to the results of the FF calculations, the synthesized compound exhibits non-zero beta values, and it might have microscopic NLO behaviour.     

Linear optical transmission measurements and computational study of linear polarizabilities, first hyperpolarizabilities of a dinuclear iron(III) complex

The optical transmission spectral study of a dinuclear metal complex [FeL(MeOH)Cl]2 (L=N-(5-methylphenyl)-3-methoxysalicylaldimine) has been carried out. The linear optical characterization shows that this molecule has transparency in the visible range. To understand linear optical and microscopic second-order nonlinear optical (NLO) behavior of the compound, we have computed the electric dipole moment (mu) and dispersion-free first hyperpolarizabilities (beta) using Finite Field second-order M?ller-Plesset perturbation (FF MP2) procedure; and also dispersion-free linear polarizabilities (alpha), frequency-dependent linear polarizabilities within the linear optical spectrum and first hyperpolarizabilities at lambda=730-1050 and 1000-1400 nm wavelength areas using time-dependent Hartree-Fock (TDHF) method. The ab-initio calculation results reveal that the examined complex might have linear optical and microscopic NLO behavior with non-zero values.     

Nonlinear optical property calculations by the long-range-corrected coupled-perturbed Kohn-Sham method

The long-range correction (LC) scheme for the exchange functional of density-functional theory (DFT) was combined with the coupled-perturbed Kohn-Sham (CPKS) method to calculate nonlinear optical response properties. By using this LC-CPKS method, we calculated the hyperpolarizabilities of typical molecules and the dipole moments, polarizabilities, and hyperpolarizabilities of push-pull pi-conjugated systems: p-nitroaniline, 4-amino-4'-nitrostilbene, and alpha,omega-nitroaminopolyenes. It was found that the LC scheme clearly improved the calculation of these optical properties for all of these systems, which have been significantly overestimated by conventional DFTs. We therefore concluded that the long-range exchange interaction played an important role in calculating the optical properties using the DFT formalism.     

Electrostatic calculation of linear and non-linear optical properties of ice Ih,II, IX and VIII

Macroscopic first- and third-order susceptibilities of ice Ih, ice II, ice IX and ice VIII are calculated using static and frequency-dependent electronic and static vibrational molecular (hyper)polarizabilities at the MP2 level. The molecular properties are in good agreement with experiment and with high-level ab initio calculations. Intermolecular electrostatic and polarization effects due to induced dipoles are taken into account using a rigorous local-field theory. The electric field due to permanent dipoles is used to calculate effective in-crystal (hyper)polarizabilities. The polarizability depends only weakly on the permanent field, but the dipole moment and the hyperpolarizabilities are strongly affected. The calculated linear susceptibility is in good agreement with available experimental data for ice Ih, and the third-order susceptibility for a third harmonic generation experiment is in reasonable agreement with experimental values for liquid water. The molecular vibrational contributions have a small effect on the susceptibilities. The electric properties of a water tetramer are calculated and used to estimate the effect of non-dipolar interactions on the susceptibilities of ice Ih, which are found to be small.     

Computer simulation of the linear and nonlinear optical susceptibilities of p-nitroaniline in cyclohexane, 1,4-dioxane, and tetrahydrofuran in quadrupolar approximation. I. Molecular polarizabilities and hyperpolarizabilities

This is the first part of a study of the local field effects on (non)linear optical susceptibilities of solutions of para-nitroaniline (pNA) in three different solvents, cyclohexane (CH), 1,4-dioxane (DI), and tetrahydrofuran (THF), using a discrete molecular representation of the condensed phase. To account for dipolar and quadrupolar effects, the latter of which are especially important for DI solution, all the electric properties necessary to compute the local fields and local field gradients in quadrupolar approximation as well as the dipolar hyperpolarizabilities for the four molecules are computed, including frequency dispersion and vibrational contributions to the dipolar properties. The convergence of the perturbation treatment for the pure vibrational (PV) contributions is examined by comparison of the values obtained at the lowest order with those of partially computed second order in mechanical and electrical anharmonicity. For pNA, for which previous computations of the hyperpolarizabilities have generally found poor agreement with experimental results, a thorough investigation of the effects of solvent-induced geometry changes, dynamic and static correlation, frequency dispersion, and classical thermal averaging over the torsional modes of the substituent groups and the inversion mode of the amino group on the dipolar properties is carried out. Computations using self-consistent continuum reaction field models show that the amino group is substantially less pyramidalized in polar solvents than in the gas phase. With all the effects taken into account, reasonable agreement with the experimental electric-field induced second harmonic generation (EFISH) result on pNA vapor of Kaatz, Donley, and Shelton is obtained.     

Problems in the comparison of theoretical and experimental hyperpolarizabilities revisited

The relationship between nonlinear susceptibilities and hyperpolarizabilities defined using different conventions is reexamined. In previous work [Willetts et al., J. Chem. Phys. 97, 7590 (1992)], relations between different conventions for microscopic hyperpolarizabilities have been derived, but the application of the corresponding conversion factors led to several inconsistencies. It is shown that different conventions for macroscopic susceptibilities have to be taken into account, too, in order to arrive at consistently comparable values. The complete set of conversion factors between several conventions are given for second harmonic generation, electric field induced second harmonic (EFISH) generation, and third harmonic generation. As an illustration, experimental EFISH and hyper-Rayleigh scattering results of p-nitroaniline are compared with each other and with recent results of ab initio computations including solvation effects. Several problems in the comparison of computational and experimental values are also discussed.     

Higher-order response in O(N) by perturbed projection

Perturbed projection for linear scaling solution of the coupled-perturbed self-consistent-field equations [V. Weber, A.M.N. Niklasson, and M. Challacombe, Phys. Rev. Lett. 92, 193002 (2004)] is extended to the computation of higher-order static response properties. Although generally applicable, perturbed projection is further developed here in the context of the self-consistent first and second electric hyperpolarizabilities at the Hartree-Fock level of theory. Nonorthogonal, density-matrix analogs of Wigner's 2n+1 rule valid for linear one-electron perturbations are given up to fourth order. Linear scaling and locality of the higher-order response densities under perturbation by a global electric field are demonstrated for three-dimensional water clusters.     

Ab initio assessment of the first hyperpolarizability of saturated and unsaturated polyaminoborane/polyphosphinoborane copolymers

The linear and nonlinear optical properties of trans-ciso?d saturated and unsaturated polyaminoborane/polyphosphinoborane alternating copolymers are studied at the MP2/6-311G(2d)//PBE0/6-31G(2d) level of approximation, by using the increasingly large oligomer series methodology. We report the evolution with chain length of geometry parameters, partial atomic charges, electric dipole moments, polarizabilities and first hyperpolarizabilities of both phosphorus- and nitrogen-terminated chains. It turns out that for the saturated copolymer, linear and nonlinear optics properties of the saturated copolymer correspond to an average of the response of polyaminoborane and polyphosphinoborane. For the conjugated copolymer, the response is guided by the least delocalizable component.     

Strong electron correlation effects on first- and second-order hyperpolarizabilities in zwitterionic sigma-conjugated systems: its dependence on substituents, conformations, spacer size, and basis sets

Nonlinear optical properties of zwitterionic sigma-conjugated systems were theoretically investigated with relation to the electron correlation effects at the ab initio molecular orbital level. We examined the strong electron correlation effects on the first- and second-order hyperpolarizabilities in the specific systems with effective "pi-sigma-pi" and (or) "pi-sigma-n" interactions. The electron correlation effects on the hyperpolarizabilities strongly depend on the type of substituents, conformations, spacer size, and basis sets. It was found that the Hartree-Fock level calculations qualitatively predict the behavior of the hyperpolarizabilities after considering the correlation effects. Through-space/-bond interaction analysis quantitatively revealed that the electron correlation effects on the hyperpolarizabilities were induced mainly by the sigma-conjugations on the spacer unit in the zwitterionic sigma-systems.     

Statistical mechanically averaged molecular properties of liquid water calculated using the combined coupled cluster/molecular dynamics method

Liquid water is investigated theoretically using combined molecular dynamics (MD) simulations and accurate electronic structure methods. The statistical mechanically averaged molecular properties of liquid water are calculated using the combined coupled cluster/molecular mechanics (CC/MM) method for a large number of configurations generated from MD simulations. The method includes electron correlation effects at the coupled cluster singles and doubles level and the use of a large correlation consistent basis set. A polarizable force field has been used for the molecular dynamics part in both the CC/MM method and in the MD simulation. We describe how the methodology can be optimized with respect to computational costs while maintaining the quality of the results. Using the optimized method we study the energetic properties including the heat of vaporization and electronic excitation energies as well as electric dipole and quadrupole moments, the frequency dependent electric (dipole) polarizability, and electric-field-induced second harmonic generation first and second hyperpolarizabilities. Comparisons with experiments are performed where reliable data are available. Furthermore, we discuss the important issue on how to compare the calculated microscopic nonlocal properties to the experimental macroscopic measurements.     

A molecular design view on the first hyperpolarizability of salicylideneaniline derivatives

Electron correlation effect was incorporated into the two-level framework through configuration interaction (CI) calculation including both occupied and unoccupied frontier orbitals, to evaluate the first hyperpolarizabilities of title compounds. Theoretical results are in excellent agreement with experimental data obtained by the solvatochromic method. Some detailed chemical and electronic information of the electron excitation process related to the nonlinear optical (NLO) properties were produced as well. Based on these data, effects of the character, number and position of donor and acceptor groups on the NLO properties are discussed from the viewpoint of molecular design. Not only the experimental data but also the theoretical analysis have suggested that a large number of intensive and properly located donor and acceptor groups may yield the optimal hyperpolarizabilities. Received: 22 May 1996 / Accepted: 9 December 1996     

The polarizability and the second hyperpolarizability of tetrakis(phenylethynyl)ethene and several of its lithiated derivatives

The polarizability (α) and the second hyperpolarizability (γ) of tetrakis(phenylethynyl)ethene (TPEE) are compared and analyzed in connection with the properties (α, γ) of a series of selected/designed molecules having different conjugation patterns. Several lithiated derivatives of TPEE are designed and shown to have very enhanced second hyperpolarizabilities; for example, one of the lithiated TPEE has a 1.6×10³ times larger second hyperpolarizability than that of benzene. The potential of the proposed derivatives for applications in photonics is noted. The polarizabilities and the hyperpolarizabilities of the considered molecules have been computed employing the PM3 method which has been proven to be adequate for the present comparative study. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 177–187, 1999