Volume 125, Issue 24, 28 December 2006
 COMMUNICATIONS


Using the histogram test to quantify reaction coordinate error
View Description Hide DescriptionMany schemes for calculating reaction rates and free energy barriers require an accurate reaction coordinate, but it is difficult to quantify reaction coordinate accuracy for complex processes like protein folding and nucleation. The histogram test, based on estimated committor probabilities, is often used as a qualitative indicator for good reaction coordinates. This paper derives the mean and variance of the intrinsic committor distribution in terms of the mean and variance of the histogram of committor estimates. These convenient formulas enable the first quantitative calculations of reaction coordinate error for complex systems. An example shows that the approximate transition state surface from Peters’ and Trout’s reaction coordinate for nucleation in the Ising model gives a mean committor probability of 0.495 and a standard deviation of 0.042.

Relativistic effective core potential calculations of Hg and ekaHg (E112) interactions with gold: Spinorbit density functional theory modeling of and systems
View Description Hide DescriptionInteractions of ekaHg (E112) and Hg atoms with small gold clusters were studied in the frame of the relativistic effective core potential model using the density functional theory(DFT) approach incorporating spindependent (magnetic) interactions. The choice of the exchangecorrelation functional was based on a comparison of the results of DFT and largescale coupled cluster calculations for and at the scalar relativistic level. A close similarity between the and equilibrium structures was observed. The E112 binding energies on are typically smaller than those for Hg by ca. 25%–32% and the equilibrium separations are always slightly larger than their counterparts.
 Top

 ARTICLES

 Theoretical Methods and Algorithms

Analogies and differences between two ways to evaluate the global hardness
View Description Hide DescriptionThe weight of the energetic components (electronic kinetic, electronnucleus and electronelectron Coulombic, and correlation energies) of the ionization potential,electron affinity,chemical potential, and global hardness is evaluated and contrasted with the energetic components of the hardness kernel and the experimental values of these properties for 40 systems. The contrast of the hardness terms obtained from finite difference and hardness kernel gives some insight on the possible implications to differentiate the electronic energy with respect to the number electrons or the electron density.

Quantal cumulant dynamics: General theory
View Description Hide DescriptionThe authors have derived coupled equations of motion of cumulants that consist of a symmetricordered product of the position and momentum fluctuation operators in one dimension. The key point is the utilization of a position shift operator acting on a potential operator, where the expectation value of the shift operator is evaluated using the cumulant expansion technique. In particular, the equations of motion of the secondorder cumulant and the expectation values of the position and momentum operators are given. The resultant equations are expressed by those variables and a quantal potential that consists of an exponential function of the differential operators and the original potential. This procedure enables us to perform quantal (semiclassical) dynamics in one dimension. In contrast to a secondorder quantized Hamilton dynamics by Prezhdo and Pereverzev which conserves the total energy only with an oddorder Taylor expansion of the potential [J. Chem. Phys.116, 4450 (2002); 117, 2995 (2002)], the present quantal cumulant dynamics method exactly conserves the energy, even if a secondorder approximation of the cumulants is adopted, because the present scheme does not truncate the given potential. The authors propose three schemes, (i) a truncation, (ii) a summation of derivatives, and (iii) a convolution method, for evaluating the quantal potentials for several types of potentials. The numerical results show that although the truncation method preserves the energy to some degree, the trajectory obtained gradually deviates from that of the summation scheme after 2000 steps. The phase space structure obtained by the truncation scheme is also different from that of the summation scheme in a strongly anharmonic region.

Comparative study of perturbative methods for computing electron transfer tunneling matrix elements with a nonorthogonal basis set
View Description Hide DescriptionThe authors consider the problem of computing tunneling matrix elements for bridgemediated electron transfer reactions using the Löwdin [J. Math. Phys.3, 969 (1962);J. Mol. Spectrosc.13, 326 (1964)] projectioniteration technique with a nonorthogonal basis set. They compare the convergence properties of two different Löwdin projections, one containing the overlap matrix and the other containing the inverse in the projected Hamiltonian. It was suggested in the literature that the projected Hamiltonian with has better convergence properties compared to the projected Hamiltonian with . The authors test this proposal using a simple analytical model, and ab initio HartreeFock calculations on different molecules with several types of basis sets. Their calculations show that, for Gaussiantype basis sets, the projected Hamiltonian containing has the best convergence properties, especially for diffuse basis sets and in the strong coupling limit. The limit of diffuse basis sets is relevant to tunneling matrix element calculations involving excited states and anionic electron transfer.

Determination of complex absorbing potentials from the electron selfenergy
View Description Hide DescriptionThe electronic conductance of a molecule making contact to electrodes is determined by the coupling of discrete molecular states to the continuum electrodedensity of states. Interactions between bound states and continua can be modeled exactly by using the (energydependent) selfenergy or approximately by using a complex potential. We discuss the relation between the two approaches and give a prescription for using the selfenergy to construct an energyindependent, nonlocal, complex potential. We apply our scheme to studying singleelectron transmission in an atomic chain, obtaining excellent agreement with the exact result. Our approach allows us to treat electronreservoir couplings independent of singleelectron energies, allowing for the definition of a onebody operator suitable for inclusion into correlated electron transport calculations.

isotope effect on porphine and porphycene molecules with multicomponent hybrid density functional theory
View Description Hide DescriptionTo analyze the isotope effect on porphine and porphycene molecules including the protonic/deuteronic quantum nature and electron correlation efficiently, the authors have developed the new scheme of the multicomponent hybrid density functional theory. The optimized geometries of porphine, porphycene, and these deuterated isotopomers by our method are in good agreement with the experimental “highsymmetric” structures, contrary to the “lowsymmetric” geometries optimized by pure multicomponent HartreeFock method. The optimized geometries for HDporphine and HDporphycene molecules, in which an inner hydrogen is replaced to a deuterium, are found to be low symmetric. Such drastic geometrical change induces the electronic polarization, and gives rise to the slight dipole moment values in these HD species. Their results clearly indicate that the difference of the nuclear quantum nature between inner proton and inner deuteron directly influences the molecular geometry and electronic structure.

Combining explicitly correlated R12 and Gaussian geminal electronic structure theories
View Description Hide DescriptionExplicitly correlated R12 methods using a single shortrange correlation factor (also known as F12 methods) have dramatically smaller basis set errors compared to the standard wave function counterparts, even when used with small basis sets.Correlations on several length scales, however, may not be described efficiently with one correlation factor. Here the authors explore a more general MP2R12 method in which each electron pair uses a set of (contracted) Gaussiantype geminals (GTGs) with fixed exponents, whose coefficients are optimized linearly. The following features distinguish the current method from related explicitly correlated approaches published in the literature: (1) only twoelectron integrals are needed, (2) the only approximations are the resolution of the identity and the generalized Brillouin condition, (3) only linear parameters are optimized, and (4) an arbitrary number of (non)contracted GTGs can appear. The present method using only three GTGs and a doublezeta quality basis computed valence correlation energies for a set of 20 small molecules only 2.2% removed from the basis set limit. The average basis set error reduces to 1.2% using a nearcomplete set of seven GTGs with the doublezeta basis set. The conventional MP2 energies computed with much larger quadruple, quintuple, and sextuple basis sets all had larger average errors: 4.6%, 2.4%, and 1.5%, respectively. The new method compares well to the published MP2R12 method using a single Slatertype geminal (STG) correlation factor. For example, the average basis set error in the absolute MP2R12 energy obtained with the correlation factor is 1.7%. Correlation contribution to atomization energies evaluated with the present method and with the STGbased method only required a doublezeta basis set to exceed the precision of the conventional sextuplezeta result. The new method is shown to always be numerically stable if linear dependencies are removed from the twoparticle basis and the zerothorder Hamiltonian matrix is made positive definite.

Quantum mechanical polarizable force field (QMPFF3): Refinement and validation of the dispersion interaction for aromatic carbon
View Description Hide DescriptionThe authors have recently introduced a general, polarizable force field QMPFF fitted solely to highlevel quantum mechanical data for simulations of biomolecular systems. Here the authors demonstrate using an advanced version QMPFF3 how the problem of insufficient accuracy of the MP2based training set for the aromatic carbon atom type can be effectively solved by a simple model correction using stateoftheart CCSD(T) data. The approach demonstrates excellent transferability, which is confirmed for three phases of matter by accurate calculations of the second virial coefficient for benzene vapor and various properties of liquid benzene and polyaromatic hydrocarbon crystals.

Automatic integration of the reaction path using diagonally implicit RungeKutta methods
View Description Hide DescriptionThe diagonally implicit RungeKutta framework is shown to be a general form for constructing stable, efficient steepest descent reaction path integrators, of any order. With this framework tolerance driven, adaptive stepsize methods can be constructed by embedding methods to obtain error estimates of each step without additional computational cost. There are many embedded and nonembedded, diagonally implicit RungeKutta methods available from the numerical analysis literature and these are reviewed for orders two, three, and four. New embedded methods are also developed which are tailored to the application of reaction path following. All integrators are summarized and compared for three systems: the MüllerBrown [Theor. Chem. Acta53, 75 (1979)] potential and two gas phase chemical reactions. The results show that many of the methods are capable of integrating efficiently while reliably keeping the error bound within the desired tolerance. This allows the reaction path to be determined through automatic integration by only specifying the desired accuracy and transition state.

Simple Hamiltonians which exhibit drastic failures by variational determination of the twoparticle reduced density matrix with some well known representability conditions
View Description Hide DescriptionCalculations on small molecular systems indicate that the variational approach employing the twoparticle reduced density matrix (2RDM) as the basic unknown and applying the , , , , and representability conditions provides an accuracy that is competitive with the best standard ab initio methods of quantum chemistry. However, in this paper we consider a simple class of Hamiltonians for which an exact ground statewave function can be written as a single Slater determinant and yet the same 2RDM approach gives a drastically nonrepresentable result. This shows the need for stronger representability conditions than the mentioned ones.

Efficient correlationcorrected vibrational selfconsistent field computation of OHstretch frequencies using a lowscaling algorithm
View Description Hide DescriptionThe authors present a new computational scheme to perform accurate and fast direct correlationcorrected vibrational selfconsistent field (CCVSCF) computations for a selected number of vibrational modes, which is aimed at predicting a few vibrations in large molecular systems. The method is based on a systematic selection of vibrational modemode coupling terms, leading to the direct ab initio construction of a sparse potential energy surface. The computational scaling of the CCVSCF computation on the generated surface is then further reduced by using a screening procedure for the correlationcorrection contributions. The proposed method is applied to the computation of the OHstretch frequency of five aliphatic alcohols. The authors investigate the influence of different pseudopotential and allelectron basis sets on the quality of the correlated potential energy surfaces computed and on the OHstretch frequencies calculated for each surface. With the help of these test systems, the authors show that their method offers a computational scaling that is two orders of magnitude lower than a standard CCVSCF method and that it is of equal accuracy.

Explicitly intruderfree valenceuniversal multireference coupled cluster theory as applied to ionization spectroscopy
View Description Hide DescriptionAlthough it is quite promising to compute the spectroscopic energies [say, ionization potential (IP)] via the traditional valenceuniversal multireference coupled cluster (VUMRCC) method based on the description of the complete model space being seriously plagued by the perennial intruder state problem, the eigenvalue independent partitioning (EIP) based VUMRCC (coined as EIPMRCC) method is quite effective to predict the spectroscopic energies in an intruderfree manner. Hence, the EIPMRCC method is suitable for generating both the principal IPs and the satellite IPs of the innervalence region. An EIP strategy converts the nonlinear VUMRCC equations for dimensional model space of hole and particle to a nonHermitian eigenproblem of larger dimension whose roots are only physically meaningful. To increase the quality of the computed energy differences in the sense of chemical accuracy and to locate the correct position of it in the spectrum, the inclusion of higherbody cluster operators on top of all the standard singlesdoubles is not the only pivotal issue, the effect of the size of the basis set is also equally important. This paper illustrates these issues by calculating the principal and satellite IPs of HF and HCl molecules using various basis sets (viz., Dunning's ccpVDZ, ccpVTZ, and ccpVQZ) via EIPMRCC method with full inclusion of triples (abbreviated as ). The results seem quite encouraging in comparison with the experimental values. The controversial satellite at of HCl of Svensson et al. [J. Chem. Phys.89, 7193 (1988)] is also reported.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Photoelectron imaging of at
View Description Hide DescriptionWe report the anion photoelectron spectrum of taken at detachment energy using velocity mapped imaging. The photoelectron spectrum exhibits bands resulting from transitions to the bound regions of the , , , and electronic states as well as bands resulting from transitions to the repulsive regions of several electronic states: the , , , , , and states. We simulate the photoelectron spectrum using literature parameters for the and ground and excited states. The photoelectron spectrum includes bands resulting from transitions to several highlying excited states of that have not been seen experimentally: , , , and the states of . Finally, the photoelectron spectrum at allows for the correction of a previous misassignment for the vertical detachment energy of the state.

Interaction of lowenergy electrons with the purine bases, nucleosides, and nucleotides of DNA
View Description Hide DescriptionThe authors report results from computational studies of the interaction of lowenergy electrons with the purine bases of DNA, adenine and guanine, as well as with the associated nucleosides, deoxyadenosine and deoxyguanosine, and the nucleotide deoxyadenosine monophosphate. Their calculations focus on the characterization of the shape resonances associated with the bases and also provide general information on the scattering of slow electrons by these targets. Results are obtained for adenine and guanine both with and without inclusion of polarization effects, and the resonance energy shifts observed due to polarization are used to predict resonance energies in associated nucleosides and nucleotides, for which staticexchange calculations were carried out. They observe slight shifts between the resonance energies in the isolated bases and those in the nucleosides.

Relativistic density functional calculations using twospinor minimax finiteelement method and linear combination of atomic orbitals for ZnO, CdO, HgO, UubO and , , ,
View Description Hide DescriptionIn previous work the authors have presented a highly accurate twospinor fully relativistic solution of the twocenter Coulomb problem utilizing the finiteelement method(FEM) and furthermore developed a relativistic minimax twospinor linear combination of atomic orbitals (LCAO). In the present paper the authors present DiracFockSlater (DFS) density functional calculations for twoatomic molecules up to super heavy systems using the fully nonlinear minimax FEM and the minimax LCAO in its linearized approximation (linear approximation to relativistic minimax). The FEM gives highly accurate benchmark results for the DFS functional. Especially considering molecules with up to super heavy atoms such as UubO and , the authors found that LCAO fails to give the correct systematic trends. The accurate FEM results shed a new light on the quality of the DFSdensity functional.

Mixed quantumclassical molecular dynamics simulation of vibrational relaxation of ions in an electrostatic field
View Description Hide DescriptionThe vibrational relaxation of ions in lowdensity gases under the action of an electrostatic field is reproduced through a molecular dynamics simulation method. The vibration is treated though quantum mechanics and the remaining degrees of freedom are considered classical. The procedure is tested through comparison against analytic results for a twodimensional quantum model and by studying energy exchange during binary ionatom collisions. Finally, the method has been applied successfully to the calculation of the mobility and the vibrational relaxation rate of in Kr as a function of the mean collision energy using a model interaction potential that reproduces the potential minimum of a previously known ab initio potential surface. The calculation of the steady mean vibrational motion of the ions in (flow) drift tubes seems straightforward, though at the expense of large amounts of computer time.
 Condensed Phase Dynamics, Structure, and Thermodynamics: Spectroscopy, Reactions, and Relaxation

Nonlinear effects on solvation dynamics in simple mixtures
View Description Hide DescriptionThe authors applied the time dependent density functional method (TDDFM) and a linear model to solvation dynamics in simple binary solvents. Changing the solutesolvent interactions at , the authors calculated the time evolution of density fields for solvent particles after the change by the TDDFM and linear model. First, the authors changed the interaction of only one component of solvents. In this case, the TDDFM showed that the solvation time decreased monotonically with a mole fraction of the solvent strongly interacting with the solute. The monotonical decreases agreed with experimental results, while the linear model did not reproduce these results. The authors also calculated the solvation time by changing the interaction of both components. The calculation showed that the mole fraction dependence had the peak. The TDDFM presented a much higher peak than the linear model. The difference between the TDDFM and the linear model was caused by a nonlinear effect on an exchange process of solvent particles.

Excessentropybased anomalies for a waterlike fluid
View Description Hide DescriptionMany thermodynamic and dynamic properties of water display unusual behavior at low enough temperatures. In a recent study, Yan et al. [Phys. Rev. Lett.95, 130604 (2005)] identified a spherically symmetric twoscale potential that displays many of the same anomalous properties as water. More specifically, for select parametrizations of the potential, one finds that the regions where isothermal compression anomalously (i) decreases the fluid’s structural order, (ii) increases its translational selfdiffusivity, and (iii) increases its entropy form nested domes in the temperaturedensity plane. These property relationships are similar to those found for more realistic models of water. In this work, the authors provide evidence that suggests that the anomalous regions specified above can all be linked through knowledge of the excess entropy. Specifically, the authors show how entropy scaling relationships developed by Rosenfeld [Phys. Rev. A15, 2545 (1977)] can be used to describe the region of diffusivity anomalies and to predict the state conditions for which anomalous viscosity and thermal conductivity behavior might be found.

Heat capacity, Raman, and Brillouin scattering studies of glasses
View Description Hide DescriptionThe authors report the results of temperaturedependent Brillouin scattering from both transverse and longitudinal acoustic waves, heat capacity studies as well as room temperature Raman scattering studies on glasses. These results were used to obtain information about structure and various properties of the studied glasses such as fragility, elastic moduli, ratio of photoelastic constants, and elastic anharmonicity. They have found that both glasses have similar properties but replacement of ions by ions in the glass network leads to decrease of elastic parameters and photoelastic constant due to increase of fragility. Based on Brillouin spectroscopy they show that a linear correlation between longitudinal and shear elastic moduli holds over a large temperature range. This result supports the literature data that the Cauchytype relation represents a general rule for amorphous solids. An analysis of the Boson peak revealed that the form of the frequency distribution of the excess density of states is in agreement with the Euclidean random matrix theory. The reason of the observed shift of the maximum frequency of the Boson peak when ions are substituted for ions is also briefly discussed.