Volume 120, Issue 1, 01 January 2004
 COMMUNICATIONS


Normal modes and frequencies from covariances in molecular dynamics or Monte Carlo simulations
View Description Hide DescriptionWe propose a simple method to obtain normal modes (NMs) and their characteristicfrequencies from molecular dynamics or Monte Carlo simulations at any temperature. The resulting NM are consistent with the vibrational density of states (DOS) (every feature of the DOS can be attributed to one or few NMs). At low temperatures they coincide with the ones obtained from the Hessian matrix. We define the NMs by imposing the condition that their velocities be uncorrelated to each other: where 〈 〉 denotes time average and is Kronecker’s delta. With this definition the modes are the eigenvectors of the matrix being the number of atoms); are masses and atomic velocities]. The eigenvalues of represent the kinetic energy in each NM. The ratio between the eigenvalues and those obtained using positions accelerations in instead of velocities are a very good approximation to the mode frequencies: We demonstrate the new method using with two cases: an isolated water molecule and a crystalline polymer.

Transition from atomic to molecular adsorption of oxygen on tungsten monomer anion
View Description Hide DescriptionUsing vibrationally resolved ultraviolet photoelectron spectroscopy, we studied oxygen adsorption on W monomer anions. Three oxygen atoms are atomically bound in a compound, whereas in the fourth oxygen atom is attached to the oxygen, forming a dioxygen species, implying that atom to molecule transition of takes place when the number of oxygen atoms attached to a W monomer anion exceeds three. Our results indicate that molecular adsorption of oxygen is preferred on electrondeficient metals, showing that the driving force of the atom to molecule transition for the chemisorption of diatomic molecules can be the variations of electronic structures of metal hosts.
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 ARTICLES

 Theoretical Methods and Algorithms

Dynamical multipletime stepping methods for overcoming resonance instabilities
View Description Hide DescriptionCurrent molecular dynamics simulations of biomolecules using multiple time steps to update the slowly changing force are hampered by instabilities beginning at time steps near the half period of the fastest vibrating mode. These “resonance” instabilities have became a critical barrier preventing the long time simulation of biomolecular dynamics. Attempts to tame these instabilities by altering the slowly changing force and efforts to damp them out by Langevin dynamics do not address the fundamental cause of these instabilities. In this work, we trace the instability to the nonanalytic character of the underlying spectrum and show that a correct splitting of the Hamiltonian, which renders the spectrum analytic, restores stability. The resulting Hamiltonian dictates that in addition to updating the momentum due to the slowly changing force, one must also update the position with a modified mass. Thus multipletime stepping must be done dynamically.

A diffusion quantum Monte Carlo study of geometries and harmonic frequencies of molecules
View Description Hide DescriptionThis article describes an approach in determination of equilibrium geometries and harmonic frequencies of molecules by the Ornstein–Uhlenbeck diffusionquantum Monte Carlo method based on the floating spherical Gaussians. In conjunction with a projected and renormalized Hellmann–Feynman gradient and an electronic energy at variational Monte Carlo and diffusionquantum Monte Carlo, respectively, the quasiNewton algorithm implemented with the Broyden–Fletcher–Goldfarb–Shanno updated Hessian was used to find the optimized molecular geometry. We applied this approach to and molecules. The geometry and harmonic frequencies calculated were consistent with some sophisticated ab initio calculated values within reasonable statistical uncertainty.

Density functional theory with alternative spin densities: Application to magnetic systems with localized spins
View Description Hide DescriptionA new method to improve the excess spin density obtained from unrestricted Hartree–Fock wave functions in terms of natural orbitals is proposed. Using this modified excess spin density to evaluate the correlation energy by means of density functionals leads to large improvements in the computed magnetic coupling constants of several materials without need to modify the exchange contribution. This is important because it reconciles the density functional theory description with the one provided by multideterminant wave functions. Using the present approach, the leading contribution to the magnetic coupling constant arises from electron correlation effects. The performance of the new method is illustrated on various materials including highcriticaltemperature superconductors parent compounds.

Longtime and unitary properties of semiclassical initial value representations
View Description Hide DescriptionWe numerically compare the semiclassical “frozen Gaussian” Herman–Kluk propagator [Chem. Phys. 91, 27 (1984)] and the “thawed Gaussian” propagator put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by studying the quantum dynamics in some nonlinear onedimensional potentials. The reasons for the lack of longtime accuracy and norm conservation in the latter method are uncovered. We amend the thawed Gaussian propagator with a global harmonic approximation for the stability of the trajectories and demonstrate that this revised propagator is a true alternative to the Herman–Kluk propagator with similar accuracy.

Improved convergence in block copolymer selfconsistent field theory by Anderson mixing
View Description Hide DescriptionA modification to real space polymeric selfconsistent field theory algorithms that greatly improves the convergence properties is presented. The method is based on Anderson mixing [D. G. Anderson, J. Assoc. Comput. Mach.12, 547 (1965)], and each iteration computed takes negligibly longer to perform than with other methods, but the number of iterations required to reach a high accuracy solution is greatly reduced. No a priori knowledge of possible phases is required to apply this method. We apply our approach to a standard diblock copolymer melt, and demonstrate iteration reductions of more than a factor of 5 in some cases.

Fluidlike behavior of a onedimensional granular gas
View Description Hide DescriptionWe study the properties of a onedimensional (1D) granular gas consisting of hard rods on a line of length (with periodic boundary conditions). The particles collide inelastically and are fluidized by a heat bath at temperature and viscosity γ. The analysis is supported by molecular dynamics simulations. The average properties of the system are first discussed, focusing on the relations between granular temperature kinetic pressure, and density Thereafter, we consider the fluctuations around the average behavior obtaining a slightly nonGaussian behavior of the velocity distributions and a spatially correlated velocity field; the density field displays clustering: this is reflected in the structure factor which has a peak in the region suggesting an analogy between inelastic hard core interactions and an effective attractive potential. Finally, we study the transport properties, showing the typical subdiffusive behavior of 1D stochastically driven systems, i.e., where for the inelastic fluid is larger than the elastic case. This is directly related to the peak of the structure factor at small wave vectors.

The welltempered auxiliaryfield Monte Carlo
View Description Hide DescriptionThe auxiliaryfield Monte Carlo (AFMC) is a method for computing groundstate and excitedstate energies and other properties of electrons in molecules. For a given basis set, AFMC is an approximation to fullconfiguration interaction and the accuracy is determined predominantly by an inverse temperature “β” parameter. A considerable amount of the dynamical correlation energy is recovered even at small values of β. Yet, nondynamical correlation energy is inefficiently treated by AFMC. This is because the statistical error grows with β, warranting increasing amount of Monte Carlo sampling. A recently introduced multideterminant variant of AFMC is studied, and the method can be tuned by balancing the sizes of the determinantal space and the βparameter with respect to a predefined target accuracy. The welltempered AFMC is considerably more efficient than a naı̈ve AFMC. As a welcome “byproduct” low lying excitation energies of the molecule are supplied as well. We demonstrate the principles on dissociating hydrogen molecule and torsion of ethylene where we calculate the (unoptimized) torsional barrier and the vertical singlettriplet splitting.

Exact effective Hamiltonian theory. II. Polynomial expansion of matrix functions and entangled unitary exponential operators
View Description Hide DescriptionOur recent exact effective Hamiltonian theory (EEHT) for exact analysis of nuclear magnetic resonance(NMR) experiments relied on a novel entanglement of unitary exponential operators via finite expansion of the logarithmic mapping function. In the present study, we introduce simple alternant quotient expressions for the coefficients of the polynomial matrix expansion of these entangled operators. These expressions facilitate an extension of our previous closed solution to the Baker–Campbell–Hausdorff problem for systems from to any and thereby the potential application of EEHT to more complex NMR spin systems. Similarity matrix transformations of the EEHT expansion are used to develop alternant quotient expressions, which are fully general and prove useful for evaluation of any smooth matrix function. The general applicability of these expressions is demonstrated by several examples with relevance for NMR spectroscopy. The specific form of the alternant quotients is also used to demonstrate the fundamentally important equivalence of Sylvester’s theorem (also known as the spectral theorem) and the EEHT expansion.

Fock space multireference coupled cluster calculations based on an underlying bivariational selfconsistent field on Auger and shape resonances
View Description Hide DescriptionThe Fock space multireference coupled cluster based on an underlying bivariational selfconsistent field is applied to the problem of computing complex energy associated with Auger and shape resonances in eatom scattering. It is concluded that the Fock space multireference coupled cluster based on a bivariational selfconsistent field provides a useful and practical approach to calculation of resonance parameters. Numerical results are presented for the shape resonance of Mg and Auger 1 s^{−1} hole of Be.

Towards an accurate representation of electrostatics in classical force fields: Efficient implementation of multipolar interactions in biomolecular simulations
View Description Hide DescriptionThe accurate simulation of biologically active macromolecules faces serious limitations that originate in the treatment of electrostatics in the empirical force fields. The current use of “partial charges” is a significant source of errors, since these vary widely with different conformations. By contrast, the molecular electrostatic potential (MEP) obtained through the use of a distributed multipole moment description, has been shown to converge to the quantum MEP outside the van der Waals surface, when higher order multipoles are used. However, in spite of the considerable improvement to the representation of the electronic cloud, higher order multipoles are not part of current classical biomolecular force fields due to the excessive computational cost. In this paper we present an efficient formalism for the treatment of higher order multipoles in Cartesian tensor formalism. The Ewald “direct sum” is evaluated through a McMurchie–Davidson formalism [L. McMurchie and E. Davidson, J. Comput. Phys. 26, 218 (1978)]. The “reciprocal sum” has been implemented in three different ways: using an Ewald scheme, a particle mesh Ewald (PME) method, and a multigridbased approach. We find that even though the use of the McMurchie–Davidson formalism considerably reduces the cost of the calculation with respect to the standard matrix implementation of multipole interactions, the calculation in direct space remains expensive. When most of the calculation is moved to reciprocal space via the PME method, the cost of a calculation where all multipolar interactions (up to hexadecapole–hexadecapole) are included is only about 8.5 times more expensive than a regular AMBER 7 [D. A. Pearlman et al., Comput. Phys. Commun. 91, 1 (1995)] implementation with only chargechargeinteractions. The multigrid implementation is slower but shows very promising results for parallelization. It provides a natural way to interface with continuous, Gaussianbased electrostatics in the future. It is hoped that this new formalism will facilitate the systematic implementation of higher order multipoles in classical biomolecular force fields.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Radiative transition probabilities, lifetimes and dipole moments for the vibrational levels of the ground state of
View Description Hide DescriptionUsing a potential energy curve (based primarily on the RKR potential of Amiot and Vergès [J. Chem. Phys. 112, 7068 (2000)]) and a dipole moment function (based primarily on ab initio calculations of Park et al. [Chem. Phys. 257, 135 (2000)]), we have calculated radiative transition probabilities (Einstein A coefficients), radiative lifetimes, and dipole moment expectation values involving all vibrational levels (for several rotational quantum numbers) of the ground state of We observe that the radiative lifetimes of vibrationally excited levels, in particular, are seconds, far too long to be significant in most ultracold experiments involving or its isotopomers. Comparison with other molecules (LiH and HF) suggests that simple scaling will predict similarly long lifetimes for many other heteronuclear molecules, e.g., RbCs.

Theoretical study of the complex. I. The two asymptotically degenerate ground state potential energy surfaces
View Description Hide DescriptionTwo threedimensional potential energy surfaces (PESs) are reported for the cationic complex they are degenerate for linear geometries of the complex and correlate with the doubly degenerate ground state of the monomer. The PESs are computed from the interaction energies of the neutral dimer and the ionization potentials of the He–HF complex and the HF molecule. Ionization potentials are obtained from the outer valence Green’s function (OVGF) method, while the energies of the neutral species are computed by means of the single and double coupledcluster method with perturbative triples [CCSD(T)]. For comparison, interaction energies of the ionic complex were computed also by the use of the partially spinrestricted variant of the CCSD(T) method. After asymptotic scaling of the OVGF results, good agreement is found between the two methods. A single global minimum is found in the PES, for the linear geometry. The well depth and equilibrium separation are 2.240 Å and respectively, at an bond length in rather good agreement with results of Schmelz and Rosmus [Chem. Phys. Lett. 220, 117 (1994)]. The well depth depends much more strongly on the internuclear H–F separation than in the neutral He–HF complex and the global minimum in a full threedimensional PES occurs at

Theoretical study of the complex. II. Rovibronic states from coupled diabatic potential energy surfaces
View Description Hide DescriptionThe bound rovibronic levels of the complex were calculated for total angular momentum and with the use of ab initio diabatic intermolecular potentials presented in Paper I and the inclusion of spin–orbit coupling. The character of the rovibronic states was interpreted by a series of calculations with the intermolecular distance fixed at values ranging from 1.5 to 8.5 Å and by analysis of the wave functions. In this analysis we used approximate angular momentum quantum numbers defined with respect to a dimer bodyfixed (BF) frame with its axis parallel to the intermolecular vector R and with respect to a moleculefixed (MF) frame with its axis parallel to the bond. The linear equilibrium geometry makes the complex a Renner–Teller system. We found both sets of quantum numbers, BF and MF, useful to understand the characteristics of the Renner–Teller effect in this system. In addition to the properties of a “normal” semirigid molecule Renner–Teller system it shows typical features caused by largeamplitude internal (bending) motion. We also present spectroscopic data: stretch and bend frequencies, spin–orbit splittings, parity splittings, and rotational constants.

Imaging the paircorrelated excitation function: The reaction
View Description Hide DescriptionThe velocity map ion imaging technique was applied to measure the reaction excitation function for the first time. It was found that the “raw” excitation function was significantly distorted by the densitytoflux transformation of the title reaction. Through a systematic investigation, possible reasons for such a dramatic effect are outlined. In addition, the stateresolved, paircorrelated excitation functions and branching ratios are presented. Effects of imperfect time slicing in the timesliced velocity imaging technique in general are also discussed.

Dissociation of multiply ionized isocyanic acid through electron impact
View Description Hide DescriptionThe dissociation of singly to triply ionized isocyanic acid (HNCO) has been investigated by two and threedimensional covariance mapping techniques through electron impact ionization at an electron energy of 200 eV. The absolute cross sections for the various dissociation channels of up to triply ionized HNCO have been measured. The HNCO dications dissociate mostly into ion pairs, while the HNCO trications dissociate mostly into ion triples, both through all the possible bond cleavages and charge allocations. Some major ionpair dissociation channels of are supposed to be sequential dissociation through initial charge separation. The metastable decay traces caused by and have been observed on the covariance map.

Low temperature pressure broadening of by
View Description Hide DescriptionWe report experimentally measured cross sections for pressure broadening of ammonia inversion transitions by ortho at temperatures of 18–40 K. These measurements were made in a quasiequilibrium cell using the collisional cooling technique. Cross sections for broadening of the metastable (2, 2) and (3, 3) inversion transitions ranged from for (1, 1) at 20.0 K to for (3, 3) at 25.0 K. The ortho cross sections were found to be consistently larger than previously measured cross sections for low temperature broadening of by both He and

The dynamics of conformational isomerization in flexible biomolecules. I. Holefilling spectroscopy of Nacetyl tryptophan methyl amide and Nacetyl tryptophan amide
View Description Hide DescriptionThe conformationalisomerizationdynamics of Nacetyl tryptophan methyl amide (NATMA) and Nacetyl tryptophan amide (NATA) have been studied using the methods of IRUV holefilling spectroscopy (HFS) and IRinduced population transfer spectroscopy (IRPTS), which were developed for this purpose. Single conformations of these molecules were selectively excited in welldefined NH stretch fundamentals. This excess energy was used to drive conformationalisomerization. By carrying out the infrared excitation early in a supersonic expansion, the excited molecules were recooled into their zeropoint levels, partially refilling the hole created in the ground state population of one of the conformers, and creating gains in population in other conformers. These changes in population were detected using laserinduced fluorescence downstream in the expansion. In HFS, the IR wavelength is fixed and the UV laser tuned in order to determine where the population went following selective infrared excitation. In IRPTS, the UV is fixed to monitor the population of a given conformation, and the IR is tuned to record the IRinduced changes in the population of the monitored conformer. Besides demonstrating the capability of the experiment to change the downstream conformational population distribution, the IRPTS scans were used to extract two quantitative results: (i) The fractional populations of the conformers in the absence of the infrared, and (ii) the isomerization quantum yields for each of the six unique amide NH stretch fundamentals (three conformers each with two amide groups). The method for obtaining quantum yields is described in detail. In both NATMA and NATA, the quantum yields show modest conformational specificity, but only a hint of vibrational mode specificity. The prospects for the holefilling technique for providing insight into energy flow in large molecules are discussed, leaving a more detailed theoretical modeling to the adjoining paper [Evans et al. J. Chem. Phys. 120, 148 (2004)].

The dynamics of conformational isomerization in flexible biomolecules. II. Simulating isomerizations in a supersonic free jet with master equation dynamics
View Description Hide DescriptionInfraredinduced conformationalisomerization of Nacetyltryptophan methyl amide is studied theoretically using a microcanonical Rice–Ramsperger–Kassel–Marcus description of the rates on potential energy surfaces calculated using the AMBER and OPLSAA force fields. The results are compared with the experimental data from Dian et al. in the preceding paper [J. Chem. Phys. 120, 133 (2004)]. An exhaustive search of the potential energy surfaces locates all minima and transition states on these surfaces. A simple model is proposed for the vibrational cooling, and an appropriate cooling rate is chosen as the standard conditions for the master equation simulations by comparison with experiment. The two potential energy surfaces differ in the relative energies of minima and the heights of key transition states, leading to differences in the dominant pathways and rates of conformationalisomerization. The predicted quantum yields depend sensitively on the cooling rate, varying from the slow cooling limit in which equilibrium populations are achieved to the fast quenching limit in which conformationalisomerization is shut off. The excitation energy is varied from 5 to 20 kcal mol^{−1}. At the lowest energies, isomerization is completely quenched, while at the highest energies, equilibrium conditions are achieved. In between these extremes, the quantum yields are sensitive to the excitation energy, and can be used to locate the ratelimiting barriers to isomerization.