Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell pi-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order M?ller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order M?ller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order M?ller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.     

Electronic and vibrational contributions to first hyperpolarizability of donor-acceptor-substituted azobenzene

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor-acceptor-substituted azobenzene. It is observed that both electronic and vibrational contributions to the electric dipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected density functional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange-correlation potentials amend the drawbacks of their conventional counterparts.     

The static polarizability and first hyperpolarizability of the water trimer anion: ab initio study

This work predicts the extraordinary hyperpolarizability of inorganic clusters: two water trimer anions. The first hyperpolarizabilities of (H2O-)(3) are considerable, beta(0)=1.715 x 10(7) a.u. for configuration A and beta(0)=1.129 x 10(7) a.u. for configuration B at MP2/d-aug-cc-pVDZ+x level. The first hyperpolarizabilities of (H2O-)(3) (configuration A) and related systems [(H2O)(3) and (H2O)(3)F-] are compared at the MP2/d-aug-cc-pVDZ+x level. These results are beta(0)=1.715 x 10(7) a.u. for (H2O-)(3), beta(0)=35 a.u. for (H2O)(3) [the neutral core of (H2O-)(3)], and beta(0)=46 a.u. for (H2O)(3)F-). Comparing the beta(0) values of related systems, we find that the dipole-bound excess electron is the key factor in the extraordinary first hyperpolarizability of (H2O-)(3) species. It will provide a future in the development of some materials with the excess electron (e.g., electrides) that exhibit large nonlinear optical response.     

Coupled Hartree-Fock calculations of the electric dipole polarizability and first hyperpolarizability of some “inorganic benzenes”

Extended basis sets of gaussian functions were used to calculate near Hartree-Fock estimates of the electric dipole polarizabilities, , and first hyperpolarizabilities, β, of the “inorganic benzenes” B₃N₃H₆, B₃O₃H₃, B₃P₃H₃ and Al₃N₃H₆. Assuming that electron delocalization is responsible for the enhanced polarizabilities of aromatic systems, an aromaticity scale can be set up according to the trend of theoretical polarizabilities obtained in this work, i.e. (B₃O₃H₃) < (B₃N₃H₆ ) < (C₆H₆ ), which is consistent with previous calculations of the degree of delocalization in these compounds.     

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 .     

Electric dipole,polarizability and structure of cesium chloride clusters with one-excess electron

The measurement of the electric dipole of gas phase one-excess electron Cs_nCl_n−1 clusters is reported together with a theoretical ab initio prediction of stable structures, dipole moments and electronic polarizabilities for these species in their ground state. Results are in agreement with NaCl cubic structures.     

Three-body contributions to the dipole polarizability of He3 clusters

Quantum-mechanical calculations of three-body contributions to the dipole polarizability in linear and triangular He₃ clusters are presented. Account is taken of electron correlation. For short distances, three-body terms can be large, dependent upon geometry, although for distances greater than the van der Waals minimum these three-body terms are small, their effect may still be of importance for dense fluids because of the number ratio of three- to two-body terms.     

Quantum chemical calculation of the structure,dipole moment,and polarizability of O-isopropyl methylphosphonofluoridate in the gas phase

Six conformers of O-isopropyl methylphosphonofluoridate (IMPF) are revealed. Their geometric parameters, dipole moments, and polarizabilities are calculated. The applicability of methods chosen for the phosphoryl compounds not distinguished by conformational diversity is evaluated for the calculation of the structure and mentioned properties of IMPF conformer. The features of the IMPF structure and stereochemistry are considered.     

Synchrotron radiation study of chloromethane clusters: effects of polarizability and dipole moment on core level chemical shifts

Free neutral chloromethane clusters have been produced by adiabatic expansion and investigated by means of photoelectron spectroscopy. By studying the differences between the cluster binding energy shifts at the Cl 2p and C 1s thresholds we have shown that antiparallel packing is the dominant local structure of the clusters. This geometry is induced by the polar character of the constituent molecules, and it accords with the structures of chloromethane solids and dimers. Furthermore, results obtained from the analysis of the outer valence levels of the clusters support the suggested local structure. The roles of the polarizability and of the dipole moment of the constituent molecules in the cluster binding energy shifts are discussed in comparison with a recent investigation of bromomethane clusters.     

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.     

The dipole moment, polarizabilities, and first hyperpolarizabilities of HArF. A computational and comparative study

The electronic and vibrational contributions to the dipole moment, polarizabilities, and first hyperpolarizabilities of HArF are reported. These have been computed by using a series of systematically built basis sets and a hierarchy of computational methods. HArF has a very large first hyperpolarizability along the z axis. This has been rationalized by invoking the difference in the electronic structure between the ground and the first excited state. The argon fluorohydride has been recently derived and characterized. The present study provides complementary data for the understanding of the electronic structure of this interesting argon derivative.     

Geometry optimizations with explicit inclusion of electron correlation

Automatic techniques for geometry optimization are applied in conjunction with configuration interaction and perturbation treatments of electron correlation. The computational effort and numerical accuracy of the optimizations are discussed, as well as problems with approximate correlation methods concerning the continuity of the potential surface. The optimized geometries of fourteen molecules obtained with different correlation treatments (MNDO SCF MOs) are compared. The configuration interaction results are reproduced satisfactorily by simple perturbation approaches. The largest change of the optimized SCF geometry is found for hydrogen peroxide.     

Lithium salt electride with an excess electron pair--a class of nonlinear optical molecules for extraordinary first hyperpolarizability

A new lithium salt electride with an excess electron pair is designed, for the first time, by means of doping two sodium atoms into the lithium salt of pyridazine. For this series of electride molecules, the structures with all real frequencies and the static first hyperpolarizability (beta 0) are obtained at the second-order M?ller-Plesset theory (MP2). Pyridazine H 4C 4N 2 becomes the lithium salt of pyridazine Li-H 3C 4N 2 as one H atom is substituted by Li. The lithium salt effect on hyperpolarizability is observed as the beta 0 value is increased by about 170 times from 5 to 859 au. For the electride effect, an electride H 4C 4N 2...Na 2 formed by doping two Na atoms into pyridazine, the beta 0 value is increased by about 3000 times from 5 to 1.5 x 10 (4) au. Furthermore, combining these two effects, that is, lithium salt effect and electride effect, more significant increase in beta 0 is expected. A new lithium salt electride Li-H 3C 4N 2...Na 2 is thus designed by doping two Na atoms into Li-H 3C 4N 2. It is found that the new lithium salt electride, Li-H 3C 4N 2...Na 2, has a very large beta 0 value (1.412 x 10 (6) au). The beta 0 value is 2.8 x 10 (5) times larger than that of H 4C 4N 2, 1644 times larger than that of Li-H 3C 4N 2, and still 93 times larger than that of the electride H 4C 4N 2...Na 2. This extraordinary beta 0 value is a new record and comes from its small transition energy and large difference in the dipole moments between the ground state and the excited state. The frequency-dependent beta is also obtained, and it shows almost the same trends as H 4C 4N 2 < Li-H 3C 4N 2 < H 4C 4N 2...Na 2 < Li-H 3C 4N 2...Na 2. This work proposes a new idea to design potential candidate molecules with high-performance NLO properties.     

Hartree-Fock-Roothaan wave functions,electron density distribution,diamagnetic susceptibility,dipole polarizability and antishielding factor for ions in crystals

Using the Hartree-Fock method the wave functions of Li⁺, Be²⁺, O^2–, F^–, Na⁺, Mg²⁺, Al³⁺, S^2–, Cl^–, K⁺, Ca²⁺, Sc³⁺ and Ti⁴⁺ have been calculated for the free ion and the ion in a potential well. The main result of these calculations is a contraction of the anion and an expansion of the cation due to the external potential. A comparison of the calculations with an experimental determination of the electron density distribution in NaCl and MgO shows qualitative agreement. The diamagnetic susceptibility , the dipole polarizability _d, and the Sternheimer antishielding factor of the ions given above were also calculated for the free ions and the spherical potential ions (SPI). The charged hollow sphere model improves the theoretical values towards the properties determined by experiment.

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Zusammenfassung Unter Verwendung der Hartree-Fock-Methode wurden analytische Wellenfunktionen für die Ionen Li⁺, Be²⁺, O^2–, F^–, Na⁺, Mg²⁺, Al³⁺, S^2–, Cl^–, K⁺, Ca²⁺, Sc³⁺ und Ti⁴⁺ berechnet. Es wurden sowohl die freien Ionen als auch Ionen im Potentialtopf untersucht. Es zeigt sich eine durch das äußere Potential hervorgerufene Kontraktion der Anionen und eine Expansion der Kationen. Der Vergleich der Rechnungen mit experimentellen Bestimmungen der Elektronendichteverteilung in NaCl und MgO zeigt qualitative Übereinstimmung zwischen Theorie und Experiment. Ferner wurden die diamagnetische Suszeptibilität , die Dipolpolarisierbarkeit _d und der Antishieldingfaktor (Sternheimerfaktor) sowohl für die freien als auch für die durch ein kugelsymmetrisches Potential gestörten Ionen berechnet. Das hier benutzte Festkörpermodell der geladenen Hohlkugel ergibt Werte, die in guter Übereinstimmung mit dem Experiment sind.

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Résumé Les fonctions d'onde de Li⁺, Be²⁺, O^2–, F^–, Na⁺, Mg²⁺, Al³⁺, S^2–, Cl^–, K⁺, Ca²⁺, Sc³⁺ et Ti⁴⁺ ont été calculées par la méthode de Hartree-Fock pour l'ion libre et pour l'ion dans un puit de potentiel. Le résultat essentiel de ces calculs montre une contraction de l'anion et une expansion du cation sous l'effet du potentiel extérieur. Les densités électroniques calculées et celles obtenues expérimentalement dans NaCl et MgO sont en accord qualitatif. La susceptibilité diamagnétique , la polarisabilité dipolaire _d, et le facteur anti-écran de Sterneimer des ions ci-dessus ont été calculés pour les ions libres et pour les ions à «potentiel sphérique» (SPI). Le modèle de la sphère creuse chargée améliore les valeurs théoriques par rapport aux données expérimentales.

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D 17 (E. Paschalis, 1967).     

Choice of quantum chemical methods and the calculation of the structure,dipole moment,and polarizability of phosphoryl compounds in the gas phase

Journal of Structural Chemistry - Molecules of phosphoryl compounds (H3PO, HF2PO, F3PO, Cl3PO, CH3POF2, CH3POCl2, and (CH3)3PO) are calculated at the Hartree-Fock, density functional theory with...     

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.     

On the calculation of dipole moment and polarizability derivatives by the analytical energy gradient method: Application to the formaldehyde molecule

Following the suggestion of Komornicki and McIver we have implemented an efficient computational scheme for the evaluation of dipole moment and polarizability derivatives at the Hartree-Fock SCF level. The derivatives are obtained by utilizing the analytical gradients of the molecular energy, calculated in the presence of an external electric field, with respect to the atomic cartesian coordinates, which are differentiated numerically with respect to the field. The implementation of the method within the framework of the MOLECULE program is discussed, concentrating on such aspects as numerical accuracy, utilization of molecular symmetry and computational efficiency. As an application, the dipole moment and polarizability derivatives of the formaldehyde molecule have been calculated, yielding infrared intensities and Raman scattering activities in the double harmonic approximation. The theoretical results are compared with the available experimental data; the agreement is satisfactory given the inherent restrictions of the SCF model.