Volume 126, Issue 24, 28 June 2007
 ANNOUNCEMENTS
 COMMUNICATIONS


Approaching the full set of energy levels of water
View Description Hide DescriptionWe report here the measurements of rovibrational levels in the electronic ground state of water molecule at the previously inaccessible energies above . The use of laser doubleresonance overtone excitation extends this limit to , which corresponds to 83% of the water dissociation energy. We use experimental data to generate a semiempirical potential energy surface that now allows prediction of water levels with sub accuracy at any energy up to the new limit.

Highenergy conformer of formic acid in solid neon: Giant difference between the proton tunneling rates of cis monomer and transcis dimer
View Description Hide DescriptionWe study the conformational reorganization of formic acid (FA) in solid neon and report the higherenergy cisFA monomer and one form of the transcis FA dimers. They were prepared by selective vibrational excitation of the transFA monomer and transtrans dimer. The protontunneling decay of cisFA monomer is surprisingly very fast in solid neon, two orders of magnitude faster than in solid argon. It was also found that the stability of the transcis dimer against protontunneling is enormously enhanced in solid neon compared to the monomer (by a factor of ). These results are discussed in terms of matrix solvation and hydrogen bonding.

Structure of coexisting liquid phases of supercooled water: Analogy with ice polymorphs
View Description Hide DescriptionThe structural changes occurring in supercooled liquid water upon moving from one coexisting liquid phase to the other have been investigated by computer simulation using a polarizable interaction potential model. The obtained results favorably compare with recent neutron scattering data of high and low density water. In order to assess the physical origin of the observed structural changes, computer simulation of several icepolymorphs has also been carried out. Our results show that there is a strict analogy between the structure of various disordered (supercooled) and ordered (ice) phases of water, suggesting that the occurrence of several different phases of supercooled water is rooted in the same physical origin that is responsible for icepolymorphism.

Photostability of amino acids: Internal conversion versus dissociation
View Description Hide DescriptionPhotodissociation dynamics for various tryptophan chromophores was studied at 193 or using multimass ion imaging techniques. The competition between internal conversion to the ground electronic state and dissociation from the repulsive excited state reveals sizedependent photostability for these amino acid chromophores. As the size of chromophore increases, internal conversion to the ground state becomes the major nonradiative process. For tryptophan and larger chromophores, dissociation directly from the repulsive state is completely quenched.
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 ARTICLES

 Theoretical Methods and Algorithms

Calculation of the distribution of eigenvalues and eigenvectors in Markovian state models for molecular dynamics
View Description Hide DescriptionMarkovian state models (MSMs) are a convenient and efficient means to compactly describe the kinetics of a molecular system as well as a formalism for using many short simulations to predict long time scale behavior. Building a MSM consists of grouping the conformations into states and estimating the transition probabilities between these states. In a previous paper, we described an efficient method for calculating the uncertainty due to finite sampling in the mean first passage time between two states. In this paper, we extend the uncertainty analysis to derive similar closedform solutions for the distributions of the eigenvalues and eigenvectors of the transition matrix, quantities that have numerous applications when using the model. We demonstrate the accuracy of the distributions on a sixstate model of the terminally blocked alanine peptide. We also show how to significantly reduce the total number of simulations necessary to build a model with a given precision using these uncertainty estimates for the blocked alanine system and for a 2454state MSM for the dynamics of the villin headpiece.

Timedependent densityfunctional theory/localized density matrix method for dynamic hyperpolarizability
View Description Hide DescriptionTimedependent densityfunctional theory/localized density matrix method (TDDFT/LDM) was developed to calculate the excited state energy, absorption spectrum and dynamic polarizability. In the present work we generalize it to calculate the dynamic hyperpolarizabilities in both time and frequency domains. We show that in the frequency domain the rule can be derived readily and the dynamic hyperpolarizabilities are thus calculated efficiently. Although the timedomain TDDFT/LDM is time consuming, its implementation is straightforward because the evaluation of the derivatives of exchangecorrelation potential with respect to electron density is avoided. Moreover, the timedomain method can be used to simulate higher order response which is very difficult to be calculated with the frequencydomain method.

Steric effect: A quantitative description from density functional theory
View Description Hide DescriptionThe concepts of steric energy, steric potential, and steric charge are introduced within the density functional theory framework. The steric energy, representing a hypothetical state with all electrons packed into the lowest orbital and other effects entirely excluded, is a measure of the intrinsic space occupied by an electronic system. It is exclusive, repulsive, and extensive, and it vanishes for homogeneous electron gas. When Bader’s zeroflux boundary condition is adopted, atoms in molecules are found to achieve balanced steric repulsion among one another with vanished steric energy density interfaces. A few molecular systems involving conformation changes and chemical reactions have been investigated to examine the relative contribution of the steric and other effects, providing insights for a few controversial topics from a different perspective.

Modeling the adiabatic connection in
View Description Hide DescriptionFull configuration interaction (FCI) data are used to quantify the accuracy of approximate adiabatic connection (AC) forms in describing the ground state potential energy curve of , within spinrestricted density functional theory(DFT). For each internuclear separation , accurate properties of the AC are determined from large basis set FCI calculations. The parameters in the approximate AC form are then determined so as to reproduce these FCI values exactly, yielding an exchangecorrelation energy expressed entirely in terms of FCIderived quantities. This is combined with other FCIderived energy components to give the total electronic energy; comparison with the FCI energy quantifies the accuracy of the AC form. Initial calculations focus on a Padébased form. The potential energy curve determined using the procedure is a notable improvement over those from existing DFT functionals. The accuracy near equilibrium is quantified by calculating the bond length and vibrational wave numbers; errors in the latter are below 0.5%. The molecule dissociates correctly, which can be traced to the use of virtual orbital eigenvalues in the slope in the noninteracting limit, capturing static correlation. At intermediate , the potential energy curve exhibits an unphysical barrier, similar to that noted previously using the random phase approximation. Alternative forms of the AC are also considered, paying attention to size extensivity and the behavior in the stronginteraction limit; none provide an accurate potential energy curve for all , although good accuracy can be achieved near equilibrium. The study demonstrates how data from correlated ab initio calculations can provide valuable information about AC forms and highlight areas where further theoretical progress is required.

Extrapolating to the oneelectron basisset limit in electronic structure calculations
View Description Hide DescriptionA simple, yet reliable, scheme based on treating uniformly singletpair and tripletpair interactions is suggested to extrapolate atomic and molecular electron correlation energies calculated at two basisset levels of ab initiotheory to the infinite oneelectron basisset limit. The novel duallevel method is first tested on extrapolating the full correlation in singlereference coupledcluster singles and doubles energies for the closedshell systems , , HF, , CO, Ne, and with correlationconsistentbasis sets of the type ccpVXZ reported by Klopper [Mol. Phys.6, 481 (2001)] against his own benchmark calculations with large uncontracted basis sets obtained from explicit correlated singles and doubles coupledcluster theory. Comparisons are also reported for the same data set but using both singlereference MøllerPlesset and coupledcluster doubles methods. The results show a similar, often better, accordance with the target results than Klopper’s extrapolations where singletpair and tripletpair energies are extrapolated separately using the popular and duallevel laws, respectively. Applications to the extrapolation of the dynamical correlation in multireference configuration interaction calculations carried out anew for He, , , , , , BH, CH, NH, OH, FH, , , , , , BO, CO, NO, BN, CN, SH, , and with standard augmented correlationconsistentbasis sets of the type are also reported. Despite lacking accurate theoretical or experimental data for comparison in the case of most diatomic systems, the new method also shows in this case a good performance when judged from the results obtained with the traditional schemes which extrapolate using the two largest affordable basis sets. For the HartreeFock and completeactive space selfconsistent field energies, a simple pragmatic extrapolation rule is examined whose results are shown to compare well with the ones obtained from the best reported schemes.

Second and thirdorder triples and quadruples corrections to coupledcluster singles and doubles in the ground and excited states
View Description Hide DescriptionSecond and thirdorder perturbation corrections to equationofmotion coupledcluster singles and doubles (EOMCCSD) incorporating excited configurations in the space of triples [ and ] or in the space of triples and quadruples have been implemented. Their groundstate counterparts—thirdorder corrections to coupledcluster singles and doubles (CCSD) in the space of triples or in the space of triples and quadruples —have also been implemented and assessed. It has been shown that a straightforward application of the RayleighSchrödinger perturbation theory leads to perturbation corrections to total energies of excited states that lack the correct size dependence. Approximations have been introduced to the perturbation corrections to arrive at , , and that provide sizeintensive excitation energies at a noniterative , , and cost ( is the number of orbitals) and and sizeextensive total energies at a noniterative and cost. All the implementations are parallel executable, applicable to open and closed shells, and take into account spin and real Abelian pointgroup symmetries. For excited states, they form a systematically more accurate series, , with the second and thirdorder corrections capturing typically and 100% of such effects, when those effects are large and the groundstatewave function has singledeterminant character. In other cases, however, the corrections tend to overestimate the triples and quadruples effects, the origin of which is discussed. For ground states, the thirdorder corrections lead to a rather small improvement over the highly effective secondorder corrections [ and ], which is a manifestation of the staircase convergence of perturbation series.

Diminished gradient dependence of density functionals: Constraint satisfaction and selfinteraction correction
View Description Hide DescriptionThe PerdewBurkeErnzerhof (PBE) generalized gradient approximation for the exchangecorrelation energy functional has two nonempirical constructions, based on satisfaction of universal exact constraints on the hole density or on the energy. We show here that, by identifying one possible free parameter in exchange and a second in correlation, we can continue to satisfy these constraints while diminishing the gradient dependence almost to zero (i.e., almost recovering the local spin density approximation or LSDA). This points out the important role played by the PerdewWang 1991 nonempirical hole construction in shaping PBE and later constructions. Only the undiminished PBE is good for atoms and molecules, for reasons we present, but a somewhat diminished PBE could be useful for solids; in particular, the surface energies of solids could be improved. Even for atoms and molecules, a strongly diminished PBE works well when combined with a scaleddown selfinteraction correction (although perhaps not significantly better than LSDA). This shows that the undiminished gradient dependence of PBE and related functionals works somewhat like a scaleddown selfinteraction correction to LSDA.

Treatment of geometric singularities in implicit solvent models
View Description Hide DescriptionGeometric singularities, such as cusps and selfintersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the PoissonBoltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solventsolute interfaces and leads to highly accurate biomolecular electrostatics in continuum electric environments. However, such a PB solver, denoted as MIBPBI, cannot maintain the designed second order convergence whenever there are geometric singularities, such as cusps and selfintersecting surfaces. Moreover, the matrix of the MIBPBI is not optimally symmetrical, resulting in the convergence difficulty. The present work presents a new interface method based PB solver, denoted as MIBPBII, to address the aforementioned problems. The present MIBPBII solver is systematical and robust in treating geometric singularities and delivers second order convergence for arbitrarily complex molecular surfaces of proteins. A new procedure is introduced to make the MIBPBII matrix optimally symmetrical and diagonally dominant. The MIBPBII solver is extensively validated by the molecular surfaces of fewatom systems and a set of 24 proteins. Converged electrostatic potentials and solvation free energies are obtained at a coarse grid spacing of and are considerably more accurate than those obtained by the PBEQ and the APBS at finer grid spacings.

Decomposition of density matrix renormalization group states into a Slater determinant basis
View Description Hide DescriptionThe quantum chemical density matrix renormalization group (DMRG) algorithm is difficult to analyze because of the many numerical transformation steps involved. In particular, a decomposition of the intermediate and the converged DMRG states in terms of Slater determinants has not been accomplished yet. This, however, would allow one to better understand the convergence of the algorithm in terms of a configuration interaction expansion of the states. In this work, the authors fill this gap and provide a determinantal analysis of DMRG states upon convergence to the final states. The authors show that upon convergence, DMRG provides the same completeactivespace expansion for a given set of active orbitals as obtained from a corresponding configuration interaction calculation. Additional insight into DMRG convergence is provided, which cannot be obtained from the inspection of the total electronic energy alone. Indeed, we will show that the total energy can be misleading as a decrease of this observable during DMRG microiteration steps may not necessarily be taken as an indication for the pickup of essential configurations in the configuration interaction expansion. One result of this work is that a fine balance can be shown to exist between the chosen orbital ordering, the guess for the environment operators, and the choice of the number of renormalized states. This balance can be well understood in terms of the decomposition of total and system states in terms of Slater determinants.

Electronic optical response of molecules in intense fields: Comparison of TDHF, TDCIS, and TDCIS(D) approaches
View Description Hide DescriptionTimedependent HartreeFock (TDHF) and timedependent configuration interaction (TDCI) methods with Gaussian basis sets have been compared in modeling the response of hydrogen molecule, butadiene, and hexatriene exposed to very short, intense laser pulses (, ). After the electric field of the pulse returns to zero, the molecular dipole continues to oscillate due to the coherent superposition of excited states resulting from the nonadiabatic excitation caused by the pulse. The Fourier transform of this residual dipole gives a measure of the nonadiabatic excitation. For low fields, only the lowest excited states are populated, and TDCI simulations using singly excited states with and without perturbative corrections for double excitations [TDCIS(D) and TDCIS, respectively] are generally in good agreement with the TDHF simulations. At higher field strengths, higher states are populated and the methods begin to differ significantly if the coefficients of the excited states become larger than . The response of individual excited states does not grow linearly with intensity because of excited state to excited state transitions. Beyond a threshold in the field strength, there is a rapid increase in the population of many higher excited states, possibly signaling an approach to ionization. However, without continuum functions, the present TDHF and TDCI calculations cannot model ionization directly. The TDHF and TDCIS simulations are in good accord because the excitation energies obtained by linear response TDHF [also known as random phase approximation (RPA)] agree very well with those obtained from singly excited configuration interaction (CIS) calculations. Because CISexcitation energies with the perturbative doubles corrections [CIS(D)] are on average lower than the CISexcitation energies, the TDCIS(D) response is generally stronger than TDCIS.

Dihedral angle principal component analysis of molecular dynamics simulations
View Description Hide DescriptionIt has recently been suggested by Mu et al. [Proteins58, 45 (2005)] to use backbone dihedral angles instead of Cartesian coordinates in a principal component analysis of molecular dynamics simulations. Dihedral angles may be advantageous because internal coordinates naturally provide a correct separation of internal and overall motion, which was found to be essential for the construction and interpretation of the free energy landscape of a biomolecule undergoing large structural rearrangements. To account for the circular statistics of angular variables, a transformation from the space of dihedral angles to the metric coordinate space was employed. To study the validity and the applicability of the approach, in this work the theoretical foundations underlying the dihedral angle principal component analysis (dPCA) are discussed. It is shown that the dPCA amounts to a onetoone representation of the original angle distribution and that its principal components can readily be characterized by the corresponding conformational changes of the peptide. Furthermore, a complex version of the dPCA is introduced, in which angular variables naturally lead to eigenvalues and eigenvectors. Applying the methodology to the construction of the free energy landscape of decaalanine from a molecular dynamics simulation, a critical comparison of the various methods is given.

Zerovariance zerobias quantum Monte Carlo estimators of the spherically and systemaveraged pair density
View Description Hide DescriptionWe construct improved quantum Monte Carlo estimators for the spherically and systemaveraged electron pair density (i.e., the probability density of finding two electrons separated by a relative distance ), also known as the spherically averaged electron position intracule density , using the general zerovariance zerobias principle for observables, introduced by Assaraf and Caffarel. The calculation of is made vastly more efficient by replacing the average of the local deltafunction operator by the average of a smooth nonlocal operator that has several orders of magnitude smaller variance. These new estimators also reduce the systematic error (or bias) of the intracule density due to the approximate trial wave function. Used in combination with the optimization of an increasing number of parameters in trial JastrowSlater wave functions, they allow one to obtain well converged correlated intracule densities for atoms and molecules. These ideas can be applied to calculating any paircorrelation function in classical or quantum Monte Carlo calculations.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Single photon ionization of hydrogen bonded clusters with a soft xray laser: and
View Description Hide DescriptionPure, neutral formic acid clusters and mixed clusters are investigated employing time of flight mass spectroscopy and single photonionization at using a very compact, capillary discharge, soft xray laser. During the ionization process, neutral clusters suffer little fragmentation because almost all excess energy above the vertical ionization energy is taken away by the photoelectron, leaving only a small part of the photon energy deposited into the cluster. The vertical ionization energy minus the adiabatic ionization energy is enough excess energy in the clusters to surmount the proton transfer energy barrier and induce the reaction making the protonated series dominant in all data obtained. The distribution of pure clusters is dependent on experimental conditions. Under certain conditions, a magic number is found at . Metastable dissociation rate constants of are measured in the range for cluster sizes . The rate constants display an odd/even alternating behavior between monomer and dimer loss that can be attributed to the structure of the cluster. When small amounts of water are added to the formic acid, the predominant signals in the mass spectrum are still cluster ions. Also observed are the protonated mixed cluster series for and . A magic number in the cluster series , is observed. The mechanisms and dynamics of formation of these neutral and ionic clusters are discussed.

Theoretical investigation of excited and Rydberg states of imidogen radical NH: Potential energy curves, spectroscopic constants, and dipole moment functions
View Description Hide DescriptionA search is conducted for the calculation of potential energy curves (PECs), spectroscopic constants, and dipole moment functions for excited and Rydberg states of imidogen radical NH, with a particular emphasis on the Rydberg states arising from configuration of nitrogen and and configurations of hydrogen. A range of about above the electronic ground state atomic separation limit which corresponds to the first eight asymptotes of dissociation is spanned. Computations are carried out at the internally contracted multireference singles plus doubles configuration interaction level of theory, including the Davidson correction to account for quadruple excitations. The Gaussian basis set used has been modified from a standard basis to give a balanced description of valenceRydberg interactions. States of , , , , , , and symmetries are computed accurately in the range of energy investigated. PECs of the three lowest states are obtained for the first time. Our spectroscopic constants show good agreement with experimental data in comparison with other theoretical studies reported in the literature. A discussion on the variations of dipole moment functions helps to understand the strong interactions between excited and Rydberg states as well as the avoided crossings. The present study may be of great practical interest for investigations in astrophysical research as well as in laboratory experiments.