Distribution function in quantal cumulant dynamics

We have derived a quantum distribution function in terms of cumulants that are expectation values of a (anti)symmetric-ordered product of position and momentum fluctuation operators. A second-order approximation leads a Gaussian distribution function, which is positive definite and has proper marginals so that the Shannon entropy can be evaluated.     

Two-particle density matrix cumulant of coupled cluster theory

A two-particle density matrix obtained from the expectation value expression for the coupled cluster wave function is separated into the antisymmetrized product of the one-particle density matrices and the remaining cumulant part. It is demonstrated that the proposed formula for the coupled cluster cumulant is a valid cumulant expression, since it is a connected, and therefore size-extensive quantity. It is also shown that the density matrices from coupled cluster gradient theory, when used to define a cumulant, result in the expression containing disconnected terms. The proposed formulation of the coupled cluster cumulant makes it easy to develop size-extensive truncation schemes. As an example, explicit equations for the cumulant at the coupled cluster single, double and triple excitation level are presented.     

Analytic gradients for density cumulant functional theory: The DCFT-06 model

Density cumulant functional theory (DCFT) is one of a number of nascent electron correlation methods that are derived from reduced density matrices and cumulants thereof, instead of the wavefunction. Deriving properties from the density cumulant naturally yields methods that are size extensive and size consistent. In this work, we derive expressions for the analytic gradient, with respect to an external perturbation, for the DCFT-06 variant of density cumulant functional theory. Despite the fact that the DCFT-06 energy functional is stationary with respect to the density cumulant, the analytic gradients of the energy require the solution of perturbation-independent equations for both orbital and cumulant response. These two sets of linear response equations are coupled in nature and are solved iteratively with the solution of orbital and cumulant response equations each macroiteration, exhibiting rapid convergence. The gradients are implemented and benchmarked against coupled cluster theory with single and double excitations (CCSD) and CCSD with perturbative triple excitations [CCSD(T)], as well as accurate empirically corrected experimental data, for a test set comprising 15 small molecules. For most of the test cases, results from DCFT-06 are closer to CCSD(T) and empirical data than those from CCSD. Although the total energy and analytic gradient have the same asymptotic scaling, the present experience shows that the computational cost of the gradient is significantly lower.     

Assessment of a new approach for the two-electron cumulant in natural-orbital-functional theory

The Piris natural orbital functional (PNOF) based on a new approach for the two-electron cumulant has been used to predict adiabatic ionization potentials, equilibrium bond distances, and harmonic vibrational frequencies of 18 diatomic molecules. Vertical ionization potentials have been calculated for the same set of diatomic molecules and another set of 20 polyatomic molecules using energy-difference methods as well as the extended Koopman theorem. The PNOF properties compare favorably with the coupled-cluster-doubles results. The calculated PNOF values are in good agreement with the corresponding experimental data, considering the basis sets used (6-31G**).     

Density cumulant functional theory: first implementation and benchmark results for the DCFT-06 model

Density cumulant functional theory [W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006)] is implemented for the first time. Benchmark results are provided for atoms and diatomic molecules, demonstrating the performance of DCFT-06 for both nonbonded and bonded interactions. The results show that DCFT-06 appears to perform similarly to coupled cluster theory with single and double excitations (CCSD) in describing dispersion. For covalently bound systems, the physical properties predicted by DCFT-06 appear to be at least of CCSD quality around equilibrium geometries. The computational scaling of both DCFT-06 and CCSD is O(N(6)), but the former has reduced nonlinearities among the variables and a Hermitian energy functional, making it an attractive alternative.     

Coarse-grained force field: general folding theory

We review the coarse-grained UNited RESidue (UNRES) force field for the simulations of protein structure and dynamics, which is being developed in our laboratory over the last several years. UNRES is a physics-based force field, the prototype of which is defined as a potential of mean force of polypeptide chains in water, where all the degrees of freedom except the coordinates of α-carbon atoms and side-chain centers have been integrated out. We describe the initial implementation of UNRES to protein-structure prediction formulated as a search for the global minimum of the potential-energy function and its subsequent molecular dynamics and extensions of molecular-dynamics implementation, which enabled us to study protein-folding pathways and thermodynamics, as well as to reformulate the protein-structure prediction problem as a search for the conformational ensemble with the lowest free energy at temperatures below the folding-transition temperature. Applications of UNRES to study biological problems are also described.     

Enzyme inhibition and activation: A general theory

The rate of an enzymatic reaction may be changed by a moderator. Usually, the effect is to reduce the rate, and this is called inhibition. Sometimes the rate of enzyme reaction is raised, and this is called activation. Not only enzyme activation is subject of a less detailed presentation, but also enzyme inhibition and activation are very often discussed independently in enzymology. I attempt to introduce a general model of enzyme inhibition and activation to allow one to interpret inhibition and activation from a mechanistic or physical perspective using the significance of cooperativity as a new approach. The magnitude of interaction between substrate and inhibitor binding sites is given by the α parameter and the magnitude of increasing catalytic reaction constant is given by the β parameter, which both parameter values characterize the type of inhibition and activation. The moderation of mushroom tyrosinse is described by application of the model as a typical.     

Vibrational coupled cluster response theory: a general implementation

The calculation of vibrational contributions to molecular properties using vibrational coupled cluster (VCC) response theory is discussed. General expressions are given for expectation values, linear response functions, and transition moments. It is shown how these expressions can be evaluated for arbitrary levels of excitation in the wave function parameterization as well as for arbitrary coupling levels in the potential and property surfaces. The convergence of the method is assessed by benchmark calculations on formaldehyde. Furthermore, excitation energies and infrared intensities are calculated for the fundamental vibrations of furan using VCC limited to up to two-mode and up to three-mode excitations, VCC[2] and VCC[3], as well as VCC with full two-mode and approximate three-mode couplings, VCC[2pt3].     

Acid-Induced Free-Radical Decomposition of Hydroperoxides: Quantal Calculations

Abstract

Quantum mechanical calculations using the GAUSSIAN 76 system of programs are used to suggest a possible mechanism for the acid-induced free-radical decomposition of hydroperoxides.     

On the properties of cumulant expansions

Cumulants represent a natural language for expressing macroscopic properties of a solid. We show that cumulants are subject to a nontrivial geometry. This geometry provides an intuitive understanding of a number of cumulant relations which have been obtained so far by using algebraic considerations. We give general expressions for their infinitesimal and finite transformations and represent a cumulant wave operator through an integration over a path in the Hilbert space. Cases are investigated where this integration can be done exactly. An expression of the ground-state wave function in terms of the cumulant wave operator is derived. In the second part of the article, we derive the cumulant counterpart of Faddeev's equations and show its connection to the method of increments. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 377–389, 1998     

Valence bond theory for chemical dynamics

This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond-molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches.     

Unconditional convergence in SCF theory: a general level shift technique

A level shift procedure is described in the framework of one-operator SCF formalisms. This procedure permits one to obtain in any case unconditional convergence to a stationary energy.     

A general theory of surface seperation processes

A thermodynamic theory of surface separation has been formulated for mixtures of both inert and chemically interacting substances. The behaviour of the surface separation lines in the vicinity of singular points in concentration diagrams has been investigated. As an example, the behaviour of the foam separation lines in dilute three- and four-component solutions has been considered. The possibility of classification of systems by means of a thermodynamic—topological rule has been exhibited.     

Toward a general theory of heterogeneous reactions

The thermochemical approach, using the quasi-equilibrium methodology of kinetic analysis and the concepts of equimolar and isobaric reaction modes (regimes), has been used to prove the common mechanism of the representative heterogeneous reactions: decompositions of CaCO₃ and of Ag₂O, reduction of NiO by H_2, and the catalytic oxidation of CO and H₂ on PtO₂. All these rate processes have been analyzed using the congruent dissociative vaporization of the participating solid reactants or catalysts and are described by similar mechanistic schemes. The possible role of atomic oxygen evolution in oxidation catalysis is discussed. Quantitative proofs of the common mechanism of these reactions were provided by agreement between calculated reaction enthalpies and the Arrhenius E parameters, the retardation effect of gaseous products on the reaction rates, and the accordance between experimental and theoretical ratios of isobaric to equimolar values of the E parameter. In conclusion, milestones in the history of the thermochemical approach during the last century are discussed.     

Structure of solvent-free grafted nanoparticles: molecular dynamics and density-functional theory

The structure of solvent-free oligomer-grafted nanoparticles has been investigated using molecular dynamics simulations and density-functional theory. At low temperatures and moderate to high oligomer lengths, the qualitative features of the core particle pair probability, structure factor, and the oligomer brush configuration obtained from the simulations can be explained by a density-functional theory that incorporates the configurational entropy of the space-filling oligomers. In particular, the structure factor at small wave numbers attains a value much smaller than the corresponding hard-sphere suspension, the first peak of the pair distribution function is enhanced due to entropic attractions among the particles, and the oligomer brush expands with decreasing particle volume fraction to fill the interstitial space. At higher temperatures, the simulations reveal effects that differ from the theory and are likely caused by steric repulsions of the expanded corona chains.     

Time-dependent density functional theory based Ehrenfest dynamics

Time-dependent density functional theory based Ehrenfest dynamics with atom-centered basis functions is developed in present work. The equation of motion for electrons is formulated in terms of first-order reduced density matrix and an additional term arises due to the time-dependence of basis functions through their dependence on nuclear coordinates. This time-dependence of basis functions together with the imaginary part of density matrix leads to an additional term for nuclear force. The effects of the two additional terms are examined by studying the dynamics of H(2) and C(2)H(4), and it is concluded that the inclusion of these two terms is essential for correct electronic and nuclear dynamics.     

Mode-coupling theory for reaction dynamics in liquids

A theory for chemical reaction dynamics in condensed phase systems based on the generalized Langevin formalism of Grote and Hynes [J. Chem. Phys. 73, 2715 (1980)] is presented. A microscopic approach to calculate the dynamic friction is developed within the framework of a combination of kinetic and mode-coupling theories. The approach provides a powerful analytic tool to study chemical reactions in realistic condensed phase environments. The accuracy of the approach is tested for a model isomerization reaction in a Lennard-Jones fluid. Good agreement is obtained for the transmission coefficient at different solvent densities, in comparison with numerical simulations based on the reactive-flux approach.