Static polarizability and second hyperpolarizability of closed- and open-shell pi-conjugated polymers

The static longitudinal linear polarizability (alpha) and second order hyperpolarizability (gamma) for neutral and charged, closed- and open-shell trans-polyacetylene (PA) chains C(2n)H(2n+2), C(2n-1)H(2n+1), C(2n-1)H(2n+1) (+), C(2n)H(2n+2) (+), and C(2n)H(2n+2) (2+) are systematically investigated and compared. The polarizabilities are calculated within the Pariser-Parr-Pople model, and the electron correlation effect is included through density matrix renormalization group. It turns out that for both alpha, and gamma, two neutral PA chains C(2n)H(2n+2) and C(2n-1)H(2n+1) give similar values, while both singly charged and doubly charged systems present significantly larger magnitude of alpha and gamma values than the two neutral chains. The two singly charged PA chains C(2n-1)H(2n+1) (+) and C(2n)H(2n+2) (+) give more apparent nonlinear optical responses than doubly charged case C(2n)H(2n+2) (2+) and both present negative second order hyperpolarizabilities for short to medium sized oligomers. The sign inversion of gamma values in singly charged PA molecules is anticipated to take place at the much longer length than ever observed due to the significant effects of electron correlation and geometry.     

Frequency-dependent polarizability of open-shell atomic systems

The time-dependent variational principle is used to calculate the frequency-dependent dipole polarizabilities of 2p open-shell atomic systems. A general theory is built up to include frequency-dependent perturbations using the Roothaan–Hartree–Fock (HFR) formalism. The excitation energies corresponding to the low-lying excited states of the system are obtained from the poles of the dynamic polarizability values. A fairly accurate knowledge of transition oscillator strengths is also obtained from a knowledge of the polarizability values near the poles. The excitation energies and oscillator strengths are compared with available data.     

Geometry, dipole moment, polarizability and first hyperpolarizability of polymethineimine: an assessment of electron correlation contributions

We have investigated the geometries as well as the longitudinal dipole moment (micro), polarizability (alpha), and first hyperpolarizability (beta) of polymethineimine oligomers using different approaches [Hartree-Fock (HF), second-order M?ller-Plesset (MP2), and hybrid density functional theory (DFT) methods (B3LYP and PBE0)] for evaluating the geometries and the nonlinear optical properties. It turns out that (i) HF and the selected DFT methods provide the incorrect sign for beta of short and medium size oligomers. (ii) The B3LYP and PBE0 electron correlation correction are too small for micro, too large for alpha, and for some oligomer lengths, they are in the wrong direction for beta. (iii) On the contrary to polyacetylene, the hybrid-DFT geometries are in poor agreement with MP2 geometries; the former showing much smaller bond length alternations.     

Evaluation of alternative sum-over-states expressions for the first hyperpolarizability of push-pull pi-conjugated systems

A dipolar-free sum-over-states expression for the diagonal components of the first hyperpolarizability (beta) tensor has been proposed by Kuzyk [Phys. Rev. A 72, 053819 (2005)] as an alternative to the traditional expression. We examine both alternatives for the longitudinal beta of four typical push-pull pi-conjugated systems using the ab initio CIS and CIS(D) schemes to approximate the excited state properties. Since they are each evaluated approximately the two SOS expressions yield different values for beta and it is found that (i) they evolve symmetrically as the number of excited states is increased so that their average is nearly constant; (ii) in the static limit, the two values agree better with one another when their average is close to the "exact" correlated result; and (iii) frequency dispersion can affect the agreement between the alternative expressions. On the basis of (i) and (ii) it appears best for typical push-pull pi-conjugated systems to estimate the static beta, and the error in the value so obtained, by averaging the Kuzyk and traditional results.     

Electron correlation and structure dependencies of the second hyperpolarizability of ethylene

We investigated an interesting behavior in electron correlation and structure dependencies of the second hyperpolarizability (γ) of the ethylene model. The γ values of the ethylene model with plain and twisted structures were examined using various ab initio MO methods. γ was found to be largely changed depending on the rotation angle of the CH₂ group in ethylene. The rotation‐angle dependence of γ is remarkably different among Hartree–Fock and higher‐order electron‐correlation results. By applying hyperpolarizability density analysis, it was found that there are negative and positive contributions to γ and that, especially, σ electrons play an important role to determine the rotation‐angle dependence of γ at high‐order electron correlation levels. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 177–183, 1999     

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

Using three typical pi-conjugated molecules (1,3,5-hexatriene, 1-formyl-6-hydroxyhexa-1,3,5- triene, and 1,1-diamino-6,6-dinitrohexa-1,3,5-triene) we investigate the level of ab initio theory necessary to produce reliable values for linear and nonlinear optical properties, with emphasis on the vibrational contributions that are known to be important or potentially important. These calculations are made feasible by employing field-induced coordinates in combination with a finite field procedure. For many, but not all, purposes the MP2/6-31+G(d) level is adequate. Based on our results the convergence of the usual perturbation treatment for vibrational anharmonicity was examined. Although this treatment is initially convergent in most circumstances, a problematic situation has been identified.     

Quadrupole polarizability and hyperpolarizability of carbon monoxide

Summary We report a study of the electric dipole-quadrupole (A _,,), quadrupole-quadrupole (C _,,), dipole-octopole (E _,) polarizability and the dipole-dipole-quadrupole (B _,,) hyperpolarizability of carbon monoxide. All values are obtained from finite-field self-consistent field (SCF) and fourth-order manybody perturbation theory (MP4) calculations. Our best values for the dipole-octopole polarizability areE _z,zzz=60.19 andE _x,xxx=–38.06e ² a ₀ ⁴ E _h ^–1 . For the dipole-dipole-quadrupole hyperpolarizability we reportB _zz,zz=–296,B _xz,xz=–170,B _xx,zz=88 andB _xx,xx=–178e ³ a ₀ ⁴ E _h ^–2 .     

Density functional theory investigation of the polarizability and second hyperpolarizability of polydiacetylene and polybutatriene chains: treatment of exact exchange and role of correlation

The static polarizability and second hyperpolarizability of increasingly large polydiacetylene and polybutatriene (PBT) chains have been evaluated using the optimized effective potential for exact exchange (OEP-EXX) method developed by Yang and Wu [Phys. Rev. Lett. 89, 143002 (2002)], where the unknown part of the effective potential is expressed as a linear combination of Gaussian functions. Various conventional atomic orbital basis sets were employed for the exchange potential (X basis) as well as for the Kohn-Sham orbitals [molecular orbital (MO) basis]. Our results were compared to coupled-perturbed Hartree-Fock (CPHF) calculations and to ab initio correlated values obtained at various levels of approximation. It turns out that (a) small conventional basis sets are, in general, unsatisfactory for the X basis; (b) the performance of a given X basis depends on the MO basis and is generally improved when using a larger MO basis; (c) these effects are exaggerated for the second hyperpolarizability compared to the polarizability; (d) except for the second hyperpolarizability of PBT chains, using 6-311++G** for the X basis gives reasonable agreement with the CPHF results for all MO basis sets; (e) our results suggest that in the limit of a complete X basis the OEP-EXX values may approach the CPHF data; and (f) in general, the quality of a given conventional X basis degrades with the length of the oligomer, which correlates with the fact that the number of X basis functions becomes a smaller fraction of the number required to reproduce exactly the finite-basis-set Hartree-Fock energies. Linear and especially nonlinear electric field responses constitute a very stringent test for assessing the quality of functionals and potentials; appropriately tailored basis sets are needed to describe the latter. Finally, this study further highlights the importance of electron correlation effects on linear and nonlinear responses, for which correlated functionals with OEP are required.     

Basis set and correlation effects on geometry of octahedral second-row transition-metal complexes

An extensive investigation of the basis-set effect on the predicted geometry of the redox pair [Ru(NH₃)₆]^2+/3+ is presented. Basis sets where the core electrons have been replaced with a relativistic core potential as well as all-electron basis sets were tested. Best agreement with observations was obtained with the all-electron basis set MIDI augmented with a set of f-type polarization functions on the metal center. Other properties such as the vibration spectrum, the relative energy of the high-spin and low-spin states, and geometry changes upon oxidation/reduction of the central metal are discussed. The importance of electron correlation on the predicted geometry was estimated at the MP2, MP3, MP4(SDQ), CCSD, and CCSD(T) levels of theory. The MIDI(f) basis set is then used for other octahedral second-row transition-metal complexes and some other related complexes. The electronic spectrum of [Ru(NH₃)₆]²⁺ is also calculated using two different CI computational schemes. Surprisingly good agreement between the predicted electronic spectrum and the observed spectrum are obtained using one of the CI computational schemes. © 1996 John Wiley & Sons, Inc.     

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     

Basis set and correlation effects on computed proton affinities of some oxygen and nitrogen bases

Basis set expansion and correlation effects on the computed proton affinities of the oxygen and nitrogen bases CH₃OH, H₂CO, CO, CH₃NH₂, CH₂NH, and HCN have been evaluated. Basis set enhancements lead to systematic changes in computed proton affinities. These effects appear to be additive, and are greater for correlated proton affinities than for Hartree-Fock energies. Inclusion of correlation decreases proton affinities, with fourth-order Møller-Plesset energies bracketed by second and third order energies.     

(Hyper)polarizability density analysis for open-shell molecular systems based on natural orbitals and occupation numbers

We have developed a method for analyzing the (hyper)polarizabilities of open-shell molecular systems. This method employs the (hyper)polarizability densities based on the natural orbitals and occupation numbers, which enables us to analyze the contributions of odd electrons having various open-shell (diradical) characters. Within broken-symmetry, i.e., spin-unrestricted, single-determinant molecular orbital and density functional theory approaches, we can also remove the spin contamination effects on these quantities through spin projection. To do that, an approximate spin projected method has been elaborated and applied to the analysis of the (hyper)polarizability of multi-radical systems. As examples, typical open-shell singlet systems, 1,3-dipoles and rectangular graphene nanoflakes, are examined.     

Quantum master equation approach to the second hyperpolarizability of nanostar dendritic systems

We investigate the dynamic second hyperpolarizability (gamma) of nanostar dendritic systems using the quantum master equation approach. In the nanostar dendritic systems composed of three-state monomers, the multistep exciton states are obtained by the dipole-dipole interactions, and the directional energy transport, i.e., exciton migration, from the periphery to the core is predicted to occur by the relaxation between exciton states originating in the exciton-phonon coupling. The effects of the intermolcecular interaction and the exciton migration, i.e., exciton relaxation, on the gamma in the third-harmonic generation (THG) are examined in the three-photon off- and on- resonance regions using the two-exciton model. Furthermore, the method for analysis of spatial contributions of excitons to gamma is presented by partitioning the total gamma into the one- and two-exciton contributions. It turns out that the exciton relaxation between exciton states causes significant broadening of the spectra of gamma and their mutual overlap as well as the relative increase of two-exciton contributions in the nanostar dendritic system.     

Basis set superposition effects on properties of interacting systems. Dipole moments and polarizabilities

Basis set superposition effects which are not removed by the counterpoise correction are shown to modify the electric properties of interacting subsystems and influence indirectly the calculated interaction energies. The role of these higher-order basis set superposition effects is illustrated by the calculation of the water molecule dipole moment and polarizability in the basis set of the water dimer.     

Cooperativity and electron correlation effects on hydrogen bonding in infinite systems

Structural and electronic properties of hydrogen-bonded infinite chains of hydrogen cyanide and formamide molecules have been investigated by the ab initio crystal orbital method using several, partly highly polarized, atomic basis sets of increasing size at the Hartree–Fock (HF ) level and by including electron correlation effects in the second order of Møller–Plesset perturbation theory. The results obtained show that hydrogen bonding in molecular crystals of the type investigated is a highly cooperative phenomenon, both from the structural and energetic points of view. Comparison with clusters of up to four monomers demonstrate how various structural parameters converge toward their limiting values in the infinite system. The results obtained for infinite HCN chains show an excellent agreement with those observed for solid HCN, whereas the infinite formamide chain proves to be a reasonable model for the corresponding liquid phase. © 1994 John Wiley & Sons, Inc.     

Basis set and correlation effects on computed lithium ion affinities of some oxygen and nitrogen bases

Basis set expansion and correlation effects on computed lithium cation affinities have been evaluated for the oxygen and nitrogen bases CH₃OH, H₂CO, CO, CH₃NH₂, CH₂NH, and HCN. The presence of diffuse functions on nonhydrogen atoms is found to be the most important single enhancement of double- and triple-split valence plus polarization basis sets. With the triple-split basis, enhancement effects are nearly additive. Correlation usually decreases computed lithium ion affinities, with the second order Møller-Plesset correlation term being the dominant term.     

Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules

In the presence of a static, nonhomogeneous magnetic field, represented by the axial vector at the origin of the coordinate system and by the polar vector , assumed to be spatially uniform, the chiral molecules investigated in this paper carry an orbital electronic anapole, described by the polar vector . The electronic interaction energy of these molecules in nonordered media is a cross term, coupling and via , one third of the trace of the anapole magnetizability a_αβ tensor, that is, . Both and W^BC have opposite sign in the two enantiomeric forms, a fact quite remarkable from the conceptual point of view. The magnitude of predicted in the present computational investigation for five chiral molecules is very small and significantly biased by electron correlation contributions, estimated at the density functional level via three different functionals. © 2016 Wiley Periodicals, Inc.