Electronic structure and bonding in heteronuclear dimers of V, Cr, Mo, and W: a CASSCF/CASPT2 study

Heteronuclear dimers like CrMo, CrW, MoW, VCr, VMo, VW, and their anions have been investigated by means of multiconfigurational quantum chemistry methods, using the complete active space self-consistent field followed by second-order perturbation theory, CASSCF/CASPT2. We explored in great detail several spectroscopic properties such as bond length, potential energy surfaces, dissociation energies, ionization potentials, electron affinities, low-lying excited states, vibrational frequencies, and dipole moments. All proposed dimers show ground states with a pronounced multireference character. The group VI heterodimers have a (1)Σ(+) ground state, while the mixed group V-group VI heterodimers show a (2)Δ ground state. Among all dimers, only VCr presents a potential energy profile with a deep minimum in the d-d region and a shelf-like potential in the s-s region. All the remaining dimers show only the short-range minimum. The largest effective bond order is obtained for the MoW, with a value of 5.2, that is, a weak sextuple bond. Most of the obtained results are valuable tools to drive future experimental investigations.     

Solvent effects on the electronic transitions of p-nitroaniline: a QM/EFP study

Solvatochromic shifts of the electronic states of a chromophore can be used as a measure of solute-solvent interactions. The shifts of the electronic states of a model organic chromophore, p-nitroaniline (pNA), embedded in solvents with different polarities (water, 1,4-dioxane, and cyclohexane) are studied using a hybrid quantum mechanics/molecular-mechanics-type technique in which the chromophore is described by the configuration interaction singles with perturbative doubles (CIS(D)) method while the solvent is treated by the effective fragment potential (EFP) method. This newly developed CIS(D)/EFP scheme includes the quantum-mechanical coupling of the Coulomb and polarization terms; however, short-range dispersion and exchange-repulsion terms of EFP are not included in the quantum Hamiltonian. The CIS(D)/EFP model is benchmarked against the more accurate equation of motion coupled cluster with singles and doubles (EOM-CCSD)/EFP method on a set of small pNA-water clusters. CIS(D)/EFP accurately predicts the red solvatochromic shift of the charge-transfer π → π* state of pNA in polar water. The shift is underestimated in less polar dioxane and cyclohexane probably because of the omission of the explicit quantum-mechanical treatment of the short-range terms. Different solvation of singlet and triplet states of pNA results in different probabilities of intersystem crossing (ISC) and internal conversion (IC) pathways of energy relaxation in solvents of different polarity. Computed singlet-triplet splittings in water and dioxane qualitatively explain the active ISC channel in dioxane and predict almost no conversion to the triplet manifold in water, in agreement with experimental findings.     

Electric-field-induced dissociation of heavy Rydberg ion-pair states

A classical trajectory Monte Carlo approach is used to simulate the dissociation of H(+)???F(-) and K(+)???Cl(-) heavy Rydberg ion pairs induced by a ramped electric field, a technique used experimentally to detect and probe ion-pair states. Simulations that include the effects of the strong short-range repulsive interaction associated with ion-pair scattering are in good agreement with experimental results for Stark wavepackets probed by a ramped field, demonstrating that many of the characteristics of field-induced dissociation can be well described using a quasi-classical model. The data also show that states with a given value of principal quantum number (i.e., binding energy) can dissociate over a broad range of applied fields, the exact field being governed by the initial orbital angular momentum and orientation of the state.     

Continuum solutions of the Klein-Gordon equation

We construct explicit solutions of the Klein-Gordon equation for continuum states. The role of the energy in the single-particle Klein-Gordon theory is elucidated. Special emphasis is laid on the determination of resonance states in the continuum for overcritical potentials. As examples for long-range interactions we depict solutions for the Coulomb potential of a point-like nucleus as well as an extended nucleus. The square-well potential and the exponential potential are treated to exemplify peculiarities of short-range interactions. We also derive continuum solutions for a scalar interaction of square-well type. Finally we discuss the behaviour of a spin-0 particle in an external homogeneous magnetic field.     

The role of surface defects in multi-exciton generation of lead selenide and silicon semiconductor quantum dots

Multi-exciton generation (MEG), the creation of more than one electron-hole pair per photon absorbed, occurs for excitation energies greater than twice the bandgap (E(g)). Imperfections on the surface of quantum dots, in the form of atomic vacancies or incomplete surface passivation, lead to less than ideal efficiencies for MEG in semiconductor quantum dots. The energetic onset for MEG is computed with and without surface defects for nanocrystals, Pb(4)Se(4), Si(7), and Si(7)H(2). Modeling the correlated motion of two electrons across the bandgap requires a theoretical approach that incorporates many-body effects, such as post-Hartree-Fock quantum chemical methods. We use symmetry-adapted cluster with configuration interaction to study the excited states of nanocrystals and to determine the energetic threshold of MEG. Under laboratory conditions, lead selenide nanocrystals produce multi-excitons at excitation energies of 3 E(g), which is attributed to the large dielectric constant, small Coulomb interaction, and surface defects. In the absence of surface defects the MEG threshold is computed to be 2.6 E(g). For lead selenide nanocrystals with non-bonding selenium valence electrons, Pb(3)Se(4), the MEG threshold increases to 2.9 E(g). Experimental evidence of MEG in passivated silicon quantum dots places the onset of MEG at 2.4 E(g). Our calculations show that the lowest multi-exciton state has an excitation energy of 2.5 E(g), and surface passivation enhances the optical activity of MEG. However, incomplete surface passivation resulting in a neutral radical on the surface drives the MEG threshold to 4.4 E(g). Investigating the mechanism of MEG at the atomistic level provides explanations for experimental discrepancies and suggests ideal materials for photovoltaic conversion.     

Visualization of electron correlation in autoionizing states above the 3p threshold in magnesium

The conditional probability density has been calculated for a number of autoionizing states (AIS) in Mg above the 3p threshold. The correlation in such high energy AIS has not been extensively studied and provides insight into the rovibrator behavior of two-electron atoms. The calculations have been done by configuration interaction (CI) with a B-spline basis. This allows for the simultaneous study of the effects of electron correlation and the widths and angular distribution of photoelectrons in multiphoton ionization. The states have been assigned approximate vibrational quantum numbers, and a correlation between the approximate quantum numbers and the photoelectron distribution is observed. Probability distribution for one electron when the other, represented by the small spike, is at its most probable distance from the nucleus. This is a distribution for the doubly-excited 1S(e) state commonly labeled as the 4s2 state.     

Large-scale parallel configuration interaction. I. Nonrelativistic and scalar-relativistic general active space implementation with application to (Rb-Ba)+

We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.     

Ewald mesh method for quantum mechanical calculations

The Fourier transform Coulomb (FTC) method has been shown to be effective for the fast and accurate calculation of long-range Coulomb interactions between diffuse (low-energy cutoff) densities in quantum mechanical (QM) systems. In this work, we split the potential of a compact (high-energy cutoff) density into short-range and long-range components, similarly to how point charges are handled in the Ewald mesh methods in molecular mechanics simulations. With this linear scaling QM Ewald mesh method, the long-range potential of compact densities can be represented on the same grid as the diffuse densities that are treated by the FTC method. The new method is accurate and significantly reduces the amount of computational time on short-range interactions, especially when it is compared to the continuous fast multipole method.     

Communication: regularizing binding energy distributions and thermodynamics of hydration: theory and application to water modeled with classical and ab initio simulations

The high-energy tail of the distribution of solute-solvent interaction energies is poorly characterized for condensed systems, but this tail region is of principal interest in determining the excess free energy of the solute. We introduce external fields centered on the solute to modulate the short-range repulsive interaction between the solute and solvent. This regularizes the binding energy distribution and makes it easy to calculate the free energy of the solute with the field. Together with the work done to apply the field in the presence and absence of the solute, we calculate the excess chemical potential of the solute. We present the formal development of this idea and apply it to study liquid water.     

Photoassociation spectroscopy of ultracold metastable 3He dimers

The bound states of the fermionic (3)He(2 (3)S(1)) + (3)He(2 (3)P(j)) system, where j = 0, 1, 2, are investigated using the recently available ab initio short-range (1,3,5)Σ(+)(g,u) and (1,3,5)Π(g,u) potentials computed by Deguilhem et al. (J. Phys. B: At., Mol. Opt. Phys., 2009, 42, 015102). Single-channel and multichannel calculations have been undertaken in order to investigate the effects of Coriolis and non-adiabatic couplings. The possible experimental observability of the theoretical levels is assessed using criteria based upon the short-range character of each level and their coupling to metastable ground states. Purely long-range levels have been identified and 30 short-range levels near five asymptotes are suggested for experimental investigation.     

Blueshift and intramolecular tunneling of NH3 umbrella mode in 4He n clusters

We present diffusion Monte Carlo calculations of the ground and first excited vibrational states of NH(3) (4)He(n) for n< or =40. We use the potential energy surface developed by one of us [M. P. Hodges and R. J. Wheatley, J. Chem. Phys. 114, 8836 (2001)], which includes the umbrella mode coordinate of NH(3). Using quantum Monte Carlo calculations of excited states, we show that this potential is able to reproduce qualitatively the experimentally observed effects of the helium environment, namely, a blueshift of the umbrella mode frequency and a reduction of the tunneling splittings in ground and first excited vibrational states of the molecule. These basic features are found to result regardless of whether dynamical approximations or exact calculations are employed.     

Multiscale theory of collective and quasiparticle modes in quantum nanosystems

A quantum nanosystem (such as a quantum dot, nanowire, superconducting nanoparticle, or superfluid nanodroplet) involves widely separated characteristic lengths. These lengths range from the average nearest-neighbor distance between the constituent fermions or bosons, or the lattice spacing for a conducting metal, to the overall size of the quantum nanosystem (QN). This suggests the wave function has related distinct dependencies on the positions of the constituent fermions and bosons. We show how the separation of scales can be used to generate a multiscale perturbation scheme for solving the wave equation. Results for electrons or other fermions show that, to lowest order, the wave function factorizes into an antisymmetric (fermion) part and a symmetric (bosonlike) part. The former manifests the short-range/exclusion-principle behavior, while the latter corresponds to collective behaviors, such as plasmons, which have a boson character. When the constituents are bosons, multiscale analysis shows that, to lowest order, the wave function can also factorize into short- and long-scale parts. However, to ensure that the product wave function has overall symmetric particle label exchange behavior, there could, in principle, be states of the boson nanosystem where both the short- and long-scale factors are either boson- or fermionlike; the latter "dual fermion" states are, due to their exclusion-principle-like character, of high energy (i.e., single particle states cannot be multiply occupied). The multiscale perturbation analysis is used to argue for the existence of a coarse-grained wave equation for bosonlike collective behaviors. Quasiparticles, with effective mass and interactions, emerge naturally as consequences of the long-scale dynamics of the constituent particles. The multiscale framework holds promise for facilitating QN computer simulations and novel approximation schemes.     

An efficient ring polymer contraction scheme for imaginary time path integral simulations

A quantum simulation of an imaginary time path integral typically requires around n times more computational effort than the corresponding classical simulation, where n is the number of ring polymer beads (or imaginary time slices) used in the calculation. However, this estimate neglects the fact that the potential energies of many systems can be decomposed into a sum of rapidly varying short-range and slowly varying long-range contributions. For such systems, the computational effort of the path integral simulation can be reduced considerably by evaluating the long-range forces on a contracted ring polymer with fewer beads than are needed to evaluate the short-range forces. This idea is developed and then illustrated with an application to a flexible model of liquid water in which the intramolecular forces are evaluated with 32 beads, the oxygen-oxygen Lennard-Jones forces with seven, and the intermolecular electrostatic forces with just five. The resulting static and dynamic properties are within a few percent of those of a full 32-bead calculation, and yet they are obtained with a computational effort less than six times (rather than 32 times) that of a classical simulation. We hope that this development will encourage future studies of quantum mechanical fluctuations in liquid water and aqueous solutions and in many other systems with similar interaction potentials.     

One-dimensional cluster growth and branching gels in colloidal systems with short-range depletion attraction and screened electrostatic repulsion

We report extensive numerical simulations of a simple model for charged colloidal particles in suspension with small nonadsorbing polymers. The chosen effective one-component interaction potential is composed of a short-range attractive part complemented by a Yukawa repulsive tail. We focus on the case where the screening length is comparable to the particle radius. Under these conditions, at low temperature, particles locally cluster into quasi one-dimensional aggregates which, via a branching mechanism, form a macroscopic percolating gel structure. We discuss gel formation and contrast it with the case of longer screening lengths, for which previous studies have shown that arrest is driven by the approach to a Yukawa glass of spherical clusters. We compare our results with recent experimental work on charged colloidal suspensions (Phys. Rev. Lett. 2005, 94, 208301).     

Pairwise additive model for the He-MgO(100) interaction

We develop a model, based on pairwise additive He-Mg and He-O interactions, for the potential energy of He adsorbates above a rigid MgO(100) surface. The attractive long-range He-Mg and He-O interactions are assumed to have the form C(6)/r(6), with the C(6) coefficients determined from atomic data within the context of the Slater-Kirkwood approximation. The repulsive short-range He-Mg and He-O interactions are assumed to have the form C(p)/r(p), with the exponent p and the C(p) coefficients taken as adjustable parameters. We find that for p = 9, the C(p) coefficients can be chosen so that the laterally averaged He-MgO(100) pairwise additive interaction supports low-lying selective adsorption states, some of whose energies agree very well with the states' apparent energies inferred from experimental measurements. However, for realistic values of the adjustable parameters that define our model, the lateral corrugation of the model pairwise additive He-MgO(100) potential energy surface far exceeds the corrugation that has been inferred both from experimental measurements and from density functional calculations of the short-range He-MgO(100) interaction.     

Six-dimensional quantum dynamics of H2 dissociative adsorption on the Pt(211) stepped surface

Results of experimental studies, and theoretical calculations utilizing classical trajectories, have shown that dissociation of H2 on the Pt(211) stepped surface is enhanced at low energies by a molecular trapping mechanism. Because quantum effects can play a large role at the low energies and long lifetimes that characterize molecular trapping, we have undertaken quantum dynamics calculations for this system, the first to treat all molecular degrees of freedom of a gas molecule reacting on a stepped metallic surface. The calculations show that molecular trapping persists in the quantum system, but only at much lower energies than experimentally seen, pointing to possible deficiencies in the potential energy surface. Classical and quasiclassical trajectory calculations on the same potential provide a reasonable picture of reaction overall, but many of the finer details are inaccurate, and certain classical reaction mechanisms are entirely invalid. We conclude that some skepticism should be shown toward any classical study for which long-lived trapping states play a role.     

Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions

We describe an Ewald-summation method to incorporate long-range electrostatic interactions into fragment-based electronic structure methods for periodic systems. The present method is an extension of the particle-mesh Ewald technique for combined quantum mechanical and molecular mechanical (QM/MM) calculations, and it has been implemented into the explicit polarization (X-Pol) potential to illustrate the computational details. As in the QM/MM-Ewald method, the X-Pol-Ewald approach is a linear-scaling electrostatic method, in which the short-range electrostatic interactions are determined explicitly in real space and the long-range Ewald pair potential is incorporated into the Fock matrix as a correction. To avoid the time-consuming Fock matrix update during the self-consistent field procedure, a mean image charge (MIC) approximation is introduced, in which the running average with a user-chosen correlation time is used to represent the long-range electrostatic correction as an average effect. Test simulations on liquid water show that the present X-Pol-Ewald method takes about 25% more CPU time than the usual X-Pol method using spherical cutoff, whereas the use of the MIC approximation reduces the extra costs for long-range electrostatic interactions by 15%. The present X-Pol-Ewald method provides a general procedure for incorporating long-range electrostatic effects into fragment-based electronic structure methods for treating biomolecular and condensed-phase systems under periodic boundary conditions.