Parameterized local hybrid functionals from density-matrix similarity metrics

We recently proposed a real-space similarity metric comparing the Kohn-Sham one-particle density matrix to the local spin-density approximation model density matrix [Janesko and Scuseria, J. Chem. Phys. 127, 164117 (2007)]. This metric provides a useful ingredient for constructing local hybrid density functionals that locally mix exact exchange and semilocal density functional theory exchange. Here we present two lines of inquiry: An approximate similarity metric comparing exact versus generalized gradient approximation (GGA), exchange and parameterized mixing functions using these similarity metrics. This approach yields significantly improved thermochemistry, including GGA local hybrids whose thermochemical performance approaches GGA global hybrids.     

Generalized-gradient exchange-correlation hole obtained from a correlation factor ansatz

The Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy is employed as reference point for the construction of an angle-averaged exchange-correlation hole. First, we develop a new model for the PBE exchange hole. In contrast to the previous model [Ernzerhof and Perdew, J. Chem. Phys. 109, 3313 (1998)], it contains an atomic exchange hole, similar to the Becke-Roussel model [Becke and Roussel, Phys. Rev. A 39, 3761 (1989)]. A correlation factor, i.e., a function multiplying the exchange hole, is proposed that turns the exchange into an exchange-correlation hole. The correlation factor has a simple form and is determined through a number of known conditions that should be satisfied by a generalized-gradient exchange-correlation hole.     

A post-Hartree-Fock model of intermolecular interactions: inclusion of higher-order corrections

We have previously demonstrated that the dipole moment of the exchange hole can be used to derive intermolecular C(6) dispersion coefficients [J. Chem. Phys. 122, 154104 (2005)]. This was subsequently the basis for a novel post-Hartree-Fock model of intermolecular interactions [J. Chem. Phys. 123, 024101 (2005)]. In the present work, the model is extended to include higher-order dispersion coefficients C(8) and C(10). The extended model performs very well for prediction of intermonomer separations and binding energies of 45 van der Waals complexes. In particular, it performs twice as well as basis-set extrapolated MP2 theory for dispersion-bound complexes, with minimal computational cost.     

Density, structure, and dynamics of water: the effect of van der Waals interactions

It is known that ab initio molecular dynamics (AIMD) simulations of liquid water at ambient conditions, based on the generalized gradient approximation (GGA) to density functional theory (DFT), with commonly used functionals fail to produce structural and diffusive properties in reasonable agreement with experiment. This is true for canonical, constant temperature simulations where the density of the liquid is fixed to the experimental density. The equilibrium density, at ambient conditions, of DFT water has recently been shown by Schmidt et al. [J. Phys. Chem. B, 113, 11959 (2009)] to be underestimated by different GGA functionals for exchange and correlation, and corrected by the addition of interatomic pair potentials to describe van der Waals (vdW) interactions. In this contribution we present a DFT-AIMD study of liquid water using several GGA functionals as well as the van der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. As expected, we find that the density of water is grossly underestimated by GGA functionals. When a vdW-DF is used, the density improves drastically and the experimental diffusivity is reproduced without the need of thermal corrections. We analyze the origin of the density differences between all the functionals. We show that the vdW-DF increases the population of non-H-bonded interstitial sites, at distances between the first and second coordination shells. However, it excessively weakens the H-bond network, collapsing the second coordination shell. This structural problem is partially associated to the choice of GGA exchange in the vdW-DF. We show that a different choice for the exchange functional is enough to achieve an overall improvement both in structure and diffusivity.     

Dispersion interactions in room-temperature ionic liquids: results from a non-empirical density functional

The role of dispersion or van de Waals (VDW) interactions in imidazolium-based room-temperature ionic liquids is studied within the framework of density functional theory, using a recently developed non-empirical functional [M. Dion, H. Rydberg, E. Schro?der, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)], as efficiently implemented in the SIESTA code [G. Roma?n-Pe?rez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009)]. We present results for the equilibrium structure and lattice parameters of several crystalline phases, finding a general improvement with respect to both the local density (LDA) and the generalized gradient approximations (GGA). Similar to other systems characterized by VDW bonding, such as rare gas and benzene dimers as well as solid argon, equilibrium distances and volumes are consistently overestimated by ≈7%, compared to -11% within LDA and 11% within GGA. The intramolecular geometries are retained, while the intermolecular distances and orientations are significantly improved relative to LDA and GGA. The quality is superior to that achieved with tailor-made empirical VDW corrections ad hoc [M. G. Del Po?polo, C. Pinilla, and P. Ballone, J. Chem. Phys. 126, 144705 (2007)]. We also analyse the performance of an optimized version of this non-empirical functional, where the screening properties of the exchange have been tuned to reproduce high-level quantum chemical calculations [J. Klimes, D. Bowler, and A. Michaelides, J. Phys.: Condens. Matter 22, 074203 (2010)]. The results for solids are even better with volumes and geometries reproduced within 2% of experimental data. We provide some insight into the issue of polymorphism of [bmim][Cl] crystals, and we present results for the geometry and energetics of [bmim][Tf] and [mmim][Cl] neutral and charged clusters, which validate the use of empirical force fields.     

The importance of middle-range Hartree-Fock-type exchange for hybrid density functionals

Hybrid functionals are responsible for much of the utility of modern Kohn-Sham density functional theory. When rigorously applied to solid-state metallic and small band gap systems, however, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally challenging and introduces unphysical effects. This can be remedied by using a range-separated hybrid which only keeps short-range nonlocal exchange, as in the functional of Heyd et al. [J. Chem. Phys. 118, 8207 (2003)]. On the other hand, many molecular properties require full long-range nonlocal exchange, which can also be included by means of a range-separated hybrid such as the recently introduced LC-omegaPBE functional [O. A. Vydrov and G. E. Scuseria, J. Chem. Phys. 125, 234109 (2006)]. In this paper, we show that a three-range hybrid which mainly includes middle-range Hartree-Fock-type exchange and neglects long- and short-range Hartree-Fock-type exchange yields excellent accuracy for thermochemistry, barrier heights, and band gaps, emphasizing that the middle-range part of the 1/r potential seems crucial to accurately model these properties.     

Parallel algorithm for the computation of the Hartree-Fock exchange matrix: gas phase and periodic parallel ONX

In this paper we present an efficient parallelization of the ONX algorithm for linear computation of the Hartree-Fock exchange matrix [J. Chem. Phys. 106, 9708 (1997)]. The method used is based on the equal time (ET) partitioning recently introduced [J. Chem. Phys. 118, 9128 (2003)] and [J. Chem. Phys. 121, 6608 (2004)]. ET exploits the slow variation of the density matrix between self-consistent-field iterations to achieve load balance. The method is presented and some benchmark calculations are discussed for gas phase and periodic systems with up to 128 processors. The current parallel ONX code is able to deliver up to 77% overall efficiency for a cluster of 50 water molecules on 128 processors (2.56 processors per heavy atom) and up to 87% for a box of 64 water molecules (two processors per heavy atom) with periodic boundary conditions.     

Monte Carlo simulations of critical cluster sizes and nucleation rates of water

We have calculated the critical cluster sizes and homogeneous nucleation rates of water at temperatures and vapor densities corresponding to experiments by Wolk and Strey [J. Phys. Chem B 105, 11683 (2001)]. The calculations have been done with an expanded version of a Monte Carlo method originally developed by Vehkamaki and Ford [J. Chem. Phys. 112, 4193 (2000)]. Their method calculates the statistical growth and decay probabilities of molecular clusters. We have derived a connection between these probabilities and kinetic condensation and evaporation rates, and introduce a new way for the calculation of the work of formation of clusters. Three different interaction potential models of water have been used in the simulations. These include the unpolarizable SPC/E [J. Phys. Chem. 91, 6269 (1987)] and TIP4P [J. Chem. Phys. 79, 926 (1983)] models and a polarizable model by Guillot and Guissani [J. Chem. Phys. 114, 6720 (2001)]. We show that TIP4P produces critical cluster sizes and a temperature and vapor density dependence for the nucleation rate that agree well with the experimental data, although the magnitude of nucleation rate is constantly overestimated by a factor of 2 x 10(4). Guissani and Guillot's model is somewhat less successful, but both the TIP4P and Guillot and Guissani models are able to reproduce a much better experimental temperature dependency of the nucleation rate than the classical nucleation theory. Using SPC/E results in dramatically too small critical clusters and high nucleation rates. The water models give different average binding energies for clusters. We show that stronger binding between cluster molecules suppresses the decay probability of a cluster, while the growth probability is not affected. This explains the differences in results from different water models.     

Vibronic coupling in asymmetric bichromophores: Theory and application to diphenylmethane

The theory for modeling vibronic interactions in bichromophores was introduced in sixties by Witkowski and Moffitt [J. Chem. Phys. 33, 872 (1960)] and extended by Fulton and Gouterman [J. Chem. Phys. 35, 1059 (1961)]. The present work describes extension of this vibronic model to describe bichromophores with broken vibrational symmetry such as partly deuterated molecules. Additionally, the model is extended to include inter-chromophore vibrational modes. The model can treat multiple vibrational modes by employing Lanczos diagonalization procedure of sparse matrices. The developed vibronic model is applied to simulation of vibronic spectra of flexible bichromophore diphenylmethane and compared to high-resolution experimental spectra [J. A. Stearns, N. R. Pillsbury, K. O. Douglass, C. W. Mu?ller, T. S. Zwier, and D. F. Plusquellic, J. Chem. Phys. 129, 224305 (2008)].     

Recovering the Crooks equation for dynamical systems in the isothermal-isobaric ensemble: a strategy based on the equations of motion

The Crooks equation [Eq. (10) in J. Stat. Phys. 90, 1481 (1998)] relates the work done on a system during a nonequilibrium transformation to the free energy difference between the final and the initial state of the transformation. Recently, the authors have derived the Crooks equation for systems in the canonical ensemble thermostatted by the Nose-Hoover or Nose-Hoover chain method [P. Procacci et al., J. Chem. Phys. 125, 164101 (2006)]. That proof is essentially based on the fluctuation theorem by Evans and Searles [Adv. Phys. 51, 1529 (2002)] and on the equations of motion. Following an analogous approach, the authors derive here the Crooks equation in the context of molecular dynamics simulations of systems in the isothermal-isobaric (NPT) ensemble, whose dynamics is regulated by the Martyna-Tobias-Klein algorithm [J. Chem. Phys. 101, 4177 (1994)]. Their present derivation of the Crooks equation correlates to the demonstration of the Jarzynski identity for NPT systems recently proposed by Cuendet [J. Chem. Phys. 125, 144109 (2006)].     

Local response dispersion method. II. Generalized multicenter interactions

Recently introduced local response dispersion method [T. Sato and H. Nakai, J. Chem. Phys. 131, 224104 (2009)], which is a first-principles alternative to empirical dispersion corrections in density functional theory, is implemented with generalized multicenter interactions involving both atomic and atomic pair polarizabilities. The generalization improves the asymptote of intermolecular interactions, reducing the mean absolute percentage error from about 30% to 6% in the molecular C(6) coefficients of more than 1000 dimers, compared to experimental values. The method is also applied to calculations of potential energy curves of molecules in the S22 database [P. Jure?ka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The calculated potential energy curves are in a good agreement with reliable benchmarks recently published by Molnar et al. [J. Chem. Phys. 131, 065102 (2009)]. These improvements are achieved at the price of increasing complexity in the implementation, but without losing the computational efficiency of the previous two-center (atom-atom) formulation. A set of different truncations of two-center and three- or four-center interactions is shown to be optimal in the cost-performance balance.     

Polarizable and flexible model for ethanol

A polarizable, flexible model for ethanol is obtained based on an extensive series of B3LYP/6-311++G(d,p) calculations and molecular dynamics simulations. The ethanol model includes electric-field dependence in both the atomic charges and the intramolecular degrees of freedom. Field-dependent intramolecular potentials have been attempted only once previously, for OH and HH stretches in water [P. Cicu et al., J. Chem. Phys. 112, 8267 (2000)]. The torsional potential involving the hydrogen-bonding hydrogen in ethanol is found to be particularly field sensitive. The methodology for developing field-dependent potentials can be readily generalized to other molecules and is discussed in detail. Molecular dynamics simulations of bulk ethanol are performed and the results are assessed based on comparisons with the self-diffusion coefficient [N. Karger et al., J. Chem. Phys. 93, 3437 (1990)], dielectric constant [J. T. Kindt and C. A. Schmuttenmaer, J. Phys. Chem. 100, 10373 (1996)], enthalpy of vaporization [R. C. Wilhoit and B. J. Zwolinski, J. Phys. Chem. Ref. Data, Suppl. 2, 2 (1973)], and experimental interatomic distributions [C. J. Benmore and Y. L. Loh, J. Chem. Phys. 112, 5877 (2000)]. The simultaneous variation of the atomic charges and the intramolecular potentials requires modified equations of motion and a multiple time step algorithm has been implemented to solve these equations. The article concludes with a discussion of the bulk structure and properties with an emphasis on the hydrogen bonding network.     

Higher excitations for an exponential multireference wavefunction Ansatz and single-reference based multireference coupled cluster Ansatz: application to model systems H(4), P(4), and BeH(2)

This article reports on the convergence of the exponential multireference wavefunction Ansatz (MRexpT) [J. Chem. Phys. 123, 84102 (2005)] and the single-reference based multireference coupled cluster Ansatz [J. Chem. Phys. 94, 1229 (1991)] with respect to higher cluster excitations. The approaches are applied to the H(4), P(4), and BeH(2) model systems according to the recently published analysis by Evangelista et al. [J. Chem. Phys. 125, 154113 (2006)]. The results show both MRexpT and SRMRCC to be highly accurate although SRMRCC shows problems due to its lack of Fermi vacuum invariance (symmetry breaking).     

The Vliegenthart-Lekkerkerker relation: the case of the Mie-fluids

The Vliegenthart-Lekkerkerker relation for the second virial coefficient value at the critical temperature found in the work of Vliegenthart and Lekkerkerker [J. Chem. Phys. 112, 5364 (2000)] is discussed in connection with the scale invariant mean-field approach proposed by Kulinskii and Bulavin [J. Chem. Phys. 133, 134101 (2010)]. We study the case of the Mie-class potentials, which is widely used in simulations of the phase equilibrium of the fluids. It is shown that due to the homogeneity property of the Mie-class potentials it is possible to connect the loci of the fluids with these model potentials in different dimensions.     

Exchange-hole dipole moment and the dispersion interaction revisited

We have recently introduced a model of the dispersion interaction based on the position-dependent dipole moment of the exchange hole [J. Chem. Phys. 122, 154104 (2005)]. The original derivation, involving simple dipole-induced-dipole electrostatics, was somewhat heuristic, however, and lacking in rigor. Here we present a much more satisfying derivation founded on second-order perturbation theory in the closure approximation and a semiclassical evaluation of the relevant interaction integrals. Expressions for C6, C8, and C10 dispersion coefficients are obtained in a remarkably straightforward manner. Their values agree very well with ab initio reference data on dispersion coefficients between the atoms H, He, Ne, Ar, Kr, and Xe. We also highlight the importance of the exchange-hole contribution to the dispersion coefficients, especially to C6.     

Symmetry broken self-consistent field approximation for coupled oscillators

A self-consistent field approximation allowing for a change of coordinates is applied to a model of two coupled oscillators considered by Davis and Heller [J. Chem. Phys. 75 , 246 (1981)]. The model accounts well for the unsymmetrical nonstationary states involved in the quantum dynamical tunneling phenomenon.     

Improved constraint satisfaction in a simple generalized gradient approximation exchange functional

Though there is fevered effort on orbital-dependent approximate exchange-correlation functionals, generalized gradient approximations, especially the Perdew-Burke-Ernzerhof (PBE) form, remain the overwhelming choice in calculations. A simple generalized gradient approximation (GGA) exchange functional [A. Vela, V. Medel, and S. B. Trickey, J. Chem. Phys. 130, 244103 (2009)] was developed that improves substantially over PBE in energetics (on a typical test set) while being almost as simple in form. The improvement came from constraining the exchange enhancement factor to be below the Lieb-Oxford bound for all but one value of the exchange dimensionless gradient, s, and to go to the uniform electron gas limit at both s = 0 and s → ∞. Here we discuss the issue of asymptotic constraints for GGAs and show that imposition of the large s constraint, lim(s→∞)s(1/2)F(xc)(n,s)<∞, where F(xc)(n, s) is the enhancement factor and n is the electron density, upon the Vela-Medel-Trickey (VMT) exchange functional yields modest further improvement. The resulting exchange functional, denoted VT{8,4}, is only slightly more complicated than VMT and easy to program. Additional improvement is obtained by combining VT{8,4} or VMT exchange with the Lee-Yang-Parr correlation functional. Extensive computational results on several datasets are provided as verification of the overall performance gains of both versions.     

A semiclassical hybrid approach to many particle quantum dynamics

We analytically derive a correlated approach for a mixed semiclassical many particle dynamics, treating a fraction of the degrees of freedom by the multitrajectory semiclassical initial value method of Herman and Kluk [Chem. Phys. 91, 27 (1984)] while approximately treating the dynamics of the remaining degrees of freedom with fixed initial phase space variables, analogously to the thawed Gaussian wave packet dynamics of Heller [J. Chem. Phys. 62, 1544 (1975)]. A first application of this hybrid approach to the well studied Secrest-Johnson [J. Chem. Phys. 45, 4556 (1966)] model of atom-diatomic collisions is promising. Results close to the quantum ones for correlation functions as well as scattering probabilities could be gained with considerably reduced numerical effort as compared to the full semiclassical Herman-Kluk approach. Furthermore, the harmonic nature of the different degrees of freedom can be determined a posteriori by comparing results with and without the additional approximation.