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.     

Electronic and vibrational hyperpolarizabilities of alkali- and alkaline-earth-doped boron nitride nanotubes

This work reports the results of the vibrational corrections and frequency dependence to the first hyperpolarizabilities of the alkali- and alkaline-earth-doped boron nitride nanotubes. The electronic contributions were computed by means of the density functional theory with the M06-2X functional, and the vibrational corrections were calculated using the perturbation theoretical method and the field-induced coordinates methodology. The results for the electronic contribution show that such materials exhibit large first hyperpolarizabilities and electride characteristic. We also show that the distribution of the excess electron, which originates from the doping atoms, plays an important role in the large electronic hyperpolarizabilities (β^el). Moreover, our findings strongly indicate that the effect of vibrations on the hyperpolarizabilities can be quite important and can even be much larger than the electronic counterpart.     

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.     

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.     

Dynamic (hyper)polarizabilities of the sulphur dioxide molecule: coupled cluster calculations including vibrational corrections

In this work we report results for dynamical (hyper)polarizabilities of the sulphur dioxide molecule with inclusion of vibrational corrections. The electronic contributions were computed analytically at the single and double coupled cluster level through response theories for the frequencies 0, 0.0239, 0.0428, 0.0656, 0.0720, and 0.0886 hartree. Contributions of the connected triple excitations to the dynamic electronic properties were also estimated through the multiplicative correction scheme. Vibrational corrections were calculated by means of the perturbation theoretical method. The results obtained show that the zero point vibrational correction is very small for all properties studied while the pure vibrational correction is relevant for the dc-Pockels effect, intensity dependent refractive index, and dc-Kerr effect. For these nonlinear optical processes, the pure vibrational corrections represent approximately 75%, 13%, and 6% of the corresponding electronic contributions for the higher frequencies quoted. The results presented for the polarizability are in good agreement with experimental values available in the literature. For the hyperpolarizabilities we have not obtained experimental results with precision sufficient for comparison.     

Frequency-dependent hyperpolarizabilities of the Ne, Ar, and Kr atoms using the approximate coupled cluster triples model CC3

The frequency-dependent electric field-induced second harmonic generation (ESHG) second hyperpolarizabilities gamma of neon, argon, and krypton are calculated using the approximate coupled cluster triples model CC3. Systematic basis set investigations are carried out to establish basis set limits, and scalar relativistic effects are accounted for by direct perturbation theory. To estimate higher-order correlation effects, full configuration-interaction results are used to benchmark the accuracy of CC3. The best theoretical estimates obtained thereby for the static second hyperpolarizabilities gamma(0) are 107.4, 1159, and 2589 a.u. for neon, argon, and krypton, respectively. These values as well as the results for the dispersion curve of the parallel component gamma( parallel) agree well with the latest experimental values from electric field-induced second harmonic generation. In addition, the dispersion of the perpendicular component gamma( perpendicular) and the hyperpolarizability ratios gamma( parallel)gamma( perpendicular) has been studied for the first time on a consistently correlated ab initio level. The analysis of the results indicates that, in particular for neon and krypton, the presently available experimental values are flawed.     

Quantitative molecular thermochemistry based on path integrals

The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal-mode analysis to calculate the vibrational and rotational contributions. We utilize path-integral Monte Carlo for going beyond the harmonic analysis and to calculate the vibrational and rotational contributions to ab initio energies. This is an application and an extension of a method previously developed in our group [J. Chem. Phys. 118, 1596 (2003)].     

Study of the Influence of the Nature and Position of the Halogen Atom in the N-Halogenophenyl-2,5-dimethylpyrrole Upon the Vibrational (Hyper)polarizability: Theoretical Study

The two contributions, vibrational and electronic, to the electrical properties polarizability and first hyperpolarizability of the N-[(2, 3, or 4)-fluorophenyl]-2,5-dimethylpyrrole are evaluated theoretically at the HF/6-31G level within the double harmonic oscillator approximation. The calculations demonstrate that, with the exception of the second harmonic generation, the vibrational contribution to the first hyperpolarizability is important. However, the vibrational polarizability, contributes at most, 10% to the total electric polarizability. The analysis upon the sum-over-states expressions shows that there are only few modes which contribute strongly and, generally, have small vibrational energies. The effect of the fluorine substitution by an other substituent is also addressed.     

Theoretical and experimental study of optical second harmonic generation in new chiral thiolates salts

The second harmonic generation ability of new chiral thiolate salts is investigated. Aromatic thiolate anions ArS⁻ are expected from semi-empirical calculations with PM3 parameterization of the MNDO Hamiltonian to possess higher intrinsic polarizabilities than the parent neutral thiols ArSH.

Salts associating (hyper)polarizable aromatic thiolate anions with chiral cations, which ensure the noncentrosymmetry necessary to have second-order nonlinear optical effects have been synthesized. The first hyperpolarizabilities, β, of the salts are measured using hyper-Rayleigh scattering technique. Second harmonic generation powder tests (Kurtz and Perry method) carried out on various salts studied, were positive indicating that these materials crystallize in noncentrosymmetric space groups.     

Theoretical investigation of the (hyper)polarizabilities of pyrrole homologues C4H4XH (X = N, P, As, Sb, Bi). A coupled-cluster and density functional theory study

Geometries, inversion barriers, static and dynamic electronic and vibrational dipole polarizability (alpha), and first (beta) and second (gamma) hyperpolarizability of the pyrrole homologues C(4)H(4)XH (X = N, P, As, Sb, Bi) have been calculated by Hartree-Fock, M?ller-Plesset second-order perturbation theory, coupled-cluster theory accounting for singles, doubles, and noniterative triple excitations methods, as well as density functional theory using B3LYP and PBE1PBE functionals and Sadlej's Pol and 6-311G basis sets. Relativistic effects on the heavier homologues stibole and bismole have been taken into account within effective core potential approximation. The results show that the electronic (hyper)polarizabilities monotonically increase with the atomic number of the heteroatom, consistent with the decrease in the molecular hardness. Ring planarization reduces the carbon-carbon bond length alternation of the cis-butadienic unit, enhancing the electronic polarizability values (alpha(e)) by 4-12% and the (hyper)polarizability values (and gamma(e)) by 30-90%. Pure vibrational and zero-point vibrational average contributions to the (hyper)polarizabilities have been determined within the clamped nucleus approach. In the static limit, the pure vibrational hyperpolarizabilities have a major contribution. Anharmonic corrections dominate the pure vibrational hyperpolarizabilities of pyrrole, while they are less important for the heavier homologues. Static and dynamic electronic response properties of the pyrrole homologues are comparable to or larger than the corresponding properties of the furan and cyclopentadiene homologue series.     

Harmonic and anharmonic contributions to parity-violating vibrational frequency difference between enantiomers of chiral molecules

A general perturbative procedure for the computation of harmonic and anharmonic contributions to parity-violating vibrational shifts is introduced and applied to PHBrF and AsHBrF. The results point out the importance of both diagonal and off-diagonal anharmonic contributions and indicate that some parity-violating shift of AsHBrF approaches the resolution forecasted for next generation experiments. The proposed approach is sufficiently general and computationally effective to allow studies of similar and larger molecular systems.     

Vibrational contributions to static linear and nonlinear optical coefficients: from two-level to two-band systems

The importance of vibrational contributions to the static linear and nonlinear optical coefficients is investigated. We apply the exact sum-over-state (SOS) formulas for polarizabilities and hyperpolarizabilities expressed in terms of vibronic states to a two-level system with a single vibrational mode. The Herzberg–Teller expansion is applied to the SOS formulas including vibrational energy levels without employing the Placzek’s approximation within both the Born–Oppenheimer approximation and electrical and mechanical harmonicities. The results include not only the vibrational contribution from the lattice relaxation expression but also the contribution arising from the higher-order correction terms. Model calculations on a diatomic system with two electronic states show that the contribution of these correction terms is small. Moreover, most of these higher-order terms are negligible in the solid-state limit. In polyacetylene, the contribution of the lattice relaxation expression is much larger than that in the diatomic case. Within the tight-binding approximation, the contribution of the lattice relaxation expression is 44% of the pure electronic contribution for the second hyperpolarizability.     

Holstein-Peirls-Hubbard trimer as a model for quadrupolar two-photon absorbing dyes

The linear and nonlinear optical properties of a Donor-Acceptor-Donor system have been investigated by using a two-electron three-point-site model system. Some basic features of electron correlations are included in the model by means of a bi-electronic density matrix. The polarizabilities and second hyperpolarizabilities have been computed with a modified version of the Collective Electronic Oscillators (CEO) method which allowed us to include the electron-phonon coupling. Both singly- and doubly-excited states are taken into account in the computation of (hyper-)polarizabilities. The effects of electron-phonon coupling on the two-photon absorption and on the third harmonic generation in the infrared region are discussed.     

Development of calculation and analysis methods for the dynamic first hyperpolarizability based on the ab initio molecular orbital-quantum master equation method

We develop novel calculation and analysis methods for the dynamic first hyperpolarizabilities β [the second-order nonlinear optical (NLO) properties at the molecular level] in the second-harmonic generation based on the quantum master equation method combined with the ab initio molecular orbital (MO) configuration interaction method. As examples, we have evaluated off-resonant dynamic β values of donor (NH(2))- and/or acceptor (NO(2))-substituted benzenes using these methods, which are shown to reproduce those by the conventional summation-over-states method well. The spatial contributions of electrons to the dynamic β of these systems are also analyzed using the dynamic β density and its partition into the MO contributions. The present results demonstrate the advantage of these methods in unraveling the mechanism of dynamic NLO properties and in building the structure-dynamic NLO property relationships of real molecules.     

NLO properties of metallabenzene-based chromophores: a time-dependent density functional study

The static and dynamic first hyperpolarizabilities for a series of substituted metallabenzene-based nonlinear optical (NLO) chromophores were determined by time-dependent density functional theory (TDDFT). The electronic excitation contributions to the first hyperpolarizability are rationalized in terms of the two-level model. The effects on the hyperpolarizabilities of (a) the metal center (Os, Ir, Pt); (b) the ligand environment (PH3, CO, Cl); (c) various donor and acceptor substituents (NH2, OH, Me, H, Cl, Br, I, COOMe, COOH, CN, NO2); and (d) the length of pi-conjugation were studied. Our calculations predict that metallabenzenes have significant second-order NLO susceptibilities, ranging from = 1.0 x 10(-29) to 5.6 x 10(-28) esu and from mu = 3.0 x 10(-47) to 1.1 x 10(-44) esu, that can be tuned by changing the metal center and/or ligand environment.     

On the vibrational linear and nonlinear optical properties of compounds involving noble gas atoms: HXeOXeH,HXeOXeF, and FXeOXeF

The vibrational (hyper)polarizabilities of some selected Xe derivatives are studied in the context of Bishop–Kirtman perturbation theory (BKPT) and numerical finite field methodology. It was found that for this set of rare gas compounds, the static vibrational properties are quite large, in comparison to the corresponding electronic ones, especially those of the second hyperpolarizability. This also holds for the dc‐Pockels β(?ω;ω,0), Kerr γ(?ω;ω,0,0) and electric field second harmonic generation γ (?2ω;ω,ω,0) effects, although the computed nuclear relaxation (nr) vibrational contributions are smaller in magnitude than the static ones. HXeOXeH was used to study the effects of electron correlation, basis set, and geometry. Geometry effects were found to lead to noticeable changes of the vibrational and electronic second hyperpolarizability. A limited study of the effect of Xe insertion to the nr vibrational properties is also reported. Assessment of the results revealed that Xe insertion has a remarkable effect on the nr (hyper)polarizabilities. In terms of the BKPT, this is associated with a remarkable increase of the electrical and mechanical anharmonicity terms. The latter is consistent with the anharmonic character of several vibrational modes reported for rare gas compounds. © 2013 Wiley Periodicals, Inc.