Three dimensional atom-diatom quantum reactive scattering calculations using absorbing potential: speed up of the propagation scheme

In this paper a new propagation scheme is proposed for atom-diatom reactive calculations using a negative imaginary potential (NIP) within a time independent approach. It is based on the calculation of a rotationally adiabatic basis set, the neglected coupling terms being re-added in the following step of the propagation. The results of this approach, which we call two steps rotationally adiabatic coupled states calculations (2-RACS), are compared to those obtained using the adiabatic DVR method (J. C. Light and Z. Bazic, J. Chem. Phys., 1987, 87, 4008; C. Leforestier, J. Chem. Phys., 1991, 94, 6388), to the NIP coupled states results of the team of Baer (D. M. Charutz, I. Last and M. Baer, J. Chem. Phys., 1997, 106, 7654) and to the exact results obtained by Zhang (J. Z. H. Zhang and W. H. Miller, J. Chem. Phys., 1989, 91, 1528) for the D + H(2) reaction. The example of implementation of our method of computation of the adiabatic basis will be given here in the coupled states approximation, as this method has proved to be very efficient in many cases and is quite fast.     

Unimolecular rovibrational bound and resonance states for large angular momentum: J=20 calculations for HO2

We explore the calculation of unimolecular bound states and resonances for deep-well species at large angular momentum using a Chebychev filter diagonalization scheme incorporating doubling of the autocorrelation function as presented recently by Neumaier and Mandelshtam [Phys. Rev. Lett. 86, 5031 (2001)]. The method has been employed to compute the challenging J=20 bound and resonance states for the HO2 system. The methodology has firstly been tested for J=2 in comparison with previous calculations, and then extended to J=20 using a parallel computing strategy. The quantum J-specific unimolecular dissociation rates for HO2-->H+O2 in the energy range from 2.114 to 2.596 eV have been reported for the first time, and comparisons with the results of Troe and co-workers [J. Chem. Phys. 113, 11019 (2000) Phys. Chem. Chem. Phys. 2, 631 (2000)] from statistical adiabatic channel method/classical trajectory calculations have been made. For most of the energies, the reported statistical adiabatic channel method/classical trajectory rate constants agree well with the average of the fluctuating quantum-mechanical rates. Near the dissociation threshold, quantum rates fluctuate more severely, but their average is still in agreement with the statistical adiabatic channel method/classical trajectory results.     

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.     

Electronic structure and spectrum of UO2 2+ and UO2Cl4 2-

A theoretical study is presented of the electronic spectra of the UO(2) (2+) and UO(2)Cl(4) (2-) ions, based on multiconfigurational perturbation theory (CASSCF/CASPT2), combined with a recently developed method to treat spin-orbit coupling [P.-A. Malmqvist et al., Chem. Phys. Lett. 357, 230 (2002); B. O. Roos and P.-A. Malmqvist, Phys. Chem. Chem. Phys. 6, 2919 (2004)]. The results are compared to the experimental spectroscopic data obtained for uranyl ions in Cs(2)UO(2)Cl(4) crystals from Denning [Struct. Bonding (Berlin) 79, 215 (1992)] and to previous theoretical calculations performed using a combined configuration-interaction spin-orbit treatment [Z. Zhang and R. M. Pitzer, J. Phys. Chem. A 103, 6880 (1999); S. Matsika and R. M. Pitzer, J. Phys. Chem. A. 105, 637 (2001)]. As opposed to the latter results, the calculations performed in this work point to a significant effect of the weakly bound equatorial chlorine ligands on the excitation energies.     

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)].     

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.     

Pair-correlated speed distributions for the OH+CH4/CD4 reactions: Further remarks on their classical trajectory calculations in a quantum spirit

Ten years ago, Liu and co-workers measured pair-correlated speed distributions for OH+CH₄/CD₄ reactions by means of velocity map imaging (VMI) techniques at a collision energy of ∼10 kcal/mol [B. Zhang, W. Shiu, J. J. Lin and K. Liu, J. Chem. Phys 122, 131102 (2005); B. Zhang, W. Shiu and K. Liu, J. Phys. Chem. A 109, 8989 (2005)]. Recently, two of us could semi-quantitatively reproduce these measurements by performing full-dimensional quasi-classical trajectory calculations in a quantum spirit on an ab-initio potential energy surface of their own [J. Espinosa-Garcia and J. C. Corchado, Theor. Chem. Acc. (2015) 134: 6; J. Phys. Chem. B 120, 1446 (2016)]. The goal of the present work is to show that these results can be significantly improved by adding a few more constraints in order to better comply with the restrictions imposed by VMI. Overall, the level of agreement between theory and experiment is remarkable owing to the large dimensionality of the reactions under scrutiny. This is an encouraging result considering the computational challenges of quantum scattering calculations for such large processes.     

Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra

The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].     

Bound state potential energy surface construction: ab initio zero-point energies and vibrationally averaged rotational constants

Collins' method of interpolating a potential energy surface (PES) from quantum chemical calculations for reactive systems (Jordan, M. J. T.; Thompson, K. C.; Collins, M. A. J. Chem. Phys. 1995, 102, 5647. Thompson, K. C.; Jordan, M. J. T.; Collins, M. A. J. Chem. Phys. 1998, 108, 8302. Bettens, R. P. A.; Collins, M. A. J. Chem. Phys. 1999, 111, 816) has been applied to a bound state problem. The interpolation method has been combined for the first time with quantum diffusion Monte Carlo calculations to obtain an accurate ground state zero-point energy, the vibrationally average rotational constants, and the vibrationally averaged internal coordinates. In particular, the system studied was fluoromethane using a composite method approximating the QCISD(T)/6-311++G(2df,2p) level of theory. The approach adopted in this work (a) is fully automated, (b) is fully ab initio, (c) includes all nine nuclear degrees of freedom, (d) requires no assumption of the functional form of the PES, (e) possesses the full symmetry of the system, (f) does not involve fitting any parameters of any kind, and (g) is generally applicable to any system amenable to quantum chemical calculations and Collins' interpolation method. The calculated zero-point energy agrees to within 0.2% of its current best estimate. A0 and B0 are within 0.9 and 0.3%, respectively, of experiment.     

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.     

Reply to “Comment on Aromatic‐Backbone Interactions in Model α‐Helical Peptides”

In response to Van Mourik's comments on our paper (J Comput Chem 2007, 28, 1208.) we present an extended version of our rotation method. We also prove that intramolecular interaction energies as well the basis set superposition errors calculated with our rotation method are comparable with those obtained by the counterpoise method of Boys and Bernardi (Mol Phys 1970, 19, 533). In intramolecular interaction energy calculations, if the interacting groups are in proximity, our rotation method is recommended to avoid artificial interactions, which can be induced by fragmentation. © 2007 Wiley Periodicals, Inc.J Comput Chem, 2008     

An ab initio investigation of the O(3P)-H2(1sigma(g)+) van der Waals well

We report an ab initio study of the van der Waals region of the O(3P)-H2 potential energy surface based on RCCSD(T) calculations with an aug-cc-pVQZ basis supplemented by bond functions. In addition, an open-shell implementation of symmetry-adapted perturbation theory (SAPT) is used to corroborate the RCCSD(T) calculations and to investigate the relative magnitudes of the various contributions to the van der Waals interaction. We also investigate the effect of the spin-orbit coupling on the position and depth of the van der Waals well. We predict the van der Waals minimum to occur in perpendicular geometry, and located at a closer distance than a secondary well in colinear geometry. The potentials obtained in the present study confirm the previous calculations of Alexander [M. H. Alexander, J. Chem. Phys., 1998, 108, 4467], but disagree with the earlier work of Harding and co-workers [Z. Li, V. A. Apkarian and L. B. Harding, J. Chem. Phys., 1997, 106, 942] as well as with recently refitted surfaces of Brand?o and coworkers [J. Brand?o, C. Mogo and B. C. Silva, J. Chem. Phys., 2004, 121, 8861]. Inclusion of spin-orbit coupling reduces the depth of the van der Waals minimum without causing a change in its position.     

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.     

Quantum-classical dynamics of scattering processes in adiabatic and diabatic representations

We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn-Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schrodinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on an adiabatic surface with ordinary Born-Oppenheimer approximation. Excellent agreement between TDDVR and DVR results is obtained in both the representations.     

Identity SN2 reactions X- + CH3X --> XCH3 + X- (X=F, Cl, Br, and I) in vacuum and in aqueous solution: a valence bond study

The recently developed (L. Song, W. Wu, Q. Zhang, S. Shaik, J. Phys. Chem. A 2004, 108, 6017) valence bond method coupled with a polarized continuum model (VBPCM) has been applied to the identity SN2 reaction of halides in the gas phase and in aqueous solution. The barriers computed at the level of the breathing orbital VB method (P. C. Hiberty, J. P. Flament, E. Noizet, Chem. Phys. Lett. 1992, 189, 259), BOVB and VBPCM//BOVB, are comparable to CCSD(T) and CCSD(T)//PCM results and to experimentally derived barriers in solution (W. J. Albery, M. M. Kreevoy, Adv. Phys. Org. Chem. 1978, 16, 85). The reactivity parameters needed to apply the valence bond state correlation diagram (VBSCD) method (S. Shaik, J. Am. Chem. Soc. 1984, 106, 1227), were also determined by VB calculations. It has been shown that the reactivity parameters along with their semiempirical derivations provide a satisfactory qualitative and quantitative account of the barriers.     

Alchemical prediction of hydration free energies for SAMPL

Hydration free energy calculations have become important tests of force fields. Alchemical free energy calculations based on molecular dynamics simulations provide a rigorous way to calculate these free energies for a particular force field, given sufficient sampling. Here, we report results of alchemical hydration free energy calculations for the set of small molecules comprising the 2011 Statistical Assessment of Modeling of Proteins and Ligands challenge. Our calculations are largely based on the Generalized Amber Force Field with several different charge models, and we achieved RMS errors in the 1.4-2.2 kcal/mol range depending on charge model, marginally higher than what we typically observed in previous studies (Mobley et al. in J Phys Chem B 111(9):2242-2254, 2007, J Chem Theory Comput 5(2):350-358, 2009, J Phys Chem B 115:1329-1332, 2011; Nicholls et al. in J Med Chem 51:769-779, 2008; Klimovich and Mobley in J Comput Aided Mol Design 24(4):307-316, 2010). The test set consists of ethane, biphenyl, and a dibenzyl dioxin, as well as a series of chlorinated derivatives of each. We found that, for this set, using high-quality partial charges from MP2/cc-PVTZ SCRF RESP fits provided marginally improved agreement with experiment over using AM1-BCC partial charges as we have more typically done, in keeping with our recent findings (Mobley et al. in J Phys Chem B 115:1329-1332, 2011). Switching to OPLS Lennard-Jones parameters with AM1-BCC charges also improves agreement with experiment. We also find a number of chemical trends within each molecular series which we can explain, but there are also some surprises, including some that are captured by the calculations and some that are not.     

Quantum Monte Carlo calculations of the dissociation energy of the water dimer

We report diffusion quantum Monte Carlo (DMC) calculations of the equilibrium dissociation energy D(e) of the water dimer. The dissociation energy measured experimentally, D(0), can be estimated from D(e) by adding a correction for vibrational effects. Using the measured dissociation energy and the modern value of the vibrational energy Mas et al., [J. Chem. Phys. 113, 6687 (2000)] leads to D(e)=5.00+/-0.7 kcal mol(-1), although the result Curtiss et al., [J. Chem. Phys. 71, 2703 (1979)] D(e)=5.44+/-0.7 kcal mol(-1), which uses an earlier estimate of the vibrational energy, has been widely quoted. High-level coupled cluster calculations Klopper et al., [Phys. Chem. Chem. Phys. 2, 2227 (2000)] have yielded D(e)=5.02+/-0.05 kcal mol(-1). In an attempt to shed new light on this old problem, we have performed all-electron DMC calculations on the water monomer and dimer using Slater-Jastrow wave functions with both Hartree-Fock approximation (HF) and B3LYP density functional theory single-particle orbitals. We obtain equilibrium dissociation energies for the dimer of 5.02+/-0.18 kcal mol(-1) (HF orbitals) and 5.21+/-0.18 kcal mol(-1) (B3LYP orbitals), in good agreement with the coupled cluster results.     

Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: applications to Tully's three model systems

The nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) 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 single-surface HK SC-IVR 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 h 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.     

Communication: Linear-expansion shooting techniques for accelerating self-consistent field convergence

Based on the corrected Hohenberg-Kohn-Sham total energy density functional [Y. A. Zhang and Y. A. Wang, J. Chem. Phys. 130, 144116 (2009)], we have developed two linear-expansion shooting techniques (LIST)- direct LIST (LISTd) and indirect LIST (LISTi), to accelerate the convergence of self-consistent field (SCF) calculations. Case studies show that overall LISTi is the most robust and efficient algorithm for accelerating SCF convergence, whereas LISTd is advantageous in the early stage of an SCF process. More importantly, LISTi outperforms Pulay's direct inversion in the iterative subspace (DIIS) [P. Pulay, J. Comput. Chem. 3, 556 (1982)] and its two recent improvements, energy-DIIS [K. N. Kudin, G. E. Scuseria, and E. Cance?s, J. Chem. Phys. 116, 8255 (2002)] and augmented Roothaan-Hall energy-DIIS [X. Hu and W. Yang, J. Chem. Phys. 132, 054109 (2010)].     

Close-coupling study of rotational energy transfer of CO (upsilon=2) by collisions with He atoms

Quantum close-coupling scattering calculations of rotational energy transfer in the vibrationally excited CO due to collisions with He atom are presented for collision energies between 10(-5) and approximately 1000 cm-1 with CO being initially in the vibrational level upsilon=2 and rotational levels j=0,1,4, and 6. The He-CO interaction potential of Heijmen et al. [J. Chem. Phys. 107, 9921 (1997)] was adopted for the calculations. Cross sections for rovibrational transitions and state-to-state rotational energy transfer from selected initial rotational levels were computed and compared with recent measurements of Carty et al. [J. Chem. Phys. 121, 4671 (2004)] and available theoretical results. Comparison in all cases is found to be excellent, providing a stringent test for the scattering calculations as well as the reliability of the He-CO interaction potential by Heijmen et al.