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.     

Gaussian induced dipole polarization model

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.     

Coupled-cluster calculation of dispersion contributions to interaction energies and polarizabilities

 The induced dipole dispersion-type contributions to the two-body and nonadditive three-body energies and electric dipole polarizabilities are studied for long-range interactions involving the He, Ne, Ar and Kr atoms and the H₂ and N₂ molecules. The coupled-cluster singles and doubles model and large basis sets are used. Comparison of the energy contributions with data derived from experiment shows in most cases the deviations to be less than 1%; therefore, it may be expected that the calculated polarizability increments are accurately determined and can be used to estimate the accuracy of approximate methods. Received: 20 March 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001     

Internal rotation in squaramide and related compounds. A theoretical ab initio study

The structural and energetic changes associated with C–N bond rotation in a squaric acid derivative as well as in formamide, 3-aminoacrolein and vinylamine have been studied theoretically using ab initio molecular orbital methods. Geometry optimizations at the MP2(full)/6-31+G* level confirmed an increase in the C–N bond length and a smaller decrease in the C=O length on going from the equilibrium geometry to the twisted transition state. Other geometrical changes are also discussed. Energies calculated at the QCISD(T)/6-311+G** level, including zero-point-energy correction, show barrier heights decreasing in the order formamide, squaric acid derivative, 3-aminoacrolein and vinylamine. The origin of the barriers were examined using the atoms-in-molecules approach of Bader and the natural bond orbital population analysis. The calculations agree with Pauling's resonance model, and the main contributing factor of the barrier is assigned to the loss of conjugation on rotating the C–N bond. Finally, molecular interaction potential calculations were used to study the changes in the nucleophilicity of N and O (carbonyl) atoms upon C–N rotation, and to obtain a picture of the abilities of the molecules to act in nonbonded interactions, in particular hydrogen bonds. The molecular interaction potential results confirm the suitability of squaramide units for acting as binding units in host–guest chemistry. Received: 13 March 2002 / Accepted: 23 June 2002 / Published online: 21 August 2002     

Linear and non-linear optical properties of some donor–acceptor oxadiazoles by ab initio Hartree-Fock calculations

The molecular hyperpolarizability of some donor–acceptor oxadiazoles was investigated using ab initio methods. Ab initio optimizations were performed at the Hartree-Fock level using different basis sets, starting with the minimal basis set, and then split valence sets. The first hyperpolarizabilities were calculated at the Hartree-Fock level employing the corresponding basis sets using Gaussian 98W. In general, the first hyperpolarizability is dependent on the choice of method and basis set. In order to understand this phenomenon in the context of molecular orbital picture, we examined the molecular HOMOs and molecular LUMOs generated via HF/6-31G level. It has also been calculated the polarizability, anisotropy of polarizability and ground state dipole moment of all the molecules. Several of these oxadiazoles display significant second-order molecular nonlinearity, β(8.57–195.05 × 10⁻³⁰ esu) and provide the basis for future design of efficient nonlinear optical materials having the oxadiazole core.     

Improved generator coordinate Hartree–Fock method for molecular systems: application to H2, Li2 and LiH

The improved generator coordinate Hartree–Fock (GCHF) method is extended to molecular systems. The Griffin–Hill–Wheeler–HF equations were solved by an integral discretization technique. The method is then implemented with the use of the GAMESS program and applied to the H₂, Li₂, and LiH molecules. For these molecules, sequences of basis sets of atom-centred Gaussian-type functions are employed to explore the accuracy achieved with our approach. For all systems studied, our ground-state HF total energies are better than those obtained with basis sets generated with the original GCHF method for molecules and larger even-tempered basis sets. For H₂, Li₂, and LiH, the differences between our best energies and the corresponding numerical HF results are about 2 × 10⁻², 1, and 4 × 10⁻¹ μhartree, respectively. The dipole, quadrupole, and octupole moments at the center of mass and electric field, the electric field gradient, the electrostatic potential, and the electron density at the nuclei were evaluated and compared with results reported in the literature. Received: 4 May 1999 / Accepted: 22 July 1999 / Published online: 2 November 1999     

Accuracy assessment of semiempirical molecular electrostatic potential of proteins

 Accurate electrostatic maps of proteins are of great importance in research of protein interaction with ligands, solvent media, drugs, and other biomolecules. The large size of real-life proteins imposes severe limitations on computational methods one can use for obtaining the electrostatic map. Well-known accurate second-order M?ller–Plesset and density functional theory methods are not routinely applicable to systems larger than several hundred atoms. Conventional semiempirical tools, as less resource demanding ones, could be an attractive solution but they do not yield sufficiently accurate calculation results with reference to protein systems, as our analysis demonstrates. The present work performs a thorough analysis of the accuracy issues of the modified neglect of differential overlap type semiempirical Hamiltonians AM1 and PM3 on example of the calculation of the molecular electrostatic potential and the dipole moment of natural amino acids. Real capabilities and limitations of these methods with application to protein modeling are discussed. Received: 26 April 2002 / Accepted: 19 September 2002 / Published online: 14 February 2003     

Dipole–reaction field interaction model for the solvent reorganization energy and its application to the benzoquinone–benzoquinone anion radical system

 Based on the spherical cavity approximation and the Onsager model, a dipole–reaction field interaction model has been proposed to elucidate the solvent reorganization energy of electron transfer (ET). This treatment only needs the cavity radius and the solute dipole moment in the evaluation of the solvent reorganization energy, and fits spherelike systems well. As an application, the ET reaction between p-benzoquinone and its anion radical has been investigated. The inner reorganization energy has been calculated at the level of MP2/6–31+G, and the solvent reorganization energies of different conformations have been evaluated by using the self-consistent reaction field approach at the HF/6–31+G level. Discussions have been made on the cavity radii and the values are found to be reasonable when compared with the experimental ones of some analogous intramolecular ET reactions. The ET matrix element has been determined on the basis of the two-state model. The fact that the value of the ET matrix element is about 10 times larger than RT indicates that this ET reaction can be treated as an adiabatic one. By invoking the classical Marcus ET model, a value of 4.9 × 10⁷M⁻¹s⁻¹ was obtained for the second-order rate constant, and it agrees quite well with the experimental one. Received: 19 October 2001 / Accepted: 17 January 2002 / Published online: 3 May 2002     

Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.     

The effect of basis set superposition error on the convergence of interaction energies

 For the intermolecular interaction energies of ion-water clusters [OH⁻(H₂O) _n (n=1,2), F⁻(H₂O), Cl⁻(H₂O), H₃O⁺(H₂O) _n (n=1,2), and NH₄ ⁺(H₂O) _n (n=1,2)] calculated with correlation-consistent basis sets at MP2, MP4, QCISD(T), and CCSD(T) levels, the basis set superposition error is nearly zero in the complete basis set (CBS) limit. That is, the counterpoise-uncorrected intermolecular interaction energies are nearly equal to the counterpoise-corrected intermolecular interaction energies in the CBS limit. When the basis set is smaller, the counterpoise-uncorrected intermolecular interaction energies are more reliable than the counterpoise-corrected intermolecular interaction energies. The counterpoise-uncorrected intermolecular interaction energies evaluated using the MP2/aug-cc-pVDZ level is reliable. Received: 14 March 2001 / Accepted: 25 April 2001 / Published online: 9 August 2001     

Role of twisting and sliding on the solvation of a stacked cytosine dimer: an ab initio study

Ab initio calculations with inclusion of correlation effects at the MP2/6-31G* level have been used to predict the interaction energy of stacked cytosine dimer (C/C) as a function of twisting and sliding in the gas phase. Systematic calculations have also been carried out on the solvation free energies of various rotated and translated C/C dimers using a polarized continuum model approach at the HF/6-31G* level with a view to probe the role of various degrees of freedom on the free energy of solvation of the C/C dimer. The interaction energy of the C/C dimer decreases upon changing from a parallel to an antiparallel conformation in the gas phase. The 180°-rotated conformation has been found to be the most stable arrangement when compared to other rotated positions. The rotated and translated dimers exhibit lower solvation free energy than the parallel conformation. The decrease in the dipole moment upon rotation from the parallel to the antiparallel conformation indicates the cancellation of charge distribution upon rotation in the z direction of one cytosine base with respect to the other. The calculation reveals that the present approach could not yield association energy, ΔΔG _Asso, in a solvent medium. This may be due to the fact that in the case of floppy molecules the contribution from translational, rotational and vibrational free energies plays a significant role in the calculation of ΔΔG _Asso. Received: 13 December 2001 / Accepted: 25 March 2002 / Published online: 13 June 2002     

A sum-over-state scheme of analysis of hyperpolarizabilities and its application to spiroconjugated molecular system

The static first and second hyperpolarizabilities of a number of spiromolecules with varying degree of polarity have been calculated at the HF and MP2 level using the 6-31+G* basis set and the B3LYP/6-31+G* optimized geometry. The variation of mean second hyperpolarizability in these molecular systems has been explained in terms of the ground state dipole moment, mean linear polarizability and second-order polarizability. A number of relationships among these quantities have been derived in the framework of the sum-over-state scheme and the generalized Thomas–Kuhn sum rule. The spiroconjugation results in the significant increase of the mean polarizability. The appreciable enhancement of first hyperpolarizability due to the spiroconjugation between two dipolar monomer units has been accounted for the rather significant increase of the mean polarizability tensor and the ground state dipole moment. The relatively larger value of the average second hyperpolarizability of the spiroconjugated molecules compared to that of the corresponding monomers arises from the rather significant increase of the nonaxial component γ _xxyy . The replacement of spirocarbon by spirosilicon results in the enhancement of the cubic polarizability manifold. The donor–acceptor substituted spirocompounds are predicted to be the superior third-order nonlinear optical (NLO) phores. The nature of π-conjugation in the monomer units around the spirocenter shows a strong modulation of the NLO properties of spirocompounds. The influence of electron correlation on the NLO properties at the MP2 level has been found to be rather significant.     

Space partitioning and the effects of molecular proximity on electrostatic moments of the crystalline formamide molecule

Application of two different spatial partitioning techniques to determine the dipole moment of the formamide molecule in the crystal indicates approximate cancellation of the effects of molecular truncation introduced by space partitioning and intermolecular interactions, leading to a solid state dipole moment which is in reasonable agreement with the gas phase value.     

BSSE‐corrected geometry and harmonic and anharmonic vibrational frequencies of formamide–water and formamide–formamide dimers

The basis set superposition error (BSSE) influence in the geometry structure, interaction energies, and intermolecular harmonic and anharmonic vibrational frequencies of cyclic formamide–formamide and formamide–water dimers have been studied using different basis sets (6‐31G, 6‐31G**, 6‐31++G**, D95V, D95V**, and D95V++**). The a posteriori “counterpoise” (CP) correction scheme has been compared with the a priori “chemical Hamiltonian approach” (CHA) both at the Hartree–Fock (HF) and second‐order Møller–Plesset many‐body perturbation (MP2) levels of theory. The effect of BSSE on geometrical parameters, interaction energies, and intermolecular harmonic vibrational frequencies are discussed and compared with the existing experimental data. As expected, the BSSE‐free CP and CHA interaction energies usually show less deep minima than those obtained from the uncorrected methods at both the HF and MP2 levels. Focusing on the correlated level, the amount of BSSE in the intermolecular interaction energies is much larger than that at the HF level, and this effect is also conserved in the values of the force constants and harmonic vibrational frequencies. All these results clearly indicate the importance of the proper BSSE‐free correlation treatment with the well‐defined basis functions. At the same time, the results show a good agreement between the a priori CHA and a posteriori CP correction scheme; this agreement is remarkable in the case of large and well‐balanced basis sets. The anharmonic frequency correction values also show an important BSSE dependence, especially for hydrogen bond stretching and for low frequencies belonging to the intermolecular normal modes. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Influence of diffuse and polarization functions on the second-order Møller–Plesset optimized dihedral angle of biphenyl

 Using 6-31G and 6-311G basis sets to which diffuse and polarization functions were added in a stepwise fashion (a total of 16 basis sets), Hartree–Fock (HF), MP2 and B3LYP geometry optimizations were performed on biphenyl. With the MP2 method, diffuse functions raise the dihedral angle φ, for example, from 46.3° for 6-31G to 54.1° for 6-311++G, while polarization functions lower it, for example, from 54.1° for 6-311++G to 42.1° for 6-311++G(2d,2p). For a single set of polarization functions, φ(MP2) lies close to or above φ(HF) (44–47°), but for a double set it is below φ(HF) and is close to B3LYP values (38–42°) which show little basis set dependence. The most reliable value for φ, 42.1° [MP2/6-311++G(2d,2p)], is expected to increase slightly by adding more diffuse functions. The corresponding best calculated energy barrier at 0° (coplanar conformation) is 2.83 kcal/mol, much higher than the experimental estimate (1.4 ± 0.5 kcal/mol). The barrier at 90° is 1.82 kcal/mol, in line with the experimental estimate (1.6 ± 0.5 kcal/mol) and with previous theoretical results. Received: 9 September 2002 / Accepted: 15 November 2002 / Published online: 1 April 2003 Correspondence to: Friedrich Grein e-mail: fritz@unb.ca Acknowledgement. The author would like to thank NSERC (Canada) for financial support.     

The fundamental nature and role of the electrostatic potential in atoms and molecules

 A variety of atomic and molecular properties can be expressed in terms of the electrostatic potential. These include energies, covalent and anionic radii, electronegativities (chemical potentials) and a variety of properties that depend upon noncovalent interactons. We present a survey of such relationships, which may be exact or approximate; they may involve the potential in three-dimensional space, along the axes between bonded atoms, at nuclei or on molecular surfaces. Thus, the electrostatic potential, which is rigorously related to the electronic density by Poisson's equation, can be regarded as, effectively, another fundamental determinant of atomic and molecular properties. Received: 6 March 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

Peculiarities of the effects of trifluoromethyl and alkoxycarbonyl groups on the structure and reactivity of acrylates

Ab initio quantum-chemical calculations of molecules of CF₃-substituted acrylates and their non-fluorinated analogs were carried out by the restricted Hartree-Fock (RHF) method and at the second-order Møller-Plesset (MP2) level of perturbation theory using the 6–31G^* basis set with full geometry optimization. Peculiarities of their molecular and electronic structure were revealed and the dipole moments, the polarizability and first molecular hyperpolarizability tensors, harmonic vibrational frequencies, electrostatic potentials, and local electron densities in the vicinity of the carbon atoms of the C=C bond were calculated. It was shown that CF₃-substituted acrylates are conjugated systems similar to their nonfluorinated analogs. Peculiarities of the structure and properties of CF₃-substituted acrylates are explained by p-π-interaction between the CF₃ group and the conjugated system.