Reconciling semiclassical and Bohmian mechanics. III. Scattering states for continuous potentials

In a previous paper [B. Poirier, J. Chem. Phys. 121, 4501 (2004)] a unique bipolar decomposition psi = psi1 + psi2 was presented for stationary bound states Psi of the one-dimensional Schrodinger equation, such that the components psi1 and psi2 approach their semiclassical WKB analogs in the large-action limit. The corresponding bipolar quantum trajectories, as defined in the usual Bohmian mechanical formulation, are classical-like and well behaved, even when Psi has many nodes or is wildly oscillatory. A modification for discontinuous potential stationary scattering states was presented in a second, companion paper [C. Trahan and B. Poirier, J. Chem. Phys.124, 034115 (2006), previous paper], whose generalization for continuous potentials is given here. The result is an exact quantum scattering methodology using classical trajectories. For additional convenience in handling the tunneling case, a constant-velocity-trajectory version is also developed.     

Reconciling semiclassical and Bohmian mechanics. II. Scattering states for discontinuous potentials

In a previous paper [B. Poirier, J. Chem. Phys. 121, 4501 (2004)] a unique bipolar decomposition, psi = psi1 + psi2, was presented for stationary bound states Psi of the one-dimensional Schrodinger equation, such that the components psi1 and psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well behaved, even when psi has many nodes or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step potential, and square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a companion paper [C. Trahan and B. Poirier, J. Chem. Phys. 124, 034116 (2006), following paper].     

Rovibrational spectroscopy calculations of neon dimer using a phase space truncated Weyl-Heisenberg wavelet basis

In a series of earlier articles [B. Poirier J. Theor. Comput. Chem. 2, 65 (2003); B. Poirier and A. Salam J. Chem. Phys. 121, 1690 (2004); B. Poirier and A. Salam J. Chem. Phys. 121, 1740 (2004)], a new method was introduced for performing exact quantum dynamics calculations in a manner that formally defeats exponential scaling with system dimensionality. The method combines an optimally localized, orthogonal Weyl-Heisenberg wavelet basis set with a simple phase space truncation scheme, and has already been applied to model systems up to 17 degrees of freedom (DOF's). In this paper, the approach is applied for the first time to a real molecular system (neon dimer), necessitating the development of an efficient numerical scheme for representing arbitrary potential energy functions in the wavelet representation. All bound rovibrational energy levels of neon dimer are computed, using both one DOF radial coordinate calculations and a three DOF Cartesian coordinate calculation. Even at such low dimensionalities, the approach is found to be competitive with another state-of-the-art method applied to the same system [J. Montgomery and B. Poirier J. Chem. Phys. 119, 6609 (2003)].     

Reconciling semiclassical and Bohmian mechanics: IV. Multisurface dynamics

In previous articles (J. Chem. Phys. 2004, 121, 4501; 2006, 124, 034115; 2006, 124, 034116) a bipolar counter-propagating wave decomposition, Psi = Psi+ + Psi-, was presented for stationary states Psi of the one-dimensional Schr?dinger equation, such that the components Psi+/- approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes or is wildly oscillatory. In this paper, the method is generalized for multisurface scattering applications and applied to several benchmark problems. A natural connection is established between intersurface transitions and (+ <--> -) transitions.     

The use of atomic intrinsic polarizabilities in the evaluation of the dispersion energy

The recent approach presented by Becke and Johnson [J. Chem. Phys. 122, 154104 (2005); 123, 024101 (2005); 123, 154101 (2005); 124, 174104 (2006); 124, 014104 (2006)] for the evaluation of dispersion interactions based on the properties of the exchange-hole dipole moment is combined with a Hirshfeld-type partitioning for the molecular polarizabilities into atomic contributions, recently presented by some of the present authors [A. Krishtal et al., J. Chem. Phys. 125, 034312 (2006)]. The results on a series of nine dimers, involving neon, methane, ethene, acetylene, benzene, and CO(2), taken at their equilibrium geometry, indicate that when the C(6), C(8), and C(10) terms are taken into account, the resulting dispersion energies can be obtained deviating 3% or 8% from high level literature data [E. R. Johnson and A. D. Becke, J. Chem. Phys. 124, 174104 (2006)], without the use of a damping function, the only outlier being the parallel face-to-face benzene dimer.     

Effect of Coulomb interactions on the vibronic couplings in C60(-)

Vibronic couplings in C(60)(-) anion are discussed on the basis of the concept of the vibronic coupling density (VCD) [T. Sato, K. Tokunaga, and K. Tanaka, J. Chem. Phys. 124, 024314 (2006); K. Tokunaga, T. Sato, and K. Tanaka, J. Chem. Phys. 124, 154303 (2006); and T. Sato, K. Tokunaga, and K. Tanaka, J. Phys. Chem. A 112, 758 (2008)]. The VCD analysis clearly reveals that the coupling to the bending h(g)(2) mode is weaker than the coupling to the stretching h(g)(7) and h(g)(8) modes. For the vibronic couplings with the stretching modes, polarizations of the electron density difference on the bonds play a crucial role in the vibronic couplings. Such a polarized electron density difference appears as a result of the Coulomb interactions between the electrons in the lowest unoccupied molecular orbital and relevant doubly-occupied orbitals.     

Semiempirical hybrid functional with improved performance in an extensive chemical assessment

It is demonstrated that there is still scope for improvement in the quality of conventional, semiempirical hybrid exchange-correlation functionals in density-functional theory. A new functional, denoted B97-3, is determined from a fit to eight chemical properties (316 data points). For a series of 25 chemical assessments (850 data points) including 17 assessments and 10 chemical properties absent from the fitting data, B97-3 provides the lowest or joint-lowest mean absolute error on 15 occasions, compared to 6, 5, and 4 occasions for B3LYP, PBE0, and B97-2, respectively [A. D. Becke, J. Chem. Phys. 98, 5648 (1993); M. Ernzerhof and G. E. Scuseria, J. Chem. Phys. 110, 5029 (1999); C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999); P. J. Wilson, T. J. Bradley, and D. J. Tozer, J. Chem. Phys. 115, 9233 (2001)]. Mean absolute errors from B97-3 are, on average, 21%, 18%, and 12% smaller than from these three functionals. The most notable improvements are obtained for classical reaction barriers, where the error reductions are 60%, 54%, and 27%.     

The AM05 density functional applied to solids

We show that the AM05 functional [Armiento and Mattsson, Phys. Rev. B 72, 085108 (2005)] has the same excellent performance for solids as the hybrid density functionals tested in Paier et al. [J. Chem. Phys. 124, 154709 (2006); 125, 249901 (2006)]. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree-Fock hybrid calculations are typically an order of magnitude slower than local or semilocal density functionals such as AM05, which is of a regular semilocal generalized gradient approximation form. The performance of AM05 is on average found to be superior to selecting the best of local density approximation and PBE for each solid. By comparing data from several different electronic-structure codes, we have determined that the numerical errors in this study are equal to or smaller than the corresponding experimental uncertainties.     

Diffusion in linear porous media with periodic entropy barriers: A tube formed by contacting spheres

The problem of transport in quasi-one-dimensional periodic structures has been studied recently by several groups [D. Reguera et al., Phys. Rev. Lett.96, 130603 (2006); P. S. Burada et al., Phys. Rev. E75, 051111 (2007); B. Q. Ai and L. G. Liu, ibid.74, 051114 (2006); B. Q. Ai et al., ibid.75, 061126 (2007); B. Q. Ai and L. G. Liu, J. Chem. Phys.126, 204706 (2007); 128, 024706 (2008); E. Yariv and K. D. Dorfman, Phys. Fluids19, 037101 (2007); N. Laachi et al., Europhys. Lett.80, 50009 (2007); A. M. Berezhkovskii et al., J. Chem. Phys.118, 7146 (2003); 119, 6991 (2003)]. Using the concept of "entropy barrier" [R. Zwanzig, J. Phys. Chem.96, 3926 (1992)] one can classify such structures based on the height of the entropy barrier. Structures with high barriers are formed by chambers, which are weakly connected with each other because they are connected by small apertures. To escape from such a chamber a diffusing particle has to climb a high entropy barrier to find an exit that takes a lot of time [I. V. Grigoriev et al., J. Chem. Phys.116, 9574 (2002)]. As a consequence, the particle intrachamber lifetime tau(esc) is much larger than its intrachamber equilibration time, tau(rel), tau(esc)>tau(rel). When the aperture is not small enough, the intrachamber escape and relaxation times are of the same order and the hierarchy fails. This is the case of low entropy barriers. Transport in this case is analyzed in the works of Schmid and co-workers, Liu and co-workers, and Dorfman and co-workers, while the work of Berezhkovskii et al. is devoted to diffusion in the case of high entropy barriers.     

Computation of methodology-independent single-ion solvation properties from molecular simulations. IV. Optimized Lennard-Jones interaction parameter sets for the alkali and halide ions in water

The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions and treatment of electrostatic interactions used during these simulations. However, as shown recently [M. A. Kastenholz and P. H. Hu?nenberger, J. Chem. Phys. 124, 224501 (2006); M. M. Reif and P. H. Hu?nenberger, J. Chem. Phys. 134, 144103 (2010)], the application of appropriate correction terms permits to obtain methodology-independent results. The corrected values are then exclusively characteristic of the underlying molecular model including in particular the ion-solvent van der Waals interaction parameters, determining the effective ion size and the magnitude of its dispersion interactions. In the present study, the comparison of calculated (corrected) hydration free energies with experimental data (along with the consideration of ionic polarizabilities) is used to calibrate new sets of ion-solvent van der Waals (Lennard-Jones) interaction parameters for the alkali (Li(+), Na(+), K(+), Rb(+), Cs(+)) and halide (F(-), Cl(-), Br(-), I(-)) ions along with either the SPC or the SPC/E water models. The experimental dataset is defined by conventional single-ion hydration free energies [Tissandier et al., J. Phys. Chem. A 102, 7787 (1998); Fawcett, J. Phys. Chem. B 103, 11181] along with three plausible choices for the (experimentally elusive) value of the absolute (intrinsic) hydration free energy of the proton, namely, ΔG(hyd)(?)[H(+)] = -1100, -1075 or -1050 kJ mol(-1), resulting in three sets L, M, and H for the SPC water model and three sets L(E), M(E), and H(E) for the SPC/E water model (alternative sets can easily be interpolated to intermediate ΔG(hyd)(?)[H(+)] values). The residual sensitivity of the calculated (corrected) hydration free energies on the volume-pressure boundary conditions and on the effective ionic radius entering into the calculation of the correction terms is also evaluated and found to be very limited. Ultimately, it is expected that comparison with other experimental ionic properties (e.g., derivative single-ion solvation properties, as well as data concerning ionic crystals, melts, solutions at finite concentrations, or nonaqueous solutions) will permit to validate one specific set and thus, the associated ΔG(hyd)(?)[H(+)] value (atomistic consistency assumption). Preliminary results (first-peak positions in the ion-water radial distribution functions, partial molar volumes of ionic salts in water, and structural properties of ionic crystals) support a value of ΔG(hyd)(?)[H(+)] close to -1100 kJ·mol(-1).     

Exact analytical evaluation of time dependent transmission coefficient from the method of reactive flux for an inverted parabolic barrier

The paper demonstrates an elegant way of combining the normal mode analysis and the method of reactive flux to evaluate the time dependent transmission coefficient for a classical particle coupled to a set of harmonic oscillators, surmounting a one dimensional barrier. The author's analysis reproduces the results of Kohen and Tannor [J. Chem. Phys. 103, 6013 (1995)] and Bao [J. Chem. Phys. 124, 114103 (2006)]. Moreover the use of normal mode analysis has a better physical meaning.     

A dual-level state-specific time-dependent density-functional theory

A highly efficient new algorithm for time-dependent density-functional theory (TDDFT) calculations is presented. In this algorithm, a dual-level approach to speed up DFT calculations (Nakajima and Hirao, J Chem Phys 2006, 124, 184108) is combined with a state-specific (SS) algorithm for TDDFT (Chiba et al., Chem Phys Lett 2006, 420, 391). The dual-level SS-TDDFT algorithm was applied to excitation energy calculations of typical small molecules, the Q bands of the chlorophyll A molecule, the charge-transfer energy of the zincbacteriochlorin-bacteriochlorin model system, and the lowest-lying excitation of the circumcoronene molecule. As a result, it was found that the dual-level SS-TDDFT gave correct excitation energies with errors of 0.2-0.3 eV from the standard TDDFT approach, with much lower CPU times for various types of excitation energies of large-scale molecules.     

An efficient first-principle approach for electronic structures calculations of nanomaterials

An efficient parallel implementation has been realized for a recently proposed central insertion scheme (Jiang, Liu, Lu, Luo. J Chem Phys 2006, 124, 214711; J Chem Phys 2006, 125, 149902) that allows to calculate electronic structures of nanomaterials at various density functional theory levels. It has adopted the sparse-matrix format for Fock/Kohn-Sham and overlap matrices, as well as a combination of implicitly restarted Arnoldi methods (IRAM) and spectral transformation for computing selected eigenvalues/eigenvectors. A systematic error analysis and control for the proposed method has been provided based on a strict mathematical basis. The efficiency and applicability of the new implementation have been demonstrated by calculations of electronic structures of two different nanomaterials consisting of one hundred thousand electrons.     

The structure and binding energies of the van der Waals complexes of Ar and N2 with phenol and its cation, studied by high level ab initio and density functional theory calculations

We have investigated, using both ab initio and density functional theory methods, the minimum energy structures and corresponding binding energies of the van der Waals complexes between phenol and argon or the nitrogen molecule, and the corresponding complexes involving the phenol cation. Structures were obtained at the MP2 level using a large basis, and the corresponding energies were corrected for basis set superposition error (BSSE), higher order electron correlation effects, and for basis set size. The structures of the global minima were further refined for the effects of BSSE and the corresponding binding energies were evaluated. For each neutral species, we find only a single true minimum, pi bonded for argon and OH bonded for nitrogen. For both cationic species, we find that the OH-bonded complex is preferred over other minima which we have identified as having Ar or N(2) between exogeneous atoms. The ab initio calculations are generally in excellent agreement with experimental binding energies and rotational constants. We find that the B3LYP functional is particularly poor at describing these complexes, while a density functional theory (DFT) method with an empirical correction for dispersive interactions (DFT-D) is very successful, as are some of the new functionals proposed by Zhao and Truhlar [J. Phys. Chem. A 109, 5656 (2005); J. Chem. Theory Comput. 2, 1009 (2006); Phys. Chem. Chem. Phys. 7, 2701 (2005); J. Phys. Chem. A 108, 6908 (2004)]. Both the ab initio and DFT-D methods accurately predict the intermolecular vibrational modes.     

Comment on "Model of saturated lithium ammonia as a single-component liquid metal" [J. Chem. Phys. 124, 074702 (2006)

We demonstrate in this Comment that the theory of simple metals applied to the saturated Li-NH3 solution in the titled paper [U. Pinsook and S. Hannongbua, J. Chem. Phys.124, 074702 (2006)] should account for the peculiarities of the solution, namely, the high solvent polarizability and different energy scales for ion-ion and electron-electron interactions. Calculations not taking into account these peculiarities contradict the experimental phase diagram of the Li-NH3 solution.     

Development of transferable interaction potentials for water. V. Extension of the flexible, polarizable, Thole-type model potential (TTM3-F, v. 3.0) to describe the vibrational spectra of water clusters and liquid water

We present a new parametrization of the flexible, polarizable Thole-type model for water [J. Chem. Phys. 116, 5115 (2002); J. Phys. Chem. A 110, 4100 (2006)], with emphasis in describing the vibrational spectra of both water clusters and liquid water. The new model is able to produce results of similar quality with the previous versions for the structures and energetics of water clusters as well as structural and thermodynamic properties of liquid water evaluated with classical and converged quantum statistical mechanical atomistic simulations. At the same time it yields accurate redshifts for the OH vibrational stretches of both water clusters and liquid water.     

Statistical mechanical theory for steady state systems. VI. Variational principles

Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.     

Smart resolution replica exchange: an efficient algorithm for exploring complex energy landscapes

A coarse-grained representation of a condensed phase system can significantly reduce the number of system degrees of freedom, making coarse-grained simulations very computationally efficient. Moreover, coarse graining can smoothen the free energy landscape of the system. Thus coarse-grained dynamics is usually faster than its fully atomistic counterpart. In this work, the smart resolution replica exchange method is introduced that incorporates the information from coarse-grained simulations into atomistic simulations in order to accelerate the sampling of rough, complex atomistic energy landscapes. Within this methodology, interactions between particles are defined by a potential energy that interpolates between a fully atomistic potential and a fully coarse-grained effective potential according to a parameter lambda. Instead of exchanging the configurations from neighboring resolutions directly, as has been done in the resolution replica exchange methods [E. Lyman et al., Phys. Rev. Lett. 96, 028105 (2006); M. Christen and W. F. v. Gunsteren, J. Chem. Phys. 124, 154106 (2006)], the configuration described at the coarser resolution is first relaxed before an exchange is attempted, similar to the smart walking method [R. Zhou and B. J. Berne, J. Chem. Phys. 107, 9185 (1997)]. This approach greatly increases the acceptance ratio of exchange and only two replicas, one at the atomistic level and one at the coarse-grained level, are usually required (although more can be implemented if desired). This new method can approximately obtain the correct canonical sampling if the exchange interval is sufficiently large to allow the system to explore the local energy landscape. The method is demonstrated for a two-dimensional model system, where the ideal population distribution can be recovered, and also for an alanine polypeptide (Ala(15)) model with explicit water, where its native structure, an alpha helix, is obtained from the extended structure within 1 ns.