Toward an accurate and efficient semiclassical surface hopping procedure for nonadiabatic problems

The derivation of a semiclassical surface hopping procedure from a formally exact solution of the Schrodinger equation is discussed. The fact that the derivation proceeds from an exact solution guarantees that all phase terms are completely and accurately included. Numerical evidence shows the method to be highly accurate. A Monte Carlo implementation of this method is considered, and recent work to significantly improve the statistical accuracy of the Monte Carlo approach is discussed.     

Two-photon absorption in solution by means of time-dependent density-functional theory and the polarizable continuum model

We present the first study of two-photon absorption (TPA) of solvated molecules based on direct evaluation of TPA cross sections from the quadratic response of time-dependent perturbations. A set of prototypical two-photon (TP) chromophores has been selected and analyzed: a pure pi system (t-stilbene) and its substituted homologs obtained employing a donor (D) and an acceptor (A) group to probe the solvent effects along the series pi, D-pi-D, A-pi-D, and A-pi-A. For the selected systems we have calculated the TPA cross sections in different environments by means of the polarizable continuum model. The data have been analyzed to evaluate how the structural and environmental parameters contribute to the final two-photon absorption cross section. These include molecular structure, geometry relaxation in solution, polarity, and refractive index of the solvent. The performances of the three common functionals SVWN, BLYP, and B3LYP have been compared. The results show a significant solvent dependence of the TPA cross section and an unusual trend when passing from cyclohexane to water. The data have also been rationalized in terms of the main orbital excitations leading to the transitions. Finally, trends along the series have been described and comparison with experiments and previous calculations has been drawn.     

A computationally efficient exact pseudopotential method. I. Analytic reformulation of the Phillips-Kleinman theory

Even with modern computers, it is still not possible to solve the Schrodinger equation exactly for systems with more than a handful of electrons. For many systems, the deeply bound core electrons serve merely as placeholders and only a few valence electrons participate in the chemical process of interest. Pseudopotential theory takes advantage of this fact to reduce the dimensionality of a multielectron chemical problem: the Schrodinger equation is solved only for the valence electrons, and the effects of the core electrons are included implicitly via an extra term in the Hamiltonian known as the pseudopotential. Phillips and Kleinman (PK) [Phys. Rev. 116, 287 (1959)]. demonstrated that it is possible to derive a pseudopotential that guarantees that the valence electron wave function is orthogonal to the (implicitly included) core electron wave functions. The PK theory, however, is expensive to implement since the pseudopotential is nonlocal and its computation involves iterative evaluation of the full Hamiltonian. In this paper, we present an analytically exact reformulation of the PK pseudopotential theory. Our reformulation has the advantage that it greatly simplifies the expressions that need to be evaluated during the iterative determination of the pseudopotential, greatly increasing the computational efficiency. We demonstrate our new formalism by calculating the pseudopotential for the 3s valence electron of the Na atom, and in the subsequent paper, we show that pseudopotentials for molecules as complex as tetrahydrofuran can be calculated with our formalism in only a few seconds. Our reformulation also provides a clear geometric interpretation of how the constraint equations in the PK theory, which are required to obtain a unique solution, are themselves sufficient to calculate the pseudopotential.     

Method of local-scaling transformations and density-functional theory in quantum chemistry

The method of local-scaling transformations is developed with a view to applications of the nonrelativistic quantum mechanical variational principle in quantum chemistry. Some properties of local-scaling transformations are studied. The method presented links local-scaling transformations and one-electron densities via the ordinary differential equation that provides a proof of the theorem on the existence of the energy density functional within any given orbit and its universality in a sense of the general theory of ordinary differential equations, and allows the construction of this functional explicitly.     

Toward an efficient synthesis of taxane analogs by dienyne ring-closing metathesis

An efficient tandem ring-closing dienyne metathesis of dienynes derived from cyclohex-2-enone affords the [5.3.1] carbon framework characteristic of taxanes in a single-step process. Further stereoselective functionalizations of the resulting [5.3.1] carbon framework lead to an advanced intermediate in a novel synthetic strategy for taxane analogs.     

Spin densities from subsystem density-functional theory: assessment and application to a photosynthetic reaction center complex model

Subsystem density-functional theory (DFT) is a powerful and efficient alternative to Kohn-Sham DFT for large systems composed of several weakly interacting subunits. Here, we provide a systematic investigation of the spin-density distributions obtained in subsystem DFT calculations for radicals in explicit environments. This includes a small radical in a solvent shell, a π-stacked guanine-thymine radical cation, and a benchmark application to a model for the special pair radical cation, which is a dimer of bacteriochlorophyll pigments, from the photosynthetic reaction center of purple bacteria. We investigate the differences in the spin densities resulting from subsystem DFT and Kohn-Sham DFT calculations. In these comparisons, we focus on the problem of overdelocalization of spin densities due to the self-interaction error in DFT. It is demonstrated that subsystem DFT can reduce this problem, while it still allows to describe spin-polarization effects crossing the boundaries of the subsystems. In practical calculations of spin densities for radicals in a given environment, it may thus be a pragmatic alternative to Kohn-Sham DFT calculations. In our calculation on the special pair radical cation, we show that the coordinating histidine residues reduce the spin-density asymmetry between the two halves of this system, while inclusion of a larger binding pocket model increases this asymmetry. The unidirectional energy transfer in photosynthetic reaction centers is related to the asymmetry introduced by the protein environment.     

Arylgold(I) complexes from base-assisted transmetalation: structures, NMR properties, and density-functional theory calculations

The synthesis of gold(I) complexes of the type LAuR (L = PCy(3), IPr; R = aryl; IPr = 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene) starting from LAuX (X = Br, OAc) and boronic acids in the presence of Cs(2)CO(3) has been investigated. The reactions proceed smoothly in good to excellent yields over the course of 24-48 h in isopropyl alcohol at 50-55 °C. The aryl groups include a variety of functionalities and steric bulk, and in two cases, are heterocyclic. All of the products have been characterized by multinuclear NMR spectroscopy and elemental analysis and most by X-ray crystallography. This work affirms that, almost without exception, base-assisted auration is a useful and reliable way to form gold-carbon bonds.     

Toward accurate and efficient dynamic computational strategy for heterogeneous catalysis: Temperature-dependent thermodynamics and kinetics for the chemisorbed on-surface CO

Computational tools on top of first principle calculations have played an indispensable role in revealing the molecular details, thermodynamics, and kinetics in catalytic reactions. Here we proposed a highly efficient dynamic strategy for the calculation of thermodynamic and kinetic properties in heterogeneous catalysis on the basis of efficient potential energy surface (PES) and MD simulations. Taking CO adsorbate on Ru(0001) surface as the illustrative model system, we demonstrated the PES-based MD can efficiently generate reliable two-dimensional potential-of-mean-force (PMF) surfaces in a wide range of temperatures, and thus temperature-dependent thermodynamic properties can be obtained in a comprehensive investigation on the whole PMF surface. Moreover, MD offers an effective way to describe the surface kinetics such as adsorbate on-surface movement, which goes beyond the most popular static approach based on free energy barrier and transition state theory (TST). We further revealed that the dynamic strategy significantly improves the predictions of both thermodynamic and kinetic properties as compared to the popular ideal statistic mechanics approaches such as harmonic analysis and TST. It is expected that this accurate yet efficient dynamic strategy can be powerful in understanding mechanisms and reactivity of a catalytic surface system, and further guides the rational design of heterogeneous catalysts.     

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.     

Structure and stability of Al-doped boron clusters by the density-functional theory

The geometries, stabilities, and electronic properties of Bn and AlBn clusters, up to n=12, have been systematically investigated by using the density-functional approach. The results of Bn clusters are in good agreement with previous conclusions. When the Al atom is doped in Bn clusters, the lowest-energy structures of the AlBn clusters favor two-dimensional and can be obtained by adding one Al atom on the peripheral site of the stable Bn when n相似文献   

Mechanism of formation of biocidal imidazolidin-4-one derivatives: an Ab initio density-functional theory study

N-halamine chemistry has been a research topic of considerable importance in these laboratories for over 2 decades because N-halamine compounds are very useful in preparing biocidal materials. To understand the utility of these compounds, the stabilities and mechanism of halogenation of cyclic N-halamine compounds should be resolved. The important precursor biocidal compound, 2,2,5,5-tetramethylimidazolidin-4-one (TMIO) was considered as a model in this theoretical study. The thermodynamic and kinetic products of monohalogenation were investigated along with tautomerization of TMIO and succinimide theoretically at the level of B3LYP/6-311+G(2d,p). Solvation effects (water and chloroform) were included using the CPCM solvation model with UAKS cavities. Several mechanisms have been proposed for the chlorine migration from the 3-position (kinetic product) to the 1-position (thermodynamic product) of the TMIO ring. The results are in agreement with experimental NMR data.     

Accurate and efficient treatment of two-electron contributions in quasirelativistic high-order Douglas-Kroll density-functional calculations

Two-component quasirelativistic approaches are in principle capable of reproducing results from fully relativistic calculations based on the four-component Dirac equation (with fixed particle number). For one-electron systems, this also holds in practice, but in many-electron systems one has to transform the two-electron interaction, which is necessary because a picture change occurs when going from the Dirac equation to a two-component method. For one-electron properties, one can take full account of picture change in a manageable way, but for the electron interaction, this would spoil the computational advantages which are the main reason to perform quasirelativistic calculations. Exploiting those picture change effects are largest in the atomic cores, which in molecular applications do not differ too much from the cores of isolated neutral atoms, we propose an elegant, efficient, and accurate approximation to the two-electron picture change problem. The new approach, called the "model potential" approach because it makes use of atomic (four- and two-component) data to estimate picture change effects in molecules, shares with the nuclear-only approach that the Douglas-Kroll operator needs to be constructed only once (not in each self-consistent-field iteration) and that no time-consuming multicenter relativistic two-electron integrals need to be calculated. The new approach correctly describes the screening of both the nearest nucleus and distant nuclei, for the scalar-relativistic as well as the spin-orbit parts of the Hamiltonian. The approach is tested on atomic and molecular-orbital energies as well as spectroscopic constants of the lead dimer.     

Diagrammatic kinetic theory for a lattice model of a liquid. I. Theory

We present a diagrammatic formalism for the time correlation functions of density fluctuations for an excluded volume lattice gas on a simple d-dimensional hypercubic lattice. We consider a multicomponent system in which particles of different species can have different transition rates. Our theoretical approach uses a Hilbert space formalism for the time dependent dynamical variables of a stochastic process that satisfies the detailed balance condition. We construct a Liouville matrix consistent with the dynamics of the model to calculate both the equation of motion for multipoint densities in configuration space and the interactions in the diagrammatic theory. A Boley basis of fluctuation vectors for the Hilbert space is used to develop two formally exact diagrammatic series for the time correlation functions. These theoretical techniques are generalizations of methods previously used for spin systems and atomic liquids, and they are generalizable to more complex lattice models of liquids such as a lattice gas with attractive interactions or polymer models. We use our formalism to construct approximate kinetic theories for the van Hove correlation and self-correlation function. The most simple approximation is the mean field approximation, which is exact for the van Hove correlation function of a one component system but an approximation for the self-correlation function. We use our first diagrammatic series to derive a two site multiple scattering approximation that gives a simple analytic expression for the spatial Fourier transform of the self-correlation function. We employ our second diagrammatic series to derive a simple mode coupling type approximation that provides a system of equations that can be solved for the self-correlation function.     

An efficient and accurate decomposition of the Fermi operator

We present a method to compute the Fermi function of the Hamiltonian for a system of independent fermions based on an exact decomposition of the grand-canonical potential. This scheme does not rely on the localization of the orbitals and is insensitive to ill-conditioned Hamiltonians. It lends itself naturally to linear scaling as soon as the sparsity of the system's density matrix is exploited. By using a combination of polynomial expansion and Newton-like iterative techniques, an arbitrarily large number of terms can be employed in the expansion, overcoming some of the difficulties encountered in previous papers. Moreover, this hybrid approach allows us to obtain a very favorable scaling of the computational cost with increasing inverse temperature, which makes the method competitive with other Fermi operator expansion techniques. After performing an in-depth theoretical analysis of computational cost and accuracy, we test our approach on the density functional theory Hamiltonian for the metallic phase of the LiAl alloy.     

Cations-modified cluster model for density-functional theory simulation of potential dependent Raman scattering from surface complex/electrode systems

Aiming to solve the problem of simulation of the potential dependent surface Raman spectra of anion containing surface complexes on electrodes, we developed a new simulation model by adding different cations (Li(+), Na(+), K(+), Rb(+) or Cs(+)) attached to the bottom layer of a large metallic cluster while the surface complex sits on the top layer.     

A computational investigation of copper-doped germanium and germanium clusters by the density-functional theory

The geometries, stabilities, and electronic properties of Ge(n) and CuGe(n) (n = 2-13) clusters have been systematically investigated by using density-functional approach. According to optimized CuGe(n) geometries, growth patterns of Cu-capped Ge(n) or Cu-substituted Ge(n+1) clusters for the small- or middle-sized CuGe(n) clusters as well as growth patterns of Cu-concaved Ge(n) or Ge-capped CuGe(n-1) clusters for the large-sized CuGe(n) clusters are apparently dominant. The average atomic binding energies and fragmentation energies are calculated and discussed; particularly, the relative stabilities of CuGe10 and Ge10 are the strongest among all different sized CuGe(n) and Ge(n) clusters, respectively. These findings are in good agreement with the available experimental results on CoGe10- and Ge10 clusters. Consequently, unlike some transition metal (TM)Si12, the hexagonal prism CuGe12 is only low-lying structure; however, the basket-like structure is located as the lowest-energy structure. Different from some TM-doped silicon clusters, charge always transfers from copper to germanium atoms in all different sized clusters. Furthermore, the calculated highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gaps are obviously decreased when Cu is doped into the Ge(n) clusters, together with the decrease of HOMO-LUMO gaps, as the size of clusters increases. Additionally, the contribution of the doped Cu atom to bond properties and polarizabilities of the Ge(n) clusters is also discussed.     

Studies of bromine modified single-walled carbon nanotubes using photoelectron spectroscopy and density-functional theory

Many applications based on single-walled carbon nanotubes (SWNTs) require chemical modification of carbon nanotube to optimize the functionalities of the device. In this contribution we discuss the properties of SWNTs immersed in a hydrobromic acid (HBr) solution. Changes of atomic and electronic structures of bromine modified SWNTs were investigated using photoelectron spectroscopy (PES). Spectra of SWNTs before and after immersion in the HBr solution exhibit different features. To understand the mechanism of interaction between SWNTs and bromine, we performed density-functional theory calculations to reveal the structural changes, adsorption energy and chemical bonding information of SWNTs interacting with bromine. In addition, based on the Gelius model, from the molecular orbitals (MOs), we calculated ultraviolet photoelectron spectra (UPS) of SWNTs with and without functionalizing and compared them with the experiment. The present study is a first step in the understanding of the functionalization mechanism of carbon nanotubes.     

Calculation of excitation energies of open-shell molecules with spatially degenerate ground states. I. Transformed reference via an intermediate configuration Kohn-Sham density-functional theory and applications to d1 and d2 systems with octahedral and tetrahedral symmetries

A method for calculating the UV-vis spectra of molecules with spatially degenerate ground states using time-dependent density-functional theory (TDDFT) is proposed. The new transformed reference via an intermediate configuration Kohn-Sham TDDFT (TRICKS-TDDFT) method avoids the difficulties caused by the multireference nature of spatially degenerate states by rather than utilizing the ground state instead taking a nondegenerate excited state with desirable properties as the reference for the TDDFT calculation. The scope and practical application of the method are discussed. Like all open-shell TDDFT calculations this method at times suffers from the inability to produce transitions to states that are eigenfunctions of the total spin operator. A technique for alleviating this difficulty to some extent is proposed. The applicability and accuracy of the TRICKS-TDDFT method is demonstrated through example calculations of several d(1) and d(2) transition metal complexes with tetrahedral and octahedral symmetries. For the most part, the results of these calculations are similar in quality to to those obtained from standard TDDFT calculations.