Third-order interactions in symmetry-adapted perturbation theory

We present an extension of many-body symmetry-adapted perturbation theory (SAPT) by including all third-order polarization and exchange contributions obtained with the neglect of intramonomer correlation effects. The third-order polarization energy, which naturally decomposes into the induction, dispersion, and mixed, induction-dispersion components, is significantly quenched at short range by electron exchange effects. We propose a decomposition of the total third-order exchange energy into the exchange-induction, exchange-dispersion, and exchange-induction-dispersion contributions which provide the quenching for the corresponding individual polarization contributions. All components of the third-order energy have been expressed in terms of molecular integrals and orbital energies. The obtained formulas, valid for both dimer- and monomer-centered basis sets, have been implemented within the general closed-shell many-electron SAPT program. Test calculations for several small dimers have been performed and their results are presented. For dispersion-bound dimers, the inclusion of the third-order effects eliminates the need for a hybrid SAPT approach, involving supermolecular Hartree-Fock calculations. For dimers consisting of strongly polar monomers, the hybrid approach remains more accurate. It is shown that, due to the extent of the quenching, the third-order polarization effects should be included only together with their exchange counterparts. Furthermore, the latter have to be calculated exactly, rather than estimated by scaling the second-order values.     

Free energy landscape analysis of two-dimensional dipolar solvent model at temperatures below and above the rotational freezing point

Ionic solvation in a polar solvent is modeled by a central charge surrounded by dipolar molecules posted on two-dimensional distorted lattice sites with simple rotational dynamics. Density of states is calculated by applying the Wang-Landau algorithm to both the energy and polarization states. The free energy landscapes of solvent molecules as a function of polarization are depicted to explore the competition between the thermal fluctuation and solvation energy. Without a central charge, for temperatures higher than the energy scale of the dipole-dipole interactions, the energy landscape for the small polarization region exhibits a parabolic shape as predicted by Marcus [Rev. Mod. Phys. 65, 599 (1993)] for electron transfer reaction, while there is an additional quartic contribution to the landscape for the large polarization region. When the temperature drops, the simulated free energy landscapes are no longer smooth due to the presence of multiple local minima arising from the frustrated interaction among the dipoles. The parabolic contribution becomes negligible and the energy landscape becomes quartic in shape. For a strong central charge, the energy landscape exhibits an asymmetric profile due to the contributions of linear and cubic terms that arise from the charge-dipole interactions.     

Propagation of polar substituent effects in 1-(substituted phenyl)-6,7-dimethoxy-3,4-dihydro- and -1,2,3,4-tetrahydroisoquinolines as explained by resonance polarization concept

[structures: see text] Propagation of inductive and resonance effects of phenyl substituents within 1-(substituted phenyl)-6,7-dimethoxy-3,4-dihydro- and -1,2,3,4-tetrahydroisoquinolines were studied with the aid of 13C and 15N NMR chemical shifts and ab initio calculations. The substituent-induced changes in the chemical shift (SCS) were correlated with a dual substituent parameter equation. The contributions of conjugative (rhoR) and nonconjugative effects (rhoF) were analyzed, and mapping of the substituent-induced changes is given over the entire isoquinoline moiety for both series. The experimental results can be rationalized with the aid of the resonance polarization concept. This means the consideration of the substituent-sensitive balance of different resonance structures, i.e., electron delocalization, and the effect of the aromatic ring substituents on their relative contributions. With tetrahydroisoquinolines, the delocalization of the nitrogen lone pair (stereoelectronic effect) particularly contributes. Correlation analysis of the Mulliken atomic charges for the dihydroisoquinoline derivatives was also performed. The results support the concept of the substituent-sensitive polarization of the isoquinoline moiety even if the polarization pattern achieved via the NMR approach is not quite the same as that predicted by the computational charges. Previously the concepts of localized pi-polarization and extended polarization have been used to explain polar substituent effects within aromatic side-chain derivatives. We consider that the resonance polarization model effectively contributes to the understanding of the polar substituent effects.     

Simulation of thermally stimulated polarization current (TSPC) based on the Frohlich two-state model and the complexity of the amorphous phase

Numerical simulations of thermally stimulated polarization current profiles have been performed using rate expressions based on the Frohlich two-state model. The qualitative behavior of simulations previously published by other researchers can be reproduced. The important feature examined is a peak in the evolution of polarization with temperature, which results in a change in sign for the polarization current profile. The previous researchers have assigned this to a crossover of the kinetic transient polarization with the equilibrium polarization described by the Langevin approximation. The origin of the peak in the evolution of polarization has been reexamined and found to be the kinetic consequence of the structure of the Frohlich model. When the field is applied, the two-state model requires that half the available dipoles are initially polarized. This high level of polarized dipoles contributes to an increased rate of the reverse process, depolarization, at high temperatures and results in the calculated decrease in polarization. The constraints of the Frohlich two-state model are too severe to represent the kinetics of a physically plausible polar solid. Further the multiple modes of aggregation in the amorphous state impose complications on the computation of polarization current.     

Surface anchoring,polarization fields and memory states in polymer dispersed liquid crystals

We have investigated the formation and development of memory states in polymer dispersed liquid crystals induced by the application of a strong electric field. Both the optical transmittance and polarization field have been followed as functions of time. We have been able to distinguish between the contributions to the memory states arising from the surface anchoring of the liquid crystal at the droplet interface and from the electrical reorientation of the mesogenic molecules. The dependence of both residual transmittance and polarization field on temperature is reported and a simple model is proposed.     

Surface anchoring, polarization fields and memory states in polymer dispersed liquid crystals

We have investigated the formation and development of memory states in polymer dispersed liquid crystals induced by the application of a strong electric field. Both the optical transmittance and polarization field have been followed as functions of time. We have been able to distinguish between the contributions to the memory states arising from the surface anchoring of the liquid crystal at the droplet interface and from the electrical reorientation of the mesogenic molecules. The dependence of both residual transmittance and polarization field on temperature is reported and a simple model is proposed.     

Totally dressed SDCI calculations: An application to HF and F2

Summary A previously proposed procedure including the linked and unlinked contributions due to Triple and Quadruple excitations into a size-consistent SDCI-like model has been applied to HF and F₂ single-bond systems. The procedure is a non-iterative approximation to the more general total dressing model, which is based on the intermediate Hamiltonians theory. Three basis sets have been employed: the correlation consistent cc-pVTZ basis, a similar one including 3d1f polarization functions, and another including one set of g polarization functions. Excellent agreement with experiment and high-quality calculations is obtained for both equilibrium distances and spectroscopic constants. The possibilities of the method in treating single-bond breaking are also demonstrated. Finally, the Linked and Non-Linked contributions from Triple and Quadruple excitations are analysed separately and it is suggested that the addition of the linked triples to the size-consistent SDCI is sufficient to have quantitatively correct spectroscopic properties in going from the size-consistent SDCI to nearly experimental values.     

Physical analysis of the through-ligand long-distance magnetic coupling: spin-polarization versus Anderson mechanism

The physical factors governing the magnetic coupling between two magnetic sites are analyzed and quantified as functions of the length of the bridging conjugated ligand. Using wave-function-theory based ab initio calculations, it has been possible to separate and calculate the various contributions to the magnetic coupling, i.e. the direct exchange, the spin polarization and the kinetic exchange. It is shown in model systems that while the Anderson mechanism brings the leading contribution for short-length ligands, the spin polarization dominates the through-long-ligand couplings. Since the spin polarization decreases more slowly than the kinetic exchange, highly spin polarizable bridging ligands would generate a good magneto-communication between interacting magnetic units.     

Exchange polarization effects in the interaction of closed-shell systems

Explicit formulae for the calculation of the exchange polarization energy in the interaction of closed-shell atoms or molecules have been derived by assuming neglect of the electron correlation within the noninteracting systems. The dispersion part of the exchange polarization energy has been represented as a sum of contributions arising from the interaction of two, three or four orbitals at a time. Each of these contributions is given by an integral involving the orbitals engaged in the interaction and the pair functions describing the dispersion interaction between these orbitals. The numerical calculations for the interaction of two ground-state beryllium atoms show that the exchange dispersion energy is positive and quenches about 5 to 10 per cent of the dispersion term. This results in a decrease of the interaction energy, computed as a sum of the SCF and dispersion components, by 6 to 30 per cent for interatomic distances ranging from 10 to 7 bohrs.Simplified formulae for estimating the exchange dispersion energy in the interaction of larger systems are also proposed and their accuracy is discussed.     

Density functional restricted-unrestricted approach for nonlinear properties: application to electron paramagnetic resonance parameters of square planar copper complexes

The density functional restricted-unrestricted approach for treatments of spin polarization effects in molecular properties using spin restricted Kohn-Sham theory has been extended from linear to nonlinear properties. It is shown that the spin polarization contribution to a nonlinear property has the form of a quadratic response function that includes the zero-order Kohn-Sham operator, in analogy to the lower order case where the spin polarization correction to an expectation value has the form of a linear response function. The developed approach is used to formulate new schemes for computation of electronic g-tensors and hyperfine coupling constants, which include spin polarization effects within the framework of spin restricted Kohn-Sham theory. The proposed computational schemes are in the present work employed to study the spin polarization effects on electron paramagnetic resonance spin Hamiltonian parameters of square planar copper complexes. The obtained results indicate that spin polarization gives rise to sizable contributions to the hyperfine coupling tensor of copper in all investigated complexes, while the electronic g-tensors of these complexes are only marginally affected by spin polarization and other factors, such as choice of exchange-correlation functional or molecular structures, will have more pronounced impact on the accuracy of the results.     

Electron spin polarization of the excited quartet state of strongly coupled triplet-doublet spin systems

The electron spin polarization associated with electronic relaxation in molecules with trip-quartet and trip-doublet excited states is calculated. Such molecules typically relax to the lowest trip-quartet state via intersystem crossing from the trip doublet, and it is shown that when spin-orbit coupling provides the main mechanism for this relaxation pathway it leads to spin polarization of the trip quartet. Analytical expressions for this polarization are derived using first- and second-order perturbation theory and are used to calculate powder spectra for typical sets of magnetic parameters. It is shown that both net and multiplet contributions to the polarization occur and that these can be separated in the spectrum as a result of the different orientation dependences of the +/-1/2<-->+/-3/2 and +1/2<-->-1/2 transitions. The net polarization is found to be localized primarily in the center of the spectrum, while the multiplet contribution dominates in the outer wings. Despite the fact that the multiplet polarization is much stronger than the net polarization for individual orientations of the spin system, the difference in orientation dependence of the transitions leads to comparable amplitudes for the two contributions in the powder spectrum. The influence of this difference on the line shape is investigated in simulations of partially ordered samples. Because the initial nonpolarized state of the spin system is not conserved for the proposed mechanism, the net polarization can survive in the doublet ground state following electronic relaxation of the triplet part of the system.     

Solubility Parameter of Acrylamide Series Polymers through Its Components and Group Contribution Technique

The chemical group contribution technique, based on the principle of additivity of molar refraction and polarization constants for groups in a molecule, has been used for determining the solubility parameters of acrylamide series polymers. The solubility parameter for a polymer is calculated through its components by using the contributions of chemical groups reported in the literature with the resultant values found to compare favorably. It is also noticed that the δ-values decrease with an increase in molar volume.     

Investigation of the stability of oligonucleotides and oligodinucleotides

The mutually-consistent-field (MCF) method together with pseudo polarization tensors has been employed to investigate in detail the intra- and inter-strand interactions in B-DNA helices. Results are reported for all four periodic homo-oligonucleotides showing that these configurations are stable only in the case of adenine and thymine. All the oligodinucleotides studied are stable, but the role of the different contributions, e.g. the two intrastrand and the interstrand interactions is dependent on the nucleotide bases. In the case of periodic guanine-cytosine base pairs, the interstrand energy is dominant, whereas in the corresponding alternating systems all three contributions are attractive. The stability of adenine-thymine systems is less sensitive with respect to periodic and alternating compositions.     

Why are the Ca2+ and K+ binding energies of formaldehyde and ammonia reversed with respect to their proton affinities?

The binding energies (BEs) of alkali metal monocations and alkaline-earth metal dications to a series of small oxygen and nitrogen bases have been evaluated by means of CCSD(T) calculations on B3-LYP optimized structures. These calculations were carried out both using all-electron basis sets, and additionally using an effective-core potential (ECP) to describe the inner electrons of the metal. A theoretical model aiming at analyzing the effects on the binding energy trends of electrostatic, polarization, and covalent contributions, as well as geometry distortion, was employed. From this analysis, we conclude that although the neutral-ion interaction energy for alkali and alkaline-earth metal cations is dominated by electrostatic contributions, in many cases the correct basicity trends are only attained once polarization effects are also included in the model. This is indeed the case when Ca2+ and K+ are bound to ammonia and formaldehyde. Geometry distortions triggered by polarization are also necessary, in some cases, to obtain the correct basicity trends. In addition, in particular for alkaline-earth dications, the energy associated with covalent interactions sometimes dictates the basicity trend. Our observations imply that simple models based on ion-dipole interactions, that are frequently used in the literature to explain affinity trends in ion-molecule reactions, are generally not likely to be reliable.     

Optical analysis of dichroism measurements in polymer science

The polarization properties of an optical system, source–interferometer–polarizer–polymer film–detector, have been calculated. Using Mueller matrices, the intensity has been obtained as a function of polarizer angle. It is shown in some detail how polarization of the beam in both interferometer and detector optics distort the spectra. The contributions from the finite extinction ratio of the polarizer are also calculated and intensity variations caused by beam-wandering are discussed. It is shown that the commonly used procedure for correcting the spectra is wrong. Better methods for correcting the spectra are proposed. The influence of a uniaxial refractive index on the data is discussed, and experimental methods that can deal with refraction effects are presented. © 1993 John Wiley & Sons, Inc.     

Amine-hydrogen halide complexes: experimental electric dipole moments and a theoretical decomposition of dipole moments and binding energies

The Stark effect has been observed in the rotational spectra of several gas-phase amine-hydrogen halide complexes and the following electric dipole moments have been determined: H(3)(15)N-H(35)Cl (4.05865 +/- 0.00095 D), (CH(3))(3)(15)N-H(35)Cl (7.128 +/- 0.012 D), H(3)(15)N-H(79)Br (4.2577 +/- 0.0022 D), and (CH(3))(3)(15)N-H(79)Br (8.397 +/- 0.014 D). Calculations of the binding energies and electric dipole moments for the full set of complexes R(n)()(CH(3))(3)(-)(n)()N-HX (n = 0-3; X = F, Cl, Br) at the MP2/aug-cc-pVDZ level are also reported. The block localized wave function (BLW) energy decomposition method has been used to partition the binding energies into contributions from electrostatic, exchange, distortion, polarization, and charge-transfer terms. Similarly, the calculated dipole moments have been decomposed into distortion, polarization, and charge-transfer components. The complexes studied range from hydrogen-bonded systems to proton-transferred ion pairs, and the total interaction energies vary from 7 to 17 kcal/mol across the series. The individual energy components show a much wider variation than this, but cancellation of terms accounts for the relatively narrow range of net binding energies. For both the hydrogen-bonded complexes and the proton-transferred ion pairs, the electrostatic and exchange terms have magnitudes that increase with the degree of proton transfer but are of opposite sign, leaving most of the net stabilization to arise from polarization and charge transfer. In all of the systems studied, the polarization terms contribute the most to the induced dipole moment, followed by smaller but still significant contributions from charge transfer. A significant contribution to the induced moment of the ion pairs also arises from distortion of the HX monomer.     

The use of inner projections of the polarization propagator to study different contributions to the magnetic shielding tensor. I. Proton deshielding by steric compression

A new method for studying different contributions to the magnetic shielding tensor is proposed. These contributions come from different molecular fragments, which are defined through a localization procedure. They are obtained by means of inner projections of the polarization propagator onto the subspace defined by the chosen molecular fragment. To illustrate the utility of this method, results are presented for the proton desheilding effect of steric crowding. Different degrees of approximation both in the polarization propagator formalism and in the ground state wave function can be used. Results presented in this paper were obtained at the INDO level, within the CHF scheme. Good agreement with experimental values is obtained.