Volume 134, Issue 13, 07 April 2011

Many quantum mechanical calculations indicate water molecules in the gas and liquid phase have much larger quadrupole moments than any of the common site models of water for computer simulations. Here, comparisons of multipoles from quantum mechanical/molecular mechanical (QM/MM) calculations at the MP2/augccpVQZ level on a B3LYP/augccpVQZ level geometry of a waterlike cluster and from various site models show that the increased square planar quadrupole can be attributed to the porbital character perpendicular to the molecular plane of the highest occupied molecular orbital as well as a slight shift of negative charge toward the hydrogens. The common site models do not account for the porbital type electron density and fitting partial charges of TIP4P or TIP5Ptype models to the QM/MM dipole and quadrupole give unreasonable higher moments. Furthermore, six partial charge sites are necessary to account reasonably for the large quadrupole, and polarizable site models will not remedy the problem unless they account for the porbital in the gas phase since the QM calculations show it is present there too. On the other hand, multipole models by definition can use the correct multipoles and the electrostatic potential from the QM/MM multipoles is much closer than that from the site models to the potential from the QM/MM electron density. Finally, Monte Carlo simulations show that increasing the quadrupole in the softsticky dipolequadrupoleoctupole multipole model gives radial distribution functions that are in good agreement with experiment.
 ARTICLES

 Theoretical Methods and Algorithms

Spinadapted openshell timedependent density functional theory. II. Theory and pilot application
View Description Hide DescriptionThe excited states of openshell systems calculated by unrestricted Kohn–Shambased timedependent density functional theory (UTDDFT) are often heavily spincontaminated and hence meaningless. This is solved ultimately by the recently proposed spinadapted timedependent density functional theory (TDDFT) (STDDFT) [J. Chem. Phys.133, 064106 (2010)]. Unlike the standard restricted openshell Kohn–Shambased TDDFT (RTDDFT) which can only access the singletcoupled single excitations, the STDDFT can capture both the singlet and tripletcoupled single excitations with the same computational effort as the UTDDFT. The performances of the three approaches (UTDDFT, RTDDFT, and STDDFT) are compared for both the spinconserving and spinflip excitations of prototypical openshell systems, the nitrogen (N_{2} ^{+}) and naphthalene (C_{10}H_{8} ^{+}) cations. The results show that the STDDFT gives rise to balanced descriptions of excited states of openshell systems.

Jastrow correlated and quantum Monte Carlo calculations for the lowlying states of the carbon atom
View Description Hide DescriptionDifferent computational methods are employed to calculate excitation energies of the carbon atom. Explicitly correlated wave functions have been obtained in a Variational Monte Carlo calculation. Fixed node DiffusionMonte Carlo calculations for the lowest energyexcited states of a given symmetry are reported. A systematic and quantitative analysis of the performance of the different schemes in the calculation of the excitation energy of up to 27 excited states of the carbon atom is carried out. The quality of the different methods have been studied in terms of the deviation with respect to the experimental excitation energies. A good agreement with the experimental values has been reached.

The operations of quantum logic gates with pure and mixed initial states
View Description Hide DescriptionThe implementations of quantum logic gates realized by the rovibrational states of a C^{12}O^{16} molecule in the X(^{1}Σ^{+}) electronic ground state are investigated. Optimal laser fields are obtained by using the modified multitarget optimal theory (MTOCT) which combines the maxima of the cost functional and the fidelity for state and quantum process. The projection operator technique together with modified MTOCT is used to get optimal laser fields. If initial states of the quantum gate are pure states, states at target time approach well to ideal target states. However, if the initial states are mixed states, the target states do not approach well to ideal ones. The process fidelity is introduced to investigate the reliability of the quantum gate operation driven by the optimal laser field. We found that the quantum gates operate reliably whether the initial states are pure or mixed.

Renormalization of the frozen Gaussian approximation to the quantum propagator
View Description Hide DescriptionThe frozen Gaussian approximation to the quantum propagator may be a viable method for obtaining “on the fly” quantum dynamical information on systems with many degrees of freedom. However, it has two severe limitations, it rapidly loses normalization and one needs to know the Gaussian averaged potential, hence it is not a purely local theory in the force field. These limitations are in principle remedied by using the Herman–Kluk (HK) form for the semiclassical propagator. The HK propagator approximately conserves unitarity for relatively long times and depends only locally on the bare potential and its second derivatives. However, the HK propagator involves a much more expensive computation due to the need for evaluating the monodromy matrix elements. In this paper, we (a) derive a new formula for the normalization integral based on a prefactor free HK propagator which is amenable to “on the fly” computations; (b) show that a frozen Gaussian version of the normalization integral is not readily computable “on the fly”; (c) provide a new insight into how the HK prefactor leads to approximate unitarity; and (d) how one may construct a prefactor free approximation which combines the advantages of the frozen Gaussian and the HK propagators. The theoretical developments are backed by numerical examples on a Morse oscillator and a quartic double well potential.

Transitionmetal 13atom clusters assessed with solid and surfacebiased functionals
View Description Hide DescriptionFirstprinciples densityfunctional theory studies have reported open structures based on the formation of double simplecubic (DSC) arrangements for Ru_{13}, Rh_{13}, Os_{13}, and Ir_{13}, which can be considered an unexpected result as those elements crystallize in compact bulk structures such as the facecentered cubic and hexagonal closepacked lattices. In this work, we investigated with the projected augmented wave method the dependence of the lowestenergy structure on the local and semilocal exchangecorrelation (xc) energy functionals employed in densityfunctional theory. We found that the localdensity approximation (LDA) and generalizedgradient formulations with different treatment of the electronic inhomogeneities (PBE, PBEsol, and AM05) confirm the DSC configuration as the lowestenergy structure for the studied TM_{13}clusters. A good agreement in the relative total energies are obtained even for structures with small energy differences, e.g., 0.10 eV. The employed xc functionals yield the same total magnetic moment for a given structure, i.e., the differences in the bond lengths do not affect the moments, which can be attributed to the atomic character of those clusters. Thus, at least for those systems, the differences among the LDA, PBE, PBEsol, and AM05 functionals are not large enough to yield qualitatively different results.

Pathintegral calculation of the third virial coefficient of quantum gases at low temperatures
View Description Hide DescriptionWe derive pathintegral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose–Einstein or Fermi–Dirac statistics). We use stateoftheart pair and threebody potentials to calculate the third virial coefficient of ^{3}He and ^{4}He in the temperature range K. We obtain uncertainties smaller than those of the limited experimental data. Inclusion of exchange effects is necessary to obtain accurate results below about 7 K.

Accelerated convergence of molecular free energy via superposition approximationbased reference states
View Description Hide DescriptionThe free energy of a molecular system can, at least in principle, be computed by thermodynamic perturbation from a reference system whose free energy is known. The convergence of such a calculation depends critically on the conformational overlap between the reference and the physical systems. One approach to defining a suitable reference system is to construct it from the onedimensional marginal probability distribution functions (PDFs) of internal coordinates observed in a molecular simulation. However, the conformational overlap of this reference system tends to decline steeply with increasing dimensionality, due to the neglect of correlations among the coordinates. Here, we test a reference system that can account for pairwise correlations among the internal coordinates, as captured by their twodimensional marginal PDFs derived from a molecular simulation. Incorporating pairwise correlations in the reference system is found to dramatically improve the convergence of the free energy estimates relative to the firstorder reference system, due to increased conformational overlap with the physical distribution.

Toward canonical ensemble distribution from selfguided Langevin dynamics simulation
View Description Hide DescriptionThis work derives a quantitative description of the conformational distribution in selfguided Langevin dynamics (SGLD) simulations. SGLD simulations employ guiding forces calculated from local average momentums to enhance lowfrequency motion. This enhancement in lowfrequency motion dramatically acceleratesconformational search efficiency, but also induces certain perturbations in conformational distribution. Through the local averaging, we separate properties of molecular systems into lowfrequency and highfrequency portions. The guiding force effect on the conformational distribution is quantitatively described using these lowfrequency and highfrequency properties. This quantitative relation provides a way to convert between a canonical ensemble and a selfguided ensemble. Using example systems, we demonstrated how to utilize the relation to obtain canonical ensembleproperties and conformational distributions from SGLD simulations. This development makes SGLD not only an efficient approach for conformational searching, but also an accurate means for conformational sampling.

Robust acceleration of self consistent field calculations for density functional theory
View Description Hide DescriptionWe show that the type 2 Broyden secant method is a robust general purpose mixer for self consistent field problems in density functional theory. The Broyden method gives reliable convergence for a large class of problems and parameter choices. We directly mix the approximation of the electronic density to provide a basis independent mixing scheme. In particular, we show that a single set of parameters can be chosen that give good results for a large range of problems. We also introduce a spin transformation to simplify treatment of spin polarized problems. The spin transformation allows us to treat these systems with the same formalism as regular fixed point iterations.

On the determination of partial differential cross sections for photodetachment and photoionization processes producing polyatomic molecules with electronic states coupled by conical intersections
View Description Hide DescriptionA formalism is derived for the computation of partial differential cross sections for electron photodetachment and photoionization processes that leave the residual or target molecule in electronic states that are strongly coupled by conical intersections. Because the electronic states of the target are nonadiabatically coupled, the standard adiabatic states approach of solving the electronic Schrödinger equation for the detached electron at fixed nuclear geometries and then vibrationally averaging must be fundamentally modified. We use a Lippmann–Schwinger equation based approach, which leads naturally to a partitioning of the transition amplitude into a Dyson orbital like part plus a scattering correction. The requisite Green's function is that developed in our previous paper for the direct determination of total integral cross sections. The method takes proper account of electron exchange, possible nonorthogonality of the orbital describing the detached electron, and nonadiabatic effects in the product molecule. The Green's function is constructed in an L ^{2} basis using complex scaling techniques. The accurate treatment of nonadiabatic effects in the residual molecule is accomplished using the multimode vibronic coupling model. For photodetachment, an approximate approach, which is less computationally demanding, is suggested.

Error analysis of molecular dynamics and fractal time approximants from a combinatorial perspective
View Description Hide DescriptionTrotter's theorem forms the theoretical basis of most modern molecular dynamics. In essence this theorem states that a time displacement operator (a Lie operator) constructed by exponentiating a sum of noncommuting operators can be approximated by a product of single operators provided the time interval is “very small.” In theory “very small” implies infinitesimally small (at which point the approximate product becomes exact), while in practical analysis a finite time interval is divided into several small subintervals or steps. It follows, therefore, that the larger the number of steps the better the approximation to the exact time displacement operator. The question therefore arises: How many steps are sufficient? For bounded operators, standard theorems are available to provide the answer. In this paper we show that a very simple combinatorial formula can be derived which allows the computation of the global differences (as a function of the number of steps) between the Taylor coefficients of the exact time displacement operator and an approximate one constructed by using a finite number of steps. The formula holds for both bounded and nonbounded operators and shows, quantitatively, what is qualitatively expected—that the error decreases with increasing number of steps. Furthermore, the formula applies irrespective of the complexity of the system, boundary conditions, or the thermodynamic ensemble employed for averaging the initial conditions. The analysis yields explicit expressions for the Taylor coefficients which are then used to compute the errors. In the case of the algorithmically based practical numerical simulations in which fixed, albeit small, steps are repeatedly applied, the rise in the number of steps does not reduce the size of the steps but increases the total time of interest. The combinatorial formula shows that, here, the errors diverge. Furthermore, this work can be used to supplement other efforts such as the use of shadow Hamiltonians where the truncation of the series expansion of the latter will produce errors in the higher order propagator moments.

Michaelis–Menten speeds up tauleaping under a wide range of conditions
View Description Hide DescriptionThis paper examines the benefits of Michaelis–Menten model reduction techniques in stochastic tauleaping simulations. Results show that although the conditions for the validity of the reductions for tauleaping remain the same as those for the stochastic simulation algorithm (SSA), the reductions result in a substantial speedup for tauleaping under a different range of conditions than they do for SSA. The reason of this discrepancy is that the time steps for SSA and for tauleaping are determined by different properties of system dynamics.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photoionization of fixedinspace molecules by partially polarized light
View Description Hide DescriptionA general equation for the threedimensional angular distribution of photoelectrons ejected from fixedinspace molecules of any symmetry by light of arbitrary polarization is derived. The state of the light polarization is described by the Stokes parameters. The equation is also valid for photoionization of polarized atoms and aligned or oriented rotating molecules. In the particular case of linear molecules the threedimensional angular distribution of photoelectrons is fully characterized by five twodimensional angular distributions. Simple ways to determine experimentally these twodimensional functions are mentioned. The application of general equations is illustrated by a numerical example of photoionization of the C Kshell of CO molecule in the region of the σ* shape resonance.

The pure rotational spectrum of HPS (): Chemical bonding in secondrow elements
View Description Hide DescriptionThe pure rotational spectrum of HPS, as well as its ^{34}S and D isotopologues, has been recorded at microwave, millimeter, and submillimeter wavelengths, the first observation of this molecule in the gas phase. The data were obtained using a combination of millimeter direct absorption, Fourier transform microwave (FTMW), and microwave–microwave doubleresonance techniques, which cover the total frequency range from 15 to 419 GHz. Quantum chemical calculations at the B3LYP and CCSD(T) levels were also performed to aid in spectral identification. HPS was created in the direct absorption experiment from a mixture of elemental phosphorus, H_{2}S, and Ar carrier gas; DPS was produced by adding D_{2}. In the FTMW study, these species were generated in a pulsed discharge nozzle from PH_{3} and H_{2}S or D_{2}S, diluted in neon. The spectra recorded for HPS and its isotopologues exhibit clear asymmetric top patterns indicating bent structures; phosphorus hyperfine splittings were also observed in HPS, but not DPS. Analysis of the data yielded rotation, centrifugal distortion, and phosphorus nuclear spinrotation parameters for the individual species. The r _{ m } ^{(1)}structure for HPS, calculated from the rotational constants, is r(H–P) = 1.438(1) Å, r(P–S) = 1.9320(1) Å, and θ(H–P–S) = 101.85(9)°. Empirically correcting for zeropoint vibrational effects yields the geometry r _{ e }(H–P) = 1.4321(2) Å, r _{ e }(P–S) = 1.9287(1) Å, and θ_{ e }(H–P–S) = 101.78(1)°, in close agreement with the r _{ m } ^{(1)}structure. A small inertial defect was found for HPS indicating a relatively rigid molecule. Based on these data, the bonding in this species is best represented as H–P=S, similar to the firstrow analog HNO, as well as HNS and HPO. Therefore, substitution of phosphorus and sulfur for nitrogen and oxygen does not result in a dramatic structural change.

Quantum and quasiclassical statetostate dynamics of the NH + H reaction: Competition between abstraction and exchange channels
View Description Hide DescriptionQuantum and quasiclassical statetostate dynamics for the NH + H′ reaction at high collision energies up to 1.6 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstraction (NH + H′ → N + HH′) and thermoneutral exchange (NH + H′ → H + NH′) channels were investigated from the same set of wave packets using an efficient coordinate transformation method. It is found that the abstraction represents a minor reaction channel in the energy range studied, primarily due to endothermicity. The cross section for the abstraction reaction increases monotonically with the collision energy, while that for the exchange reaction is relatively energy insensitive. As a result, the thermal rate constant for the abstraction reaction follows the Arrhenius law, where that for the exchange reaction is nearly temperature independent. Finally, it is shown that the quantum mechanical results can be reasonably reproduced by the Gaussianbinning quasiclassical trajectory method and to a lesser extent by a quantum statistical model.

Measurement and analysis of the diffuse reflectance of powdered samples at terahertz frequencies using a quantum cascade laser
View Description Hide DescriptionWe report terahertz (THz) diffuse reflectance measurements of bulk powdered samples at a frequency of 2.83 THz using a narrowband quantum cascade laser. Samples studied comprise polydisperse powders with absorption coefficients extending over two orders of magnitude from ∼3 cm^{−1} to >200 cm^{−1}. Diffuse reflectance measurements are used to obtain the effective absorption coefficient of these samples from the backscattering crosssection, predicted under the quasicrystalline approximation (QCA) in the Tmatrix formulation and in conjunction with the PercusYevick pair distribution function. Results are compared with effective absorption coefficients obtained from THz timedomain spectroscopy measurements on pressed pellet samples, and show good agreement over the range of effective absorption coefficients studied. We observe that the backscattering crosssection predicted under the QCA is strongly dependent on both the real and imaginary components of the complex permittivity of the sample, and we show that reliable determination of the absorption coefficient from diffuse reflectance measurements therefore requires knowledge of the sample's refractive index. This work demonstrates the applicability of diffuse reflectance measurements, using a THz frequency quantum cascade laser, to the highresolution spectroscopic analysis of bulk powdered samples at THz frequencies.

Monohydrates of cuprous chloride and argentous chloride: H_{2}O⋅⋅⋅CuCl and H_{2}O⋅⋅⋅AgCl characterized by rotational spectroscopy and ab initio calculations
View Description Hide DescriptionPure rotational spectra of the ground vibrational states of ten isotopologues of each of H_{2}O⋅⋅⋅CuCl and H_{2}O⋅⋅⋅AgCl have been measured and analyzed to determine rotational constants and hyperfine coupling constants for each molecule. The molecular structure and spectroscopic parameters determined from the experimental data are presented alongside the results of calculations at the CCSD(T) level. Both experiment and theory are consistent with structures that are nonplanar at equilibrium. The heavy atoms are collinear while the local C _{2} axis of the water molecule intersects the axis defined by the heavy atoms at an angle, ϕ = 40.9(13)° for Cu and ϕ = 37.4(16)° for Ag. In the zeropoint state, each molecule is effectively planar, undergoing rapid inversion between two equivalent structures where ϕ has equal magnitude but opposite sign. The equilibrium geometry has C _{ s } symmetry, however. The ab initio calculations confirm that the timescale of this inversion is at least an order of magnitude faster than that of rotation of the molecule in the lowest rotational energy levels. The molecular geometries are rationalized using simple rules that invoke the electrostatic interactions within the complexes. Centrifugal distortion constants, Δ_{ J } and Δ_{ JK }, nuclear quadrupole coupling constants, χ_{ aa }(Cu), χ_{ aa }(Cl), (χ_{ bb } – χ_{cc})(Cu), and (χ_{ bb } – χ_{cc})(Cl), and the nuclear spinrotation constant of the copper atom, , are also presented.

Two and threebody photodissociation dynamics of diiodobromide (I_{2}Br^{−}) anion
View Description Hide DescriptionThe photodissociation of gasphase I_{2}Br^{−} was investigated using fast beam photofragment translational spectroscopy. Anions were photodissociated from 300 to 270 nm (4.13–4.59 eV) and the recoiling photofragments were detected in coincidence by a time and positionsensitive detector. Both two and threebody channels were observed throughout the energy range probed. Analysis of the twobody dissociation showed evidence for four distinct channels: Br^{−} + I_{2}, I^{−} + IBr, , and I + IBr^{−}. In threebody dissociation, Br(^{2} P _{3/2}) + I(^{2} P _{3/2}) + I^{−} and Br^{−} + I(^{2} P _{3/2}) + I(^{2} P _{3/2}) were produced primarily from a concerted decay mechanism. A sequential decay mechanism was also observed and attributed to followed by predissociation of I_{2}(B).

Slow photoelectron velocitymap imaging spectroscopy of the nmethylvinoxide anion
View Description Hide DescriptionHigh resolution photoelectron spectra of the nmethylvinoxide anion and its deuterated isotopologue are obtained by slow electron velocitymap imaging. Transitions between the ^{1} A′ anion ground electronic state and the radical ^{2} A″ and ^{2} A′ states are observed. The major features in the spectra are attributed to transitions involving the lower energy cis conformers of the anion and neutral, while the higher energy trans conformers contribute only a single small peak. Franck–Condon simulations of the ^{2} A″ ← ^{1} A′ and ^{2} A′ ← ^{1} A′ transitions are performed to assign vibrational structure in the spectrum and to aid in identifying peaks in the cisnmethylvinoxy ^{2} A″ band that occur only through vibronic coupling. The experimental electron affinity and state term energy are found to be EA = 1.6106 ± 0.0008 eV and T_{0} = 1.167 ± 0.002 eV for cisnmethylvinoxy.

A study of electron scattering from benzene: Excitation of the ^{1}B_{1u }, ^{3}E_{2g }, and ^{1}E_{1u } electronic states
View Description Hide DescriptionWe report results from measurements for differential and integral cross sections of the unresolved ^{1}B_{1u } and ^{3}E_{2g } electronic states and the ^{1}E_{1u } electronic state in benzene. The energy range of this work was 10–200 eV, while the angular range of the differential cross sections was ∼3°–130°. To the best of our knowledge there are no other corresponding theoretical or experimental data against which we can compare the present results. A generalized oscillator strength analysis was applied to our 100 and 200 eV differential cross section data, for both the ^{1}B_{1u } and ^{1}E_{1u } states, with optical oscillator strengths being derived in each case. The respective optical oscillator strengths were found to be consistent with many, but not all, of the earlier theoretical and experimental determinations. Finally, we present theoretical integral cross sections for both the ^{1}B_{1u } and ^{1}E_{1u } electronic states, as calculated within the BEfscaling formalism, and compare them against relevant results from our measurements. From that comparison, an integral cross section for the optically forbidden ^{3}E_{2g } state is also derived.