Volume 130, Issue 9, 07 March 2009
 ARTICLES

 Theoretical Methods and Algorithms

A discrete variable representation method for studying the rovibrational quantum dynamics of molecules with more than three atoms
View Description Hide DescriptionEstablished multidimensional discrete variable representations (DVRs) are derived from a direct product basis. They are commonly used to compute vibrational spectra and have also been employed to determine rovibrational spectra of triatomic molecules. We show that for calculations the DVR is also advantageous for molecules with more than three atoms. We use a basis of products of Wigner functions (for rotation) and DVR functions (for vibration). A key advantage of the DVR is the fact that one can prune the basis: many DVR functions can be discarded from the original direct product basis. This significantly reduces the cost of the calculation. We have implemented a mapping procedure to exploit this pruneability. We explain how to treat Coriolis terms in a parityadapted basis. The method is tested by computing rovibrational levels of HFCO.

Numerical solution of boundaryintegral equations for molecular electrostatics
View Description Hide DescriptionNumerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundaryintegral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundaryelement method simulations of the integralequation formulation known as the apparentsurfacecharge (ASC) method or polarizablecontinuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integralequation formulations is also discussed, and two equivalences between integralequation methods are derived.

A new quantum control scheme for multilevel systems based on effective decomposition by intense laser fields
View Description Hide DescriptionA new quantum control scheme for general multilevel systems using intense laser fields is proposed. In the present scheme, the target subspace consisting of several quantum levels is effectively isolated by applying intense cw lasers with specific conditions. The formulation is carried out using the Green function with the help of projection operator method. Dynamics of the isolated target subspace is governed by an effective Hamiltonian. The developed scheme is applied to the quantum control of dissipative four and fivelevel systems. It is clarified that the present method makes it possible not only to manipulate the coherent population dynamics but also to suppress the dissipative dynamics.

The multinomial simulation algorithm for discrete stochastic simulation of reactiondiffusion systems
View Description Hide DescriptionThe Inhomogeneous Stochastic Simulation Algorithm (ISSA) is a variant of the stochastic simulation algorithm in which the spatially inhomogeneous volume of the system is divided into homogeneous subvolumes, and the chemical reactions in those subvolumes are augmented by diffusive transfers of molecules between adjacent subvolumes. The ISSA can be prohibitively slow when the system is such that diffusive transfers occur much more frequently than chemical reactions. In this paper we present the Multinomial Simulation Algorithm (MSA), which is designed to, on the one hand, outperform the ISSA when diffusive transfer events outnumber reaction events, and on the other, to handle small reactant populations with greater accuracy than deterministicstochastic hybrid algorithms. The MSA treats reactions in the usual ISSA fashion, but uses appropriately conditioned binomial random variables for representing the net numbers of molecules diffusing from any given subvolume to a neighbor within a prescribed distance. Simulation results illustrate the benefits of the algorithm.

Modeling solute clustering in the diffusion layer around a growing crystal
View Description Hide DescriptionThe mechanism of crystal growth from solution is often thought to consist of a mass transferdiffusion step followed by a surface reaction step. Solute molecules might form clusters in the diffusion step before incorporating into the crystal lattice. A model is proposed in this work to simulate the evolution of the cluster size distribution due to the simultaneous aggregation and breakage of solute molecules in the diffusion layer around a growing crystal in the stirred solution. The crystallization of from aqueous solution is studied to illustrate the effect of supersaturation and diffusion layer thickness on the numberaverage degree of clustering and the size distribution of solute clusters in the diffusion layer.

Relative importance of first and second derivatives of nuclear magnetic resonance chemical shifts and spinspin coupling constants for vibrational averaging
View Description Hide DescriptionRelative importance of anharmonic corrections to molecular vibrational energies, nuclear magnetic resonance(NMR)chemical shifts, and coupling constants was assessed for a model set of methane derivatives, differently charged alanine forms, and sugar models. Molecular quartic force fields and NMR parameter derivatives were obtained quantum mechanically by a numerical differentiation. In most cases the harmonic vibrational function combined with the property second derivatives provided the largest correction of the equilibrium values, while anharmonic corrections (third and fourth energy derivatives) were found less important. The most computationally expensive offdiagonal quartic energy derivatives involving four different coordinates provided a negligible contribution. The vibrational corrections of NMR shifts were small and yielded a convincing improvement only for very accurate wave function calculations. For the indirect spinspin coupling constants the averaging significantly improved already the equilibrium values obtained at the density functional theory level. Both first and complete second shielding derivatives were found important for the shift corrections, while for the coupling constants the vibrational parts were dominated by the diagonal second derivatives. The vibrational corrections were also applied to some isotopic effects, where the corrected values reasonably well reproduced the experiment, but only if a full secondorder expansion of the NMR parameters was included. Contributions of individual vibrational modes for the averaging are discussed. Similar behavior was found for the methane derivatives, and for the larger and polar molecules. The vibrational averaging thus facilitates interpretation of previous experimental results and suggests that it can make future molecular structural studies more reliable. Because of the lengthy numerical differentiation required to compute the NMR parameter derivatives their analytical implementation in future quantum chemistry packages is desirable.

Excited state calculations using phaseless auxiliaryfield quantum Monte Carlo: Potential energy curves of lowlying singlet states
View Description Hide DescriptionWe show that the recently developed phaseless auxiliaryfield quantum Monte Carlo (AFQMC) method can be used to study excited states, providing an alternative to standard quantum chemistry methods. The phaseless AFQMC approach, whose computational cost scales as with system size , has been shown to be among the most accurate manybody methods in ground state calculations. For excited states, prevention of collapse into the ground state and control of the Fermion sign/phase problem are accomplished by the approximate phaseless constraint with a trial wave function. Using the challenging molecule as a test case, we calculate the potential energy curves of the ground and two lowlying singlet excited states. The trial wave function is obtained by truncating complete active space wave functions, with no further optimization. The phaseless AFQMC results using a small basis set are in good agreement with exact full configurationinteraction calculations, while those using large basis sets are in good agreement with experimental spectroscopic constants.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

An isolated lineshape model based on the Keilson and Storer function for velocity changes. I. Theoretical approaches
View Description Hide DescriptionThis paper presents new results for the modeling of isolated line shapes from the Doppler to the collisional regime, thus including the effects of confinement (Dicke narrowing) and of the speed dependence of collisional parameters. They are obtained within a classical description of the time evolution of the autocorrelation function of the optical transition moment, combined with the use of the Keilson and Storer model for the changes in the radiator translational velocity. A purely numerical solution to the subsequent differential equations, which uses discretized grids for the radiatingmolecule velocity vector, is first described. An alternative approach, using projections onto generalized Laguerre polynomials (for the velocity modulus) and spherical harmonics (for the velocity orientation), is also presented. A first test of these approaches is made in the particular case of the Raman line of the fundamental band of pure at room temperature (others will be presented in paper II). It is shown that the two models lead to exactly the same results, as expected, and to satisfactory agreement with measured values of the linewidth at various densities.

Fouriertransform microwave spectroscopy of the CCCCl radical
View Description Hide DescriptionPure rotational spectra of the CCCCl radical in a supersonic jet have been observed for the first time by Fouriertransform microwave spectroscopy. The radical was produced by a pulsed electric discharge in a and mixture diluted to 0.3% and 0.2% with Ne, respectively. Transitions with spin and hyperfine splittings were observed for two isotopologs, and , in the region from 11.4 GHz for to 34.2 GHz for . The molecular constants including the hyperfine coupling constants due to the Cl nucleus have been determined precisely. From the rotational analyses and highlevel ab initio calculations, the molecular structure of the CCCCl radical is concluded to be bent in the ground electronic state.

Tensor cross sections and the collisional evolution of state multipoles:
View Description Hide DescriptionBy means of a kinetic analysis, we show that the overall rate constant for the collisional loss of orientation or alignment of a rotational level is the sum of the rate constant for elastic depolarization and the sum of the rate constants for all rotationally inelastic transitions out of the level under consideration. An expression for the depolarization cross section is derived in terms of tensor cross sections, and the relationship of depolarization to resolved transitions is discussed. We use this formalism in simulations, based on highquality ab initio potential energy surfaces, of the depolarization of the openshell molecule through collisions with Ar. Good agreement is seen with the results of the twocolor polarization spectroscopy experiments of Paterson et al. [J. Chem. Phys.129, 074304 (2008)]. In addition, we show that the major contribution to elastic collisional depolarization occurs not from weak, glancing collisions but from encounters which probe the inner wall of the potential energy surface.

Potential energy curves and interpretation of electronic spectrum of the rhodium monoxide
View Description Hide DescriptionPotential energy curves of 17 electronic states of rhodium monoxide (RhO) are calculated by multireference configuration interaction with single and double excitations (MRCISD). The ground state of RhO is determined to be a state with equilibrium bond length of 1.710 Å and harmonic vibrational frequency of at the MRCISD level of theory. It dissociates into with a dissociation energy of 3.77/4.26 eV , which is in agreement with the experimental value of . Two lowlying excited states and are located at 4152 and above the ground state. The with the adjacent , , and states can be strongly coupled via spinorbit interaction leading to a large splitting between states with the value of , which is comparable with the experimental value of . Two higher doublets, and , have the same dominant configuration, , and their transitions to the ground state, i.e., and , correspond to the two visible bands of RhO.

Twophoton resonant second harmonic generation in atomic xeon
View Description Hide DescriptionVacuum ultraviolet (VUV)radiation at 124.8 nm (9.93 eV) was produced from twophoton resonant second harmonic generation(SHG) in a xeon gaseous medium and used to probe molecular samples of acetone, furan, thiophene, ammonia, and methane. The mass spectra recorded from the species with ionization energies below 9.93 eV were dominated by the parent ions. The parent ions were only observed when the incident UV radiation was tuned to resonate with the twophoton transition of Xe at . The pressure dependence and the resonant nature of the parent ions observed support the mechanism for SHG as the ionizationinitiated electric field induced SHG via the thirdorder nonlinear susceptibility , which is enhanced by the coupling between the and the nearby states of Xe atoms.

Magnetic coupling in bisnitronylnitroxide radicals: The role of aromatic bridges
View Description Hide DescriptionConfiguration interaction calculations have been applied to the study of the magnetic coupling in bisnitronyl nitroxide radicals with benzene bridges. Molecular orbitals obtained with different localization schemes have been considered in the generation of the CI space, with the aim of investigating the role played by the various fragments in the magnetic interaction. The aromatic bridge is found significant, while fragments outside the magneticbridgemagnetic moiety can be neglected. Using simplified model molecular species, an accurate analysis of the ferromagnetic/antiferromagnetic coupling in the meta and para diradicals is reported.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Empirical relaxation function and spectral density for underdamped vibrations at low temperatures
View Description Hide DescriptionA new relaxation function which accounts for electronic dephasing (electronic phase loss and excited state lifetime) is presented, whose applicability for underdamped motion at low temperatures is examined in detail. This new empirical relaxation function yields linear and nonlinear spectral/temporal profiles that render accurate dephasing time in the underdamped regime. The relaxation function is normally expressed in terms of the coupling functions and on which the time evolution of the vibrational modes in question depends. The corresponding spectral density, which is a central quantity in probing dynamics, is derived and compared to that of the multimode Brownian oscillator model. Derivation and discussion of the new position and momentum autocorrelation functions in terms of our new spectral density are presented. While the position autocorrelation function plays a key role in representing solvation structure in polar or nonpolar medium, the momentum correlation function projects out the molecular vibrational motion. The Liouville space generating function (LGF) for harmonic and anharmonic systems is expressed in terms of our new empirical and spectral density, leading to more physical observation. Several statistical quantities are derived from the position and momentum correlation function, which in turn contribute to LGF. Model calculations reflecting the infinite population decay in the low temperature limit in linear and nonlinear spectroscopic signals are presented. The herein quantum dipole momentcorrelation function is compared to that derived in [M. Toutounji, J. Chem. Phys.118, 5319 (2003)] using mixed quantumclassical dynamics framework, yielding reasonable results, in fact identical at higher temperatures. The results herein are found to be informative, useful, and consistent with experiments.

Watermediated interactions between hydrophobic and ionic species in cylindrical nanopores
View Description Hide DescriptionWe use Metropolis Monte Carlo and umbrella sampling to calculate the free energies of interaction of two methane molecules and their charged derivatives in cylindrical waterfilled pores. Confinement strongly alters the interactions between the nonpolar solutes and completely eliminates the solvent separated minimum (SSM) that is seen in bulk water. The free energy profiles show that the methane molecules are either in contact or at separations corresponding to the diameter and the length of the cylindrical pore. Analytic calculations that estimate the entropy of the solutes, which are solvated at the pore surface, qualitatively explain the shape of the free energy profiles. Adding charges of opposite sign and magnitude or (where is the electronic charge) to the methane molecules decreases their tendency for surface solvation and restores the SSM. We show that confinement induced ionpair formation occurs whenever , where is the Bjerrum length and is the pore diameter. The extent of stabilization of the SSM increases with ion charge density as long as . In pores with , in which the water is strongly layered, increasing the charge magnitude from to reduces the stability of the SSM. As a result, ionpair formation that occurs with negligible probability in the bulk is promoted. In larger diameter pores that can accommodate a complete hydration layer around the solutes, the stability of the SSM is enhanced.

Composition dependence of glass transition temperature and fragility. I. A topological model incorporating temperaturedependent constraints
View Description Hide DescriptionWe present a topological model for the composition dependence of glass transition temperature and fragility. Whereas previous topological models are derived for zero temperature conditions, our approach incorporates the concept of temperaturedependent constraints that freeze in as the system is cooled from high temperature. Combining this notion of temperaturedependent constraints with the Adam–Gibbs model of viscosity, we derive an analytical expression for the scaling of glass transition temperature and fragility in the binary system. In the range of , we reproduce the modified Gibbs–DiMarzio equation of Sreeram et al. [J. NonCryst. Solids127, 287 (1991)] but without any empirical fitting parameters. The modified Gibbs–DiMarzio equation breaks down for , where the glass transition temperature decreases with increasing germanium content.

Onedimensional counterion gas between charged surfaces: Exact results compared with weak and strongcoupling analyses
View Description Hide DescriptionWe evaluate exactly the statistical integral for an inhomogeneous onedimensional (1D) counteriononly Coulomb gas between two charged boundaries and from this compute the effective interaction, or disjoining pressure, between the bounding surfaces. Our exact results are compared to the limiting cases of weak and strong couplings which are the same for 1D and threedimensional (3D) systems. For systems with a large number of counterions it is found that the weakcoupling (meanfield) approximation for the disjoining pressure works perfectly and that fluctuations around the meanfield in 1D are much smaller than in 3D. In the case of few counterions it works less well and strongcoupling approximation performs much better as it takes into account properly the discreteness of the counterion charges.

Vibrational solvatochromism and electrochromism: Coarsegrained models and their relationships
View Description Hide DescriptionA theoretical description of vibrational solvatochromism and electrochromism is presented by using a coarsegrained model based on a distributed charge and multipole interaction theory. Solvatochromic frequency shift has been described by considering the interaction between distributed charges of a solute and electrostatic potential due to distributed charges of solvent molecules. Another approach was based on the expansion of the solvatochromic frequency shift in terms of solventelectric field and its gradient at distributed sites on solute. The relationship between these two approaches is elucidated and their validities are discussed. It is also shown that the distributed charge and multipole model for solvatochromism developed here can be used to describe vibrational Stark effects on frequency and transitiondipole moment. The relationship between the vibrational Stark tuning rate and the parameters obtained from recent vibrational solvatochromism studies is clarified and used to determine the vibrational Stark tuning rates of a few stretching modes, which are then directly compared with experimentally measured values. We anticipate that the present theoretical model can be used to study a variety of vibrational solvatochromic and electrochromic phenomena and to extract critical information on local electrostatic environment around a small IR probe in solution or protein from linear and nonlinear IR spectroscopic studies.

A theoretical study on the frequencydependent electric conductivity of electrolyte solutions. II. Effect of hydrodynamic interaction
View Description Hide DescriptionThe theory on the frequencydependent electric conductivity of electrolyte solutions proposed previously by Yamaguchi et al. [J. Chem. Phys.127, 234501 (2007)] is extended to include the hydrodynamic interaction between ions. The theory is applied to the aqueous solution of NaCl and the concentration dependence of the conductivity agrees well with that determined by experiments. The effects of the hydrodynamic and relaxation effects are highly nonadditive in the concentrated solution, because the hydrodynamic interaction between ions affects the timedependent response of the ionic atmosphere. The decrease in the electric conductivity is divided into the contributions of ion pair distribution at various distances. The longrange ionic atmosphere plays a major role at the concentration as low as 0.01 mol/kg, whereas the contribution of the contact ion pair region is important at 1 mol/kg. The magnitude of the contribution of the contact ion pair region is scarcely dependent on the presence of the hydrodynamic interaction. The transport number of cation is calculated to be a decreasing function of concentration as is observed in experiments.

Diffusioninfluenced reactions involving a reactant with two active sites
View Description Hide DescriptionWe consider the kinetics of diffusioninfluenced reactions which involve a reactant species that can be modeled as a sphere with two reactive patches located on its surface at an arbitrary angular distance. An approximate analytic expression for the rate coefficient is derived based on the Wilemski–Fixman–Weiss decoupling approximation and a multivariable Padé approximation. The accuracy of the rate expression is evaluated against computer simulations as well as an exact analytic expression available for a special case. The present theory provides accurate estimates for the magnitude of diffusive interference effects between the two reactive patches. We also present an efficient Brownian dynamics method for calculating the timedependent rate coefficient, which is applicable when the reactants involve multiple active sites.