Extended multi-configuration quasi-degenerate perturbation theory: the new approach to multi-state multi-reference perturbation theory

The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 1(1)A(')-2(1)A(') conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 1(1)A(1) to 2(1)A(1) electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems.     

A nondiagonal quasidegenerate fourth-order perturbation theory

A canonical quasidegenerate Rayleigh-Schrödinger perturbation theory, correct through fourth order in the energy, is explored for a block-diagonal unperturbed Hamiltonian. The theory is developed completely within a Lie Algebra in Hilbert space. Explicit equations forn-particle transition elements in terms of solutions of simultaneous linear equations are presented. A two-dimensional anisotropic anharmonic oscillator is used to provide numerical results. The perturbation theory is shown to be stable under small separation of model and complement spaces. An iterative variant of the fourth order perturbation theory is introduced; the iterative variant is related to the non-iterative one in much the same way as nondegenerate coupled cluster theories are related to nondegenerate perturbation theory. The quasidegenerate coupled cluster theory appears to be stable in the presence of multiple intruder states.     

Semiclassical theory of vibrational collisions in a laser field

A sennclassical theory of multiphoton enhancement of vibrational excitations by molecular collisions is developed. The vibrational-field surfaces (quasienergies) which exhibit avoided crossings are determined via Floquet theory. Transition among the dressed quasienergies are studied using semiclassical time-dependent theory. The effect of collisional velocity, anharmonicity and light intensity upon vibrational transition probability is evaluated for collinear collision of A+BC(v).     

Spherically and system-averaged pair density functional theory

In a couple of recent papers Gori-Giorgi and Savin [Phys. Rev. A 71, 032513 (2005)] proposed a theory that provides simple radial equations to generate the spherically and system averaged pair density. In a recent density matrix functional theory [A. Nagy, Phys. Rev. A 66, 022505 (2002)] it was shown that the problem of an arbitrary system can be reduced to a two-particle problem. Based on this theory, via a double adiabatic connection, it is rigorously derived that the square root of the ground-state spherically and system averaged pair density is the solution of a simple radial equation, that is, contrary to the theory of Gori-Giorgi and Savin only a single equation has to be considered.     

Steric stabilization II

Summary A theory of steric stabilization is developed that is essentially an extension ofFischer's solvency theory. It treats both interpenetration and compression using a latice approach. This permits the introduction of segment density distribution functions. One virtue of the new theory is that it is in good qualitative agreement with the results of experiment. Some limitations of the theory are also noted.     

Spreading kinetics of liquids on liquids

A simple theory is presented for the spreading rate of film forming organic liquids on thick water layers. This theory is an extension of that of Ahmad and Hansen for thin water layers. The theory is compared with experimental data, and fair agreement is obtained. The analogy to longitudinal waves is discussed.     

Spectral theory of anisotropic fluids

The spectral theory of symmetric viscoelastic fluids with arbitrary anisotropy, which is based on the generalized Maxwell relaxation law, is developed. A feature of the proposed approach is the use of a spectral (canonical) representation of tensors that describe the anisotropic properties of fluids. Simple special cases of the spectra of viscosity and relaxation-time tensors are considered. The orientation dynamics of anisotropic fluids is discussed. A theory of generation of eigenmodes that are related to stress relaxation is developed. On the basis of the spectral theory, the possibility of the existence of soft (zero energy) modes in anisotropic fluids with deep anisotropy is considered. The proposed theory opens up new alternatives for classifying anisotropic fluids.     

A simple theory of liquid—solid phase transitions

A simple phenomenological theory of liquid—solid phase transitions, based on the use of perturbation theory about a hard-sphere fluid, is examined. A temperature dependent hard-sphere diameter is determined which permits the prediction of solid and liquid densities and melting pressures. Calculations presented here for the Lennard-Jones 12-6 fluid show good agreement with the computer simulation results. Provided pair potentials are available, the theory may also be used for other fluids, including liquid metals.     

Theory and simulation of anisotropic pair correlations in ferrofluids in magnetic fields

Anisotropic pair correlations in ferrofluids exposed to magnetic fields are studied using a combination of statistical-mechanical theory and computer simulations. A simple dipolar hard-sphere model of the magnetic colloidal particles is studied in detail. A virial-expansion theory is constructed for the pair distribution function (PDF) which depends not only on the length of the pair separation vector, but also on its orientation with respect to the field. A detailed comparison is made between the theoretical predictions and accurate simulation data, and it is found that the theory works well for realistic values of the dipolar coupling constant (λ = 1), volume fraction (φ ≤ 0.1), and magnetic field strength. The structure factor is computed for wavevectors either parallel or perpendicular to the field. The comparison between theory and simulation is generally very good with realistic ferrofluid parameters. For both the PDF and the structure factor, there are some deviations between theory and simulation at uncommonly high dipolar coupling constants, and with very strong magnetic fields. In particular, the theory is less successful at predicting the behavior of the structure factors at very low wavevectors, and perpendicular Gaussian density fluctuations arising from strongly correlated pairs of magnetic particles. Overall, though, the theory provides reliable predictions for the nature and degree of pair correlations in ferrofluids in magnetic fields, and hence should be of use in the design of functional magnetic materials.     

A molecular theory of pretransitional behaviour in smectogenic liquid crystals

The nature of the pretransitional behaviour in the isotropic phase prior to the formation of a liquid crystal mesophase depends critically on whether this is a nematic or a smectic A. The McMillan theory of the smectic A mesophase is used to provide a molecular theory of this difference in pretransitional behaviour.     

Nonlinear coupling model for reactions in dense media

A reaction rate theory for dense‐phase reactions, based on the assumption of nonlinear coupling between reactant and medium, is proposed. The relations between the exact dynamic theory, the stochastic rate theory, and the transition state theory is discussed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 1–3, 2001     

Theory of inhomogeneous weakly charged polyelectrolytes

A theory of inhomogeneous multicomponent systems containing weakly charged polyelectrolytes is developed. The theory treats the polymer conformation and the electrostatics simultaneously using a functional integral representation of the partition function. A mean‐field approximation to the theory leads to two sets of coupled mean‐field equations: a Poisson‐Boltzmann type equation describing the electrostatic potential, and a set of self‐consistent field equations describing the equilibrium densities. Asymptotic forms of the theory at weak and strong segregation limits are derived. The theory can be used to study the interfacial properties, microphase structures, and adsorptions of a variety of weakly charged polyelectrolyte systems. As a simple example, the interface between the polymer‐rich and polymer‐poor phases of a polyelectrolyte solution is studied.     

Generalized Langevin theory on the dynamics of simple fluids under external fields

A theory on the time development of the density and current fields of simple fluids under an external field is formulated through the generalized Langevin formalism. The theory is applied to the linear solvation dynamics of a fixed solute regarding the solute as the external field on the solvent. The solute-solvent-solvent three-body correlation function is taken into account through the hypernetted-chain integral equation theory, and the time correlation function of the random force is approximated by that in the absence of the solute. The theoretical results are compared with those of molecular-dynamics (MD) simulation and the surrogate theory. As for the transient response of the density field, our theory is shown to be free from the artifact of the surrogate theory that the solvent can penetrate into the repulsive core of the solute during the relaxation. We have also found a large quantitative improvement of the solvation correlation function compared with the surrogate theory. In particular, the short-time part of the solvation correlation function is in almost perfect agreement with that from the MD simulation, reflecting that the short-time expansion of the theoretical solvation correlation function is exact up to t(2) with the exact three-body correlation function. A quantitative improvement is found in the long-time region, too. Our theory is also applied to the force-force time correlation function of a fixed solute, and similar improvement is obtained, which suggests that our present theory can be a basis to improve the mode-coupling theory on the solute diffusion.     

Chain length effects in the second virial coefficient of linear polymer molecules

A generalized perturbation theory is presented for the second virial coefficient of linear and branched polymer systems. Results have been computed for linear chains having two to five hundred statistical segments. These are found to differ significantly from the long-chain asymptotic results of Zimm. A semi-empirical modification of the Flory--Orofino theory is also suggested.     

Dynamical optimization for partition theory

How to partition a chemical system into its constituent parts is a classic problem of theoretical chemistry. A formally exact solution has recently been developed, partition theory (PT), based on density functional theory [Cohen, M. H.; Wasserman, A. J. Phys. Chem. A 2007, 111, 2229]. PT presents a constrained optimization problem to which the Car-Parrinello (CP) method of electronic structure theory is well suited. We propose here a generalization of the CP method suitable for PT and thereby make way for its practical numerical implementation. We demonstrate that this CP implementation of PT need not increase the complexity of the computation of the system's electronic structure. The scheme provides an exact DFT formulation of, e.g., atoms in molecules theory that is amenable to numerical implementation.     

Binary theory of dephasing in liquid solutions. I. The non-markovian theory of encounters

A non-markovian version of encounter theory is proposed which consistently takes into account fast dissipative processes. Kinetic equations of vibrational molecular states dephasing at binary encounters in solutions are derived in terms of this theory. A particular case of fast molecular rotation is considered. The characteristic impurity dephasing time is calculated for the case of weak molecular interactions.     

Diffusion in polymer–solvent systems. II. A predictive theory for the dependence of diffusion coefficients on temperature,concentration, and molecular weight

A new free-volume theory is combined with the thermodynamic theory of Flory and the entanglement theory of Bueche to provide a means of predicting the temperature, concentration, and molecular weight dependence of mutual-diffusion coefficients in amorphous polymer–solvent systems. The predictions of the theory are compared with actual data for the ethylbenzene–polystyrene system.     

Auxiliary density perturbation theory

A new approach, named auxiliary density perturbation theory, for the calculation of second energy derivatives is presented. It is based on auxiliary density functional theory in which the Coulomb and exchange-correlation potentials are expressed by auxiliary function densities. Different to conventional coupled perturbed Kohn-Sham equations the perturbed density matrix is obtained noniteratively by solving an inhomogeneous equation system with the dimension of the auxiliary function set used to expand the auxiliary function density. A prototype implementation for the analytic calculation of molecular polarizabilities is presented. It is shown that the polarizabilities obtained with the newly developed auxiliary density perturbation approach match quantitative with the ones from standard density functional theory if augmented auxiliary function sets are used. The computational advantages of auxiliary density perturbation theory are discussed, too.