Volume 123, Issue 14, 08 October 2005
 ARTICLES

 Theoretical Methods and Algorithms

Timedependent quasirelativistic densityfunctional theory based on the zerothorder regular approximation
View Description Hide DescriptionA timedependent quasirelativistic densityfunctional theory for excitation energies of systems containing heavy elements is developed, which is based on the zerothorder regular approximation (ZORA) for the relativistic Hamiltonian and a noncollinear form for the adiabatic exchangecorrelation kernel. To avoid the gauge dependence of the ZORA Hamiltonian a model atomic potential, instead of the full molecular potential, is used to construct the ZORA kinetic operator in groundstate calculations. As such, the ZORA kinetic operator no longer responds to changes in the density in response calculations. In addition, it is shown that, for closedshell ground states, timereversal symmetry can be employed to simplify the eigenvalue equation into an approximate form that is similar to that of timedependent nonrelativistic densityfunctional theory. This is achieved by invoking an independentparticle approximation for the induced density matrix. The resulting theory is applied to investigate the global potentialenergy curves of lowlying  and coupled electronic states of the AuH molecule. The derived spectroscopic parameters, including the adiabatic and vertical excitation energies, equilibrium bond lengths, harmonic and anharmonic vibrational constants, fundamental frequencies, and dissociation energies, are in good agreement with those of timedependent fourcomponent relativistic densityfunctional theory and ab initio multireference secondorder perturbation theory. Nonetheless, this twocomponent relativistic version of timedependent densityfunctional theory is only moderately advantageous over the fourcomponent one as far as computational efforts are concerned.

Constantpressure simulations with dissipative particle dynamics
View Description Hide DescriptionDissipative particle dynamics (DPD) is a mesoscopic simulation method for studying hydrodynamic behavior of complex fluids. Ideally, a mesoscopic model should correctly represent the thermodynamic and hydrodynamicproperties of a real system beyond certain length and time scales. Traditionally defined DPD quite successfully mimics hydrodynamics but is not flexible enough to accurately describe the thermodynamics of a real system. The socalled multibody DPD (MDPD) is a pragmatic extension of the classical DPD that allows one to prescribe the thermodynamic behavior of a system with only a small performance impact. In an earlier paper [S. Y. Trofimov, E. L. F. Nies, and M. A. J. Michels, J. Chem. Phys.117, 9383 (2002)] we much improved the accuracy of the MDPD model for strongly nonideal systems, which are of most practical interest. The ability to correctly reproduce the equation of state of realistic systems in turn makes simulations at constant pressure sensible and useful. This situation of constantpressure conditions is very common in experimental studies of (soft) condensed matter but has so far remained unexplored with the traditional DPD. Here, as a proof of concept, we integrate a modified version of the Andersen barostat into our improved MDPD model and make an evaluation of the performance of the new model on a set of single and multicomponent systems. The modification of the barostat suppresses the “unphysical” volume oscillations after a sudden pressure change and simplifies the equilibration of the system.

MMM1D: A method for calculating electrostatic interactions in onedimensional periodic geometries
View Description Hide DescriptionWe present a new method to accurately calculate the electrostatic energy and forces on charges in a system with periodic boundary conditions in one of three spatial dimensions. We transform the Coulomb sum via a convergence factor into a series of fast decaying functions similar to the Lekner method. Rigorous error bounds for the energies and the forces are derived and numerically verified. The method has a computational complexity of , but is faster and easier to use than previously reported methods.

Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: “Umbrella integration”
View Description Hide DescriptionWe present a method to analyze biased moleculardynamics and Monte Carlo simulations, also known as umbrella sampling. In the limiting case of a strong bias, this method is equivalent to thermodynamic integration. It employs only quantities with easily controllable equilibration and greatly reduces the statistical errors compared to the standard weighted histogram analysis method. We show the success of our approach for two examples, one analytic function, and one biological system.

Calculation of excitation energies of openshell molecules with spatially degenerate ground states. I. Transformed reference via an intermediate configuration KohnSham densityfunctional theory and applications to and systems with octahedral and tetrahedral symmetries
View Description Hide DescriptionA method for calculating the UVvis spectra of molecules with spatially degenerate ground states using timedependent densityfunctional theory (TDDFT) is proposed. The new transformed reference via an intermediate configuration KohnSham TDDFT (TRICKSTDDFT) 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 openshell 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 TRICKSTDDFT method is demonstrated through example calculations of several and 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.

Nonadiabatic surface hopping HermanKluk semiclassical initial value representation method revisited: Applications to Tully’s three model systems
View Description Hide DescriptionThe nonadiabaticsurface hopping HermanKluk (HK) semiclassical initial value representation (SCIVR) method for nonadiabatic problems is reformulated. The method has the same spirit as Tully’s surface hopping technique [J. Chem. Phys.93, 1061 (1990)] and almost keeps the same structure as the original singlesurface HK SCIVR method except that trajectories can hop to other surfaces according to the hopping probabilities and phases, which can be easily integrated along the paths. The method is based on a rather general nonadiabatic semiclassical surface hopping theory developed by Herman [J. Chem. Phys.103, 8081 (1995)], which has been shown to be accurate to the first order in and through all the orders of the nonadiabatic coupling amplitude. Our simulation studies on the three model systems suggested by Tully demonstrate that this method is practical and capable of describing nonadiabatic quantum dynamics for various coupling situations in very good agreement with benchmark calculations.

Adaptive local refinement of the electron density, oneparticle density matrices, and electron orbitals by hierarchical wavelet decomposition
View Description Hide DescriptionThe common experience that the distribution and interaction of electrons widely vary by scanning over various parts of a molecule is incorporated in the atomicorbital expansion of wave functions. The application of Gaussiantype atomic orbitals suffers from the poor representation of nuclear cusps, as well as asymptotic regions, whereas Slatertype orbitals lead to unmanageable computational difficulties. In this contribution we show that using the toolkit of wavelet analysis it is possible to find an expansion of the electron density and density operators which is sufficiently precise, but at the same time avoids unnecessary complications at smooth and slightly detailed parts of the system. The basic idea of wavelet analysis is a coarse description of the system on a rough grid and a consecutive application of refinement steps by introducing new basis functions on a finer grid. This step could highly increase the number of required basis functions, however, in this work we apply an adaptive refinement only in those regions of the molecule, where the details of the electron structure require it. A molecule is split into three regions with different detail characteristics. The neighborhood of a nuclear cusp is extremely well represented by a moderately fine wavelet expansion; the domains of the chemical bonds are reproduced at an even coarser resolution level, whereas the asymptotic tails of the electron structure are surprisingly precise already at a grid distance of The strict localization property of waveletfunctions leads to an especially simple calculation of the electron integrals.

On the accuracy of correlationenergy expansions in terms of local increments
View Description Hide DescriptionThe incremental scheme for obtaining the energetic properties of extended systems from wavefunctionbased ab initio calculations of small (embedded) building blocks, which has been applied to a variety of van der Waalsbound, ionic, and covalent solids in the past few years, is critically reviewed. Its accuracy is assessed by means of model calculations for finite systems, and the prospects for applying it to delocalized systems are given.

An idealized model for nonequilibrium dynamics in molecular systems
View Description Hide DescriptionThe nonequilibrium dynamics of highly nonlinear and multidimensional systems can give rise to emergent chemical behavior which can often be tracked using lowdimensional order parameters such as a reaction path. Such behavior cannot be readily surmised by stationary projected stochastic representations such as those described by the Langevin equation or the generalized Langevin equation (GLE). The irreversible generalized Langevin equation (iGLE) contains a nonstationary friction kernel that in certain limits reduces to the GLE with spacedependent friction. For more general forms of the friction kernel, the iGLE was previously shown to be the projection of a mechanical system with a timedependent Hamiltonian [R. Hernandez, J. Chem. Phys.110, 7701 (1999)]. In the present work, the corresponding open Hamiltonian system is shown to be amenable to numerical integration despite the presence of a nonlocal term. Simulations of this mechanical system further confirm that the time dependence of the observed total energy and the correlations of the solvent force are in precise agreement with the projected iGLE. This extended nonstationary Hamiltonian is thus amenable to the study of nonequilibrium bounds and fluctuation theorems.

Phase diagram of softly repulsive systems: The Gaussian and inversepowerlaw potentials
View Description Hide DescriptionWe redraw, using stateoftheart methods for freeenergy calculations, the phase diagrams of two reference models for the liquid state: the Gaussian and inversepowerlaw repulsive potentials. Notwithstanding the different behaviors of the two potentials for vanishing interparticle distances, their thermodynamic properties are similar in a range of densities and temperatures, being ruled by the competition between the bodycenteredcubic (bcc) and facecenteredcubic (fcc) crystalline structures and the fluid phase. We confirm the existence of a reentrant bcc phase in the phase diagram of the Gaussiancore model, just above the triple point. We also trace the bccfcc coexistence line of the inversepowerlaw model as a function of the power exponent and relate the common features in the phase diagrams of such systems to the softness degree of the interaction.

Correlation energy functionals dependent on an effective number of electrons: Charged species and equilibrium geometries
View Description Hide DescriptionRecently proposed spindependent and spinindependent correlationenergy functionals [PérezJiménez et al., J. Chem. Phys.116, 10571 (2002)] based on an effective number of electrons are extended to deal with charged systems. By introducing the concept of an effective atomic number analogous to , the spindependent functional in combination with Becke’s exchange [Becke, Phys. Rev. A38, 3098 (1988)] yields a mean absolute error (MAE) of for the 88 ionization potentials and 58 electron affinities included in the extended G2 set, and a MAE of for the 312 data comprising the above plus the 148 enthalpies of formation of the extended G2 set and the 18 total energies of the neutral atoms H through Ar. Geometry optimizations performed on the 53 molecules of the G21 test set with the above combination of exchange and correlation functionals yield MAEs of 0.017 Å and 1.5° for the 68 bond lengths and 29 angles analyzed as compared with the experimental estimates.

Firstprinciples matrix calculations of doubleionization energy spectra of atoms and molecules
View Description Hide DescriptionStrong electron correlation plays an important role in the determination of double ionization energy, which is required for removing or adding two electrons, particularly in smallsized systems. Starting from the stateoftheart approximation, we evaluate the particleparticle ladder diagrams up to the infinite order by solving the BetheSalpeter equation of the matrix theory to calculate the doubleionization energy spectra of atoms and molecules (Be, Mg, Ca, Ne, Ar, Kr, CO, , , , and ) from first principles. The ladder diagrams up to the infinite order are significant to calculations of doubleionization energy spectra. The present results are in good agreement with available experimental data as well as the previous calculations using, e.g., the configurationinteraction method.

A study of the partitioning of the firstorder reduced density matrix according to the theory of atoms in molecules
View Description Hide DescriptionThis work describes a simple spatial decomposition of the firstorder reduced density matrix corresponding to an electron system into firstorder density matrices, each of them associated to an atomic domain defined in the theory of atoms in molecules. A study of the representability of the density matrices arisen from this decomposition is reported and analyzed. An appropriate treatment of the eigenvectors of the matrices defined over atomic domains or over unions of these domains allows one to describe satisfactorily molecular properties and chemical bondings within a determined molecule and among its fragments. Numerical determinations, performed in selected molecules, confirm the reliability of our proposal.

Overcoming stiffness in stochastic simulation stemming from partial equilibrium: A multiscale Monte Carlo algorithm
View Description Hide DescriptionIn this paper the problem of stiffness in stochastic simulation of singularly perturbed systems is discussed. Such stiffness arises often from partial equilibrium or quasisteadystate type of conditions. A multiscale Monte Carlo method is discussed that first assesses whether partial equilibrium is established using a simple criterion. The exact stochastic simulation algorithm (SSA) is next employed to sample among fast reactions over short time intervals (microscopic time steps) in order to compute numerically the proper probability distribution function for sampling the slow reactions. Subsequently, the SSA is used to sample among slow reactions and advance the time by large (macroscopic) time steps. Numerical examples indicate that not only long times can be simulated but also fluctuations are properly captured and substantial computational savings result.

Molecular ionization energies and ground and ionicstate properties using a nonDyson electron propagator approach
View Description Hide DescriptionAn earlier proposed propagator method for the treatment of molecular ionization is tested in first applications. The method referred to as the nonDyson thirdorder algebraicdiagrammatic construction [nDADC(3)] approximation for the electron propagator represents a computationally promising alternative to the existing Dyson ADC(3) method. The advantage of the nDADC(3) scheme is that the electronic parts of the oneparticle Green’s function are decoupled from each other and the corresponding equations can be solved separately. For a test of the method the nDADC(3) results for the vertical ionization transitions in , CO, CS, , , , HF, , and Ne are compared with available experimental and theoretical data including results of full configuration interaction (FCI) and coupled cluster computations. The mean error of the nDADC(3) ionization energies relative to the experimental and FCI results is about . The nDADC(3) method, scaling as with the number of orbitals, requires the solution of a relatively simple Hermitian eigenvalue problem. The method renders access to groundstate properties such as dipole moments. Moreover, also oneelectron properties of electron states can now be studied as a consequence of a specific intermediatestate representation (ISR) formulation of the nDADC approach. Corresponding secondorder ISR equations are presented.

Electrondensity topology in molecular systems: Paired and unpaired densities
View Description Hide DescriptionThis work studies the partitioning of the electron density into two contributions which are interpreted as the paired and the effectively unpaired electron densities. The topological features of each density field as well as of the total density are described localizing the corresponding critical points in simple selected molecules (local formalism). The results show that unpaired electrondensity concentrations occur out of the topological bonding regions whereas the paired electron densities present accumulations inside those regions. A comparison of these results with those arising from population analysis techniques (nonlocal or integrated formalisms) is reported.

Secondharmonic generation of solvated molecules using multiconfigurational selfconsistentfield quadratic response theory and the polarizable continuum model
View Description Hide DescriptionWe present the first implementation of the quadratic response function for multiconfigurational selfconsistentfield wave functions of solvated molecules described by a polarizable continuum model employing a moleculeshaped cavity. We apply the methodology to the first hyperpolarizability and, in particular, the secondharmonic generation process for a series of conjugated pushpull oligomers, as well as for paranitroaniline. The effect of solvation on the dispersion of the hyperpolarizability and the change in the hyperpolarizability for increasing chain length of the oligomers in vacuum and in solution is considered. The effect of a correlated description is analyzed by comparing the HartreeFock hyperpolarizabilities to the multiconfigurational selfconsistentfield hyperpolarizabilities. The effect of geometry relaxation in the solvent on the properties of the solvated molecules are also investigated.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Parallel tempering simulations of the 13center LennardJones dipoledipole cluster
View Description Hide DescriptionWe investigate the thermodynamic behavior of the thirteen center uniform LennardJones dipoledipole cluster for a wide range of dipole moment strengths. We find a relatively wide range of potential parameters where solidsolid coexistence manifests itself. Using structural characterization methods we determine the shape of the few isomers that contribute to the solidsolid coexistence region. The thermal distributions of the size of the net dipole moment are broad even at the coldest temperatures of the simulation where the cluster is solid.

A vacuum ultraviolet pulsed field ionizationphotoelectron study of cyanogen cation in the energy range of 13.2–15.9 eV^{a)}
View Description Hide DescriptionThe vacuum ultraviolet pulsed field ionizationphotoelectron and photoionization efficiency spectra of NCCN have been measured in the energy region of 13.25–17.75 eV. The analyses of these spectra have provided accurate ionizationenergy (IE) values of , , , and for the formation of in the , , , and states, respectively. The ionizationenergy value determined here indicates that the origin of the state lies lower in energy by 25 meV than previously reported. A set of spectroscopic parameters for has been calculated using high level ab initio calculations. The experimental spectra are found to consist of ionizing transitions populating the vibronic levels of , which consist of pure vibronic progressions, combination modes involving the symmetric CN stretch, the CC stretch, and even quanta of the antisymmetric CN stretch, and bending vibrations. These bands are identified with the guidance of the present ab initio calculations.

Density functional theory calculations for endohedral complexes of non cage with small guest molecules
View Description Hide DescriptionHybrid densityfunctional theory (B3LYP) calculations were carried out to determine the structures and energies of endohedral complexes of non with , CO, and LiH. It was demonstrated that the endohedral complexes of with the above three guest molecules are more stable than the corresponding complexes with . Furthermore, the interaction between and the inside or CO is negligible, but the formation of the complex is exothermic with a stabilization energy of . While the bond lengths of and CO changed a little when placed inside the cages, that of the LiH molecule increased and decreased inside and , respectively.