Search

Structure–property relationships play a central role in condensed matter physics, chemistry, and materials science. However, the problem of predicting the structure of a material, given its chemical composition, remains immensely challenging. Here, we review some of the progress that has been made in this area for both crystalline materials and atomic clusters. Early work consisted of heuristic rules-of-thumb or structure maps using descriptors that were obtained largely by inspection. Increasingly, these approaches are being expanded to use descriptors that have been obtained by applying machine learning techniques to big data containing information from the experiment and/or first principles calculations. Improved techniques for global optimization in the multi-dimensional coordinate space have also led to major advances in the field.

The elastic network model (ENM) is an effective method to extract the intrinsic dynamical properties encoded in protein tertiary structures. We have proposed a new ENM-based analysis method to reveal the motion modes directly responsible for a specific protein function, in which an internal coordinate related to the specific function was introduced to construct the internal/Cartesian hybrid coordinate space. In the present work, the function-related internal coordinates combined with a linear perturbation method were applied to identify the key sites controlling specific protein functional motions. The change in the fluctuations of the internal coordinate in response to residue perturbation was calculated in the hybrid coordinate space by using the linear response theory. The residues with the large fluctuation changes were identified to be the key sites that allosterically control the specific protein function. Two proteins, i.e., human DNA polymerase β and the chaperonin from Methanococcus maripaludis, were investigated as case studies, in which several collective and local internal coordinates were applied to identify the functionally key residues of these two studied proteins. The calculation results are consistent with the experimental observations. It is found that different collective internal coordinates lead to similar results, where the predicted functionally key sites are located at similar positions in the protein structure. While for the local internal coordinates, the predicted key sites tend to be situated at the region near to the coordinate-involving residues. Our studies provide a starting point for further exploring other function-related internal coordinates for other interesting proteins.

An approach to the construction of diabatic free energy surfaces (FESs) for ultrafast electron transfer (ET) in a supramolecule with an arbitrary number of electron localization centers (redox sites) is developed, supposing that the reorganization energies for the charge transfers and shifts between all these centers are known. Dimensionality of the coordinate space required for the description of multistage ET in this supramolecular system is shown to be equal to N − 1, where N is the number of the molecular centers involved in the reaction. The proposed algorithm of FES construction employs metric properties of the coordinate space, namely, relation between the solvent reorganization energy and the distance between the two FES minima. In this space, the ET reaction coordinate znn′ associated with electron transfer between the nth and n′th centers is calculated through the projection to the direction, connecting the FES minima. The energy-gap reaction coordinates znn′ corresponding to different ET proces...

Effective mass theory and variation method are used to calculate the ground state energies of excitons in coupled three-quantum dot (3-QD) systems. To calculate multicenter integrals involving two particle wave functions, a series of spheres are used to cover the coordinate space and further approximation has been made when the radii of the integral spheres are suitably selected around the three spherical QDs in near equal radius. The results obtained from the calculation of In0.5Ga0.5As/GaAs and GaAs/Al0.2Ga0.8As coupled 3-QD systems are basically in agreement with the experiments. Based on the energy level schemes in these systems, we make suggestions for the application of far-infrared and/or terahertz sources.

We constructed a full dimensional potential energy function of H2CO that can describe both the dissociation and isomerization channels by the modified Shepard interpolation method. Ab initio calculations at the MP2/cc-pVTZ level were carried out to obtain the local potential functions at about 4700 points. The interpolant points were sampled by classical trajectory calculations and by the grid searches in the internal coordinate space. Classical trajectory calculations were performed to examine the intramolecular dynamics associated with the dissociation as well as the product state distributions. The time scale of intramolecular vibrational energy randomization was much faster than that of the dissociation reaction. The dissociation rate was obtained from the classical trajectory results and the effect of the isomerization channel on the dissociation was estimated. The calculated rate constants were compared with those by Rice–Ramsperger–Kassel–Marcus theory.

In this paper, the single-particle Green’s function approach is applied to the atomic many-body problem. We present the self-consistent solution of the Dyson equation up to second order in the self-energy for nonrelativistic spin-compensated atoms. This Dyson second-order scheme requires the solution of the Hartree–Fock integro-differential equations as a preliminary step, which is performed in coordinate space (i.e., without an expansion in a basis set). To cope with the huge amount of poles generated in the iterative approach to tackle Dyson’s equation in second order, the BAGEL (BAsis GEnerated by Lanczos) algorithm is employed. The self-consistent scheme is tested on the atomic systems He, Be, Ne, Mg, and Ar with spin-saturated ground state 1S0. Predictions of the total binding energy, ionization energy, and single-particle levels are compared with those of other computational schemes [density functional theory, Hartree–Fock (HF), post-HF, and configuration interaction] and with experiment. The correl...

We present an accurate, efficient, and flexible method for propagating spatially distributed density matrices in anharmonic potentials interacting with solvent and strong fields. The method is based on the Nakajima–Zwanzig projection operator formalism with a correlated reference state of the bath that takes memory effects and initial/final correlations to second order in the system–bath interaction into account. A key feature of the method proposed is a special parametrization of the bath spectral density leading to a set of coupled equations for primary and N auxiliary density matrices. These coupled master equations can be solved numerically by representing the density operator in eigenrepresentation or on a coordinate space grid, using the Fourier method to calculate the action of the kinetic and potential energy operators, and a combination of split operator and Cayley implicit method to compute the time evolution. The key advantages of the method are: (1) The system potential may consist of any numb...

Transition state theory (TST) approximates the reactive flux in an elementary chemical reaction by the instantaneous flux passing through a hypersurface (the transition state) which completely divides the reactant and product regions of phase space. The rigorous classical evaluation of this instantaneous flux is carried out as a trace in phase space: effectively a multidimensional integral. We present an analysis of the momentum-space component of this flux integral for the case of a generalized reaction coordinate. The classic analysis of the canonical flux by Marcus [J. Chem. Phys. 41, 2624 (1964)] is refined by reducing the determinant which appears in the transition state partition function to a very simple form, facilitating the ensuing integration over coordinate space. We then extend the analysis to provide analytic expressions for the momentum flux integrals in both the energy-resolved, and the energy+angular-momentum-resolved microcanonical ensembles. These latter expressions allow substantial gains in the efficiency of microcanonical variational implementations of Transition State Theory with generalized reaction coordinates. (C) 1999 American Institute of Physics. [S0021-9606(99)00528-0].

An expression for the rate of vapor phase nucleation is developed that is based on variational transition state theory. The method depends on a definition of a dividing surface in phase space that separates reactants from products. For this surface we choose a spherical shell in coordinate space that is centered about the center of mass of a cluster of i molecules having an interior volume v. In a manner that is consistent with variational transition state theory, we vary v to minimize the reactive flux through our chosen dividing surface. The resulting expression for the rate constant involves a definition of a physical cluster that is consistent with previous developments in nucleation theory. In formulating the rate in this manner we obtain a new expression for the evaporation rate constant that is proportional to the derivative with respect to v of the Helmholtz free energy for cluster formation. In addition, we have a fundamentally justified procedure for selecting a unique volume v for each i cluste...

Direct losses of highly energetic helically trapped particles, especially of superbananas, are analytically investigated in torsatrons and heliotrons [Uo, J. Phys. Soc. Jpn. 16, 1380 (1961)] with a vertically asymmetric helical field ripple. It is found that the vertically asymmetric helical ripple causes an additional net radial drift of suprathermal superbananas, leading to convective losses of these particles from the confinement volume mainly in the vertical direction. For a vertically asymmetric rippled torsatron, a location of the particle loss region in the coordinate space and a dominated direction of the particle escape from the confinement volume is predicted on the basis of the probabilities of the particle trapping/detrapping in/from the helical ripple wells. Analytical predictions are confirmed by numerical computations of direct losses of highly energetic helically trapped particles for a number of torsatrons/heliotrons of today.

The convergence of large-order expansions in δ=1/D, where D is the dimensionality of coordinate space, for energies E(δ) of Coulomb systems is strongly affected by singularities at δ=1 and δ=0. Pade–Borel approximants with modifications that completely remove the singularities at δ=1 and remove the dominant singularity at δ=0 are demonstrated. A renormalization of the interelectron repulsion is found to move the dominant singularity of the Borel function F(δ)=∑jEj′/j!, where Ej′ are the the expansion coefficients of the energy with singularity structure removed at δ=1, farther from the origin and thereby accelerate summation convergence. The ground-state energies of He and H2+ are used as test cases. The new methods give significant improvement over previous summation methods. Shifted Borel summation using Fm(δ)=∑jEj′/Γ(j+1−m) is considered. The standard deviation of results calculated with different values of the shift parameter m is proposed as a measure of summation accuracy.

A Brownian dynamics treatment in torsional angle space is presented for the simulation of conformational dynamics of macromolecules with fixed bond lengths and bond angles and with an arbitrary intramolecular potential energy function. The advantages of the torsional angle space treatment over similar treatments (Brownian dynamics or molecular dynamics) in atomic coordinate space are that, first, the number of variables is reduced by roughly a factor of 10 and, second, the integration time step size is increased by 3 to 4 orders of magnitude (because, by confining the treatment to the torsional angle space, the time step size is not limited by the fast oscillation modes of covalent bonds but rather by the slow motion of macromolecular segments whose time scale is roughly 3 to 4 orders of magnitude larger than that of bond oscillations). Consequently, the exploration of global conformational relaxation processes becomes computationally possible. The treatment is tested by studying the folding kinetics of off-lattice chains with fixed bond lengths and bond angles and with prescribed sequences. The present treatment is a general purpose one applicable to all macromolecular conformational relaxation processes (e.g., protein folding kinetics, drug/ligand docking on to target proteins, conformational multiple-minima problems, etc.). It serves as a complement to the molecular dynamics or Brownian dynamics treatments in atomic coordinate space.

The torsional angle space macromolecular conformational dynamics treatment presented in the preceding paper is used to study the mechanism and kinetics of protein folding by using continuum rigid chain molecules. The main purpose is to test the treatment using simple macromolecular systems. It is found that the torsional angle space approach is much faster and more reliable than similar approaches in atomic coordinate space. The simulation results also suggest that the short-ranged Lennard-Jones binary interactions alone are not sufficient to fold the chain molecules, and that hydrophobic collapse is essential for the folding processes. In our simplified protein folding model, the hydrophobic collapse is achieved by introducing global dipole interactions. The collapse of the chain molecule induced by dipole interactions significantly reduces the folding time. The chain collapse processes effectively bring the atoms into the (short) range of Lennard-Jones attractions, which then, in turn, are able to play their role in the folding processes; without such collapse the folding processes are highly frustrated.

The reactant‐product decoupling (RPD) equations are a rigorous formulation of state‐to‐state reactive scattering recently introduced by Peng and Zhang. For an N‐arrangement reaction there are a total of N RPD equations, each of which describes the dynamics in just one region of coordinate space. One of the regions (the r‐region) encloses the reactant channel and the strong interaction region; each of the other N−1 regions encloses one of the product channels. In this paper we develop a suggestion later made by Kouri and co‐workers: that the original RPD equations can be further partitioned into a set of new RPD equations, in which the original r‐region is now partitioned into three regions—two enclosing the reactant channel, and one enclosing the strong interaction region. After introducing the new RPD equations, we derive the time-independent wave‐packet (TIW) form of the equations, and show how to solve them using an extended version of the Chebyshev propagator. We test the new RPD equations (and the me...

A formalism for relating dynamic observables of collision processes to the electronic structure of the colliding species is illustrated for the case of He collision-induced rotational excitation of H2. Expressions are presented for the functional derivative of transition cross sections and rate constants with respect to the electronic wave function. Regions of electronic coordinate space in which the electron probability densities have particularly strong influence on one or more inelastic transitions are identified. The possible role of functional derivatives of this sort for guiding electronic structure calculations to produce intermolecular potentials is discussed.

The energies and lifetimes (i.e., inverse decay rates) of resonance (quasibound) states in chemical reactions are associated with the complex eigenvalues of the complex scaled Hamiltonian. The corresponding eigenfunctions are square integrable and are compact, localized functions in the coordinate space. Complex scaling is applicable when the potential, V(x), is dilation analytic. Ab initio potentials, however, are given on a grid, Vn=V(xn). Starting from the theoretical work of Moiseyev and Hirschfelder [J. Chem. Phys. 88, 1063 (1988)], we propose an efficient numerical method of calculating V(xn exp(iθ)) by acting on the unscaled potential with a grid represented scaling operator S.

This is the first of a series of papers in which we investigate the unimolecular dissociation of hydroperoxyl. Using the DMBE IV potential energy surface [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)], in the present study 726 bound states of HO2(X) up to the H+O2 dissociation threshold are calculated in an attempt to access the extent of the coupling between the modes of the system. The first approach involves an analysis of the nodal structure of the wave functions. While the wave functions for the lowest states are regular and assignable, the degree of mixing and complexity rapidly increases with energy. The wave functions close to the dissociation threshold are mostly irregular without any clear cut nodal structure and fill the entire coordinate space available. Nevertheless, a small number of regular states, that are associated with large excitation in the O2 stretching coordinate and no or only little excitation in the other modes, are found even at high energies. The second approach used to stu...

The effects of the geometric phase on vibronic states associated with the lower potential surface of two electronic level Hamiltonians are examined. We obtain the general formula for the gauge potential arising from the vibronic interaction. It is shown that this gauge potential is split into a topological part and a magnetic part, where the topological part gives rise to the phase factor of +1 or −1 when it is integrated along a closed trajectory in the nuclear coordinate space, and the magnetic part gives rise to a contribution depending on the local character of the trajectory and exists only in systems without time‐reversal symmetry. For particular examples, we consider the E⊗e and E⊗(b1+b2) Jahn–Teller systems with strong vibronic interactions. It is demonstrated that the ground states have vibronic standing wave states whose nuclear probability density distributions are localized in one of the equivalent minima on the lower potential surface. We also consider Zeeman splittings of degenerate vibronic...

In the context of wave packet methodology we show how to take advantage of the diffractive scattering symmetry arising when the incident beam is normal to the surface or to a surface principal axis. This may lead to a reduction in dimensionality being up to a factor of 8. The Fourier transformation is applied to evaluate the translational kinetic energy operator. Two alternative treatments are possible depending on whether the transformation is utilized to calculate the kinetic energy matrix elements in coordinate space, or whether it is applied to the wave function itself to switch between coordinate and momentum representations. The first approach is similar to the discrete variable representation treatment in the spirit of Light and co‐workers whereas the second one enables the use of the fast Fourier transform (FFT) scheme of Kosloff and Kosloff. We provide a detailed comparison between the two approaches as a function of the size of the grid, with and without the presence of symmetry in the diffracti...

A new approximation to the propagator is presented. The approximation as applied to the thermal propagator (coordinate space density matrix) is obtained by using an analog of the McLachlan variational principle for the solution of the Bloch equation. The approximation as applied to the real time propagator is obtained by using the McLachlan variational principle for the solution of the time‐dependent Schrodinger equation. The approximate coordinate space density matrix has the same functional form of the high temperature limit of the density matrix, while the approximate real time propagator has the same functional form as the short time propagator. We present numerical results for the thermal propagator for several test systems and compare these results to previous work of Zhang, Levy, and Freisner [Chem. Phys. Lett. 144, 236 (1988)], Mak and Andersen [J. Chem. Phys. 92, 2953 (1990)], and Cao and Berne [J. Chem. Phys. 92, 7531 (1990)]. We also present numerical results for the approximate real time propa...

A simple electronic‐structure‐based construction of diabatic states from adiabatic states is formulated. It is accomplished by maximizing the configurational uniformity of the diabatic states with respect to the dominant configurations throughout the entire coordinate space. No configurational constraints are introduced. No matrix elements of additional, derivative, or nonderivative operators have to be calculated. The matrix elements between the diabatic states are simply expressible in terms of the adiabatic energies and wave function coefficients.

Freed et al. have recently developed a lattice cluster theory of polymer solutions that involves series expansions in momentum space. Here we reformulate the lattice cluster theory in coordinate space. The present treatment has certain useful features. In particular, the terms in the reformulated theory can be obtained readily from existing exhaustive computer enumerations. Also, the Flory–Huggins theory can be shown to arise as the first term in a recentered coordinate‐space expansion. Generalization to treat polymers in confined space is straightforward.

A new method is proposed for locating saddle points on potential energy surfaces. The method involves walking on the ridge separating reactants’ and products’ valleys toward its minimum, which is a saddle point in coordinate space. Of particular advantage for ab initio calculations, the ridge method does not require evaluation of second derivatives of the potential energy. Another important feature of the method is that no assumptions about the transition state geometry are needed, and it is easy to impose linear constraints on the molecular structure. The ridge method is supplemented by a heuristic detour algorithm, which enables one to deal with unfortunate choices of reactants’ and products’ coordinates. Both algorithms are illustrated by several examples where the complexity of the potential energy surface ranges from a simple analytical formula to a numerical many‐body ab initio potential.

The quantum adiabatic theorem is explored as a potentially useful tool for obtaining highly excited eigenstates without requiring the calculation of all lower states. Starting in an eigenstate of some H0, the Hamiltonian is deformed adiabatically to the final H; the state of the system at the final time is an eigenstate of the final H which correlates with the eigenstates of H0. The method is free from the difficulties which are present in classical adiabatic switching, i.e., separatrix crossing (tunneling of both the coordinate space and dynamical type) presents no problem, isolated avoided crossings are accurately reproduced, and final states of the correct symmetry are obtained perforce by starting out with properly symmetrized states of the H0. The key issue concerning the possible utility of the technique is the ability to take large time steps in the propagation. The physical motivation for large time steps is that the spatial change in the wave function over a single period of motion is minor. The ...

This paper extends our new method for the study of the mechanism of molecular photodissociation. This method involves the time-independent study of the growth of photofragment flux, governed by photon absorption, and the subsequent redistribution of the flux, governed by the Hamiltonian in the excited, unbound state. The flux analysis can be carried out easily in either a diabatic (asymptotic), locally adiabatic, or fully adiabatic basis. The redistribution of the photofragment flux can be investigated in either internal state space or coordinate space at each excitation energy. Application is made to one- and two-dimensional models for the photodissociation of CH3I. © 1992 American Institute of Physics.

In this paper we describe a numerically efficient pseudospectral method for solving the time‐dependent Schrodinger equation in spherical coordinates. In this method the translational kinetic energy operator is evaluated with a Fourier transform. The angular dependence of the wave function is expanded on a two‐dimensional grid in coordinate space and the angular part of the Laplacian is evaluated by a Gauss–Legendre–Fourier transform between the coordinate and conjugate angular momentum representations. The potential energy operator is diagonal. Calculations performed for a model system representing H2 scattering from a static corrugated surface yield transition probabilities identical to those obtained with the close coupled wave packet (CCWP) method. The new algorithm will be more efficient than the CCWP method for problems in which a large number of rotational states are coupled.

In this paper, the reflection and transmission of plane waves are examined from a complex potential. Such potentials have the property of absorbing wave packets incident on them and are used widely in time‐dependent quantum scattering theory. The purpose of the study is to determine the optimal form of potential to be used for absorbing wave packets near the edges of finite grids in coordinate space. The best potentials for such purposes lead to the minimum possible transmission and reflection of the incident wave packet. The Jeffreys–Wentzel–Kramers–Brillouin (JWKB) theory is used to address this problem and a new form for the optimal complex potential is proposed. A scaled dimensionless form of the Schrodinger equation is also derived, so that the parameters of any optimized potential obtained for a particular collision energy and mass combination may be readily converted to apply to a new set of masses and energies.

The photodissociation dynamics of methyl iodide is investigated on a three‐dimensional grid using a time‐dependent quantum‐mechanical method. Two electronic states which correlate with I and I* fragments are explicitly included in the calculation. The potential‐energy functions and the nonadiabatic coupling are adapted from a recent ab initio calculation by Morokuma and co‐workers. The dynamically active degrees of freedom include the dissociation coordinate, the umbrella bend of the methyl group which is treated as a stretch between a hypothetic atom X (X=H3) and the carbon atom, and the H3–C–I bend. The discrete variable representation is used to describe the dynamics in the bending coordinate θ while the other two degrees of freedom are treated by a fast Fourier transform (FFT) based approach. The time propagation of the wave packet is carried out using the Chebychev expansion of the time propagator and the grid in the translational coordinate space is shifted during the propagation to avoid reflection...

A new approach is proposed for the determination of transition states and reaction paths for conformational transitions. The method makes use of adiabatic energy surfaces in the space of ‘‘essential’’ degrees of freedom of the molecule. The reduced dimensionality of this space, compared to the full Cartesian space, offers improved computational efficiency and should allow determination of exact reaction paths in systems much larger than those currently amenable to study in Cartesian space. A procedure to obtain reaction paths and free energy profiles in solution is also proposed. The free energy profile along the path in solution is calculated utilizing a free energy perturbation method with constrains and perturbations in internal coordinate space. Applications to a conformational transition of the alanine dipeptide and the folding transition of a model reverse turn in water are presented. For the reverse turn, the sequential flip of dihedral angles reported by Czerminsky and Elber on a similar peptide [...

The application of the time‐dependent Schrodinger equation/Fourier method to triatomic systems in hyperspherical coordinates is described. In particular, we consider the high symmetry situation of three identical particles, and focus on the reduced dimensional dynamics in the hyperspherical coordinate χ, which contains all the symmetry of the general problem. The periodic structure of the wave functions in the χ coordinate leads to a discrete spectrum in k space. The additional finite symmetry of the wave functions in this coordinate gives rise to selection rules, analogous to rotational selection rules for symmetric top molecules, which ensure that only one out of six of these integer k values has nonzero intensity. It is possible to reduce the range of the wave function (and the calculation) by a factor of 6 by selecting only one replica of the coordinate space wave function. The FFT automatically increases the spacing in k space by a factor of 6, eliminating the lines in k space with nonzero amplitude. For each different symmetry of wave function in coordinate space it is necessary to shift the compacted grid in k space by a different amount, in accord with k space selection rules.

We extend the periodic von Neumann basis to non-Cartesian coordinates. The bound states of two isomerizing triatomic molecules, LiCN/LiNC and HCN/HNC, are calculated using the vibrational Hamiltonian in Jacobi coordinates. The phase space localization of the basis functions leads to a flexible and accurate representation of the Hamiltonian. This results in significant savings compared to a basis localized just in coordinate space. The favorable scaling of the method with dimensionality makes it promising for applications to larger systems.

We have developed a fully numerical, basis‐set‐free algorithm for solution of the Schrodinger single‐particle equation in polyatomic molecules. As a test of the algorithm, the Hartree–Fock energy of H+3 is computed and compared with previous momentum‐space benchmarks. The present calculations are the first successful basis‐set‐free calculations in coordinate space on a polyatomic molecular system.

The quenching of the excitonic splitting in hydrogen bonded molecular dimers has been explained recently in terms of exciton coupling theory involving Förster's degenerate perturbation theoretical approach [P. Ottiger S. Leutwyler and H. Köppel J. Chem. Phys.136 174308 (2012) 10.1063/1.4705119]. Here we provide an alternative explanation based on the properties of the adiabatic potential energy surfaces. In the proper limit the lower of these surfaces exhibits a double minimum shape with an asymmetric distortion that destroys the geometric equivalence of the excitonically coupled monomers. An effective mode is introduced that exactly reproduces the energy gain and amount of distortion that occurs in a multi dimensional normal coordinate space. This allows to describe the quenched exciton splitting as the energy difference of the two (S1 and S2) vibronic band origins in a one dimensional (rather than multi dimensional) vibronic calculation. The agreement with the earlier result (based on Förster theory) is excellent for all five relevant cases studied. A simple rationale for the quenched exciton splitting as nonadiabatic tunneling splitting on the lower double minimum potential energy surface is given.

In two previous papers we have introduced a method to generate coupled quasi-diabatic Hamiltonians (H(d)) that are capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, two new synergistic features are introduced. Firstly, the functional form of H(d) is generalized. Rather than requiring there to be a low energy point of high symmetry to serve as the unique origin, functions centered on points distributed in nuclear coordinate space are used in the polynomials that comprise the matrix elements in H(d). The use of functions with distributed origins, allows reproduction of the ab initio data with lower order expansions, and offers the possibility of describing multichannel dissociation. The fitting algorithm is combined with a three-step procedure in which the domain of H(d) is extended from a core set of nuclear configurations to a region of nuclear coordinate space appropriate for nuclear dynamics, with a prescribed accuracy. This significant extension of the domain of definition compared to our original work, which is facilitated by the distributed origin approach, is achieved largely through the use of surface hopping trajectories. The 1,2(1)A states of NH(3), which provide an archetypical example of nonadiabatic dynamics, are used to demonstrate the utility of this approach. The representation describes 21 points on the 1(1)A-2(1)A seam of conical intersection and their local topography flawlessly and on the entire domain, the electronic structure data is represented to an accuracy of 77.00 (46.90) cm(-1), as measured by the root mean square (mean unsigned) error for energies lower than 50 000 cm(-1). This error is a factor of 10 lower than that of the most accurate representation of high quality ab initio data, on a comparable domain, previously reported for this system.

Chemical substitutions are powerful molecular design tools to enhance the performance of organic semiconductors, for instance, to improve solubility, intermolecular stacking, or film quality. However, at the microscopic level, substitutions in general tend to increase the molecular reorganization energy and thus decrease the intrinsic charge-carrier mobility. Through density functional theory calculations, we elucidate strategies that could be followed to reduce the reorganization energy upon chemical substitution. Specific examples are given here for hole-transport materials including indolo-carbazoles and several triarylamine derivatives. Through decomposition of the total reorganization energy into the internal coordinate space, we are able to identify the molecular segment that provides the most important contributions to the reorganization energy. It is found that when substitution reduces (enhances) the amplitude of the relevant frontier molecular orbital in that segment, the total reorganization energy decreases (increases). In particular, chlorination at appropriate positions can significantly reduce the reorganization energy. Several other substituents are shown to play a similar role, to a greater or lesser extent.

The quadratic vibronic coupling model is an important computational tool for simulating photoelectron spectra involving strongly coupled electronic states in polyatomic molecules. However, recent work has indicated the need for higher order terms, with most of the initial studies focusing on molecules with symmetry-required degeneracies. In this study we report an extension of our approach for constructing fully quadratic representations of bound electronic states coupled by conical intersections, which allows for the inclusion of higher order terms, demonstrated here employing a quartic expansion. Procedures are developed that eliminate unphysical behavior for large displacements, a problem likely to be an endemic to anharmonic expansions. Following work on representing dissociative electronic states, Lagrange multipliers are used to constrain the constructed representation to reproduce exactly the energy, energy gradients, and∕or derivative couplings at specific points, or nodes, in nuclear coordinate space. The approach is illustrated and systematically studied using the four lowest electronic states of triazolyl, (CH)(2)N(3).

An algorithm for constructing a quasidiabatic, coupled electronic state Hamiltonian, in a localized region of nuclear coordinate space, suitable for determining bound state spectra, is generalized to determine a nonlocal Hamiltonian capable of describing, for example, multichannel nonadiabatic photodissociation. For N(state) coupled electronic states, the Hamiltonian, H(d), is a symmetric N(state) x N(state) matrix whose elements are polynomials involving: decaying exponentials exp(-ar(i,j) (n)) n=1,2, where r(i,j)=R(i)-R(j), r(i,j)=|r(i,j)|, R(j) locates the jth nucleus; and scaled dot-cross product coordinates, proportional to r(i,j) x r(i,k) *r(i,l). The constructed Hamiltonian is constrained to reproduce, exactly, the ab initio data, energies, gradients, and derivative coupling at selected points, or nodes, in nuclear coordinate space. The remainder of the ab initio data is approximated in a least-squares sense using a normal equations approach. The fitting procedure includes a damping term that precludes oscillations due to the nodal constraints or local excesses of parameters. To illustrate the potential of the fitting procedure an H(d) is constructed, with the full nuclear permutation-inversion symmetry, which describes portions of the 1,2 (1)A potential energy surfaces of NH(3), including the minimum energy point on the 1,2 (1)A seam of conical intersection and the NH(2)+H asymptote. Ab initio data at 239 nuclear configurations was used in the construction which was tested at 48 additional nuclear configurations. While the energy range on the ground and excited potential energy surface is each individually approximately 45,000 cm(-1), the root mean square error for the energies at all points is only 93.6 cm(-1). The location and local conical topography of the minimum energy conical intersection is exactly reproduced. The derivative couplings are shown to be well reproduced, justifying the attribute quasidiabatic.

The quasi-self-consistent-field dispersion-corrected density-functional theory formalism (QSCF-DC-DFT) is developed and presented as an efficient and reliable scheme for the DFT treatment of van der Waals dispersion complexes, including full geometry optimizations and frequency calculations with analytical energy derivatives in a routine way. For this purpose, the long-range-corrected Perdew-Burke-Ernzerhof exchange functional and the one-parameter progressive correlation functional of Hirao and co-workers are combined with the Andersson-Langreth-Lundqvist (ALL) long-range correlation functional. The time-consuming self-consistent incorporation of the ALL term in the DFT iterations needed for the calculation of forces and force constants is avoided by an a posteriori evaluation of the ALL term and its gradient based on an effective partitioning of the coordinate space into global and intramonomer coordinates. QSCF-DC-DFT is substantially faster than SCF-DC-DFT would be. QSCF-DC-DFT is used to explore the potential energy surface (PES) of the benzene dimer. The results for the binding energies and intermolecular distances agree well with coupled-cluster calculations at the complete basis-set limit. We identify 16 stationary points on the PES, which underlines the usefulness of analytical energy gradients for the investigation of the PES. Furthermore, the inclusion of analytically calculated zero point energies reveals that large-amplitude vibrations connect the eight most stable benzene dimer forms and make it difficult to identify a dominating complex form. The tilted T structure and the parallel-displaced sandwich form have the same D(0) value of 2.40 kcal/mol, which agrees perfectly with the experimental value of 2.40+/-0.40 kcal/mol.

A random walk sampling algorithm allows the extraction of the density of states distribution in energy-reaction coordinate space. As a result, the temperature dependences of thermodynamic quantities such as relative energy, entropy, and heat capacity can be calculated using first-principles statistical mechanics. The strategies for optimal convergence of the algorithm and control of its accuracy are proposed. We show that the saturation of the error [Q. Yan and J. J. de Pablo, Phys. Rev. Lett. 90, 035701 (2003); E. Belardinelli and V. D. Pereyra, J. Chem. Phys. 127, 184105 (2007)] is due to the use of histogram flatness as a criterion of convergence. An application of the algorithm to methane dimer hydrophobic interactions is presented. We obtained a quantitatively accurate energy-entropy decomposition of the methane dimer cavity potential. The presented results confirm the previous results, and they provide new information regarding the thermodynamics of hydrophobic interactions. We show that the finite-difference approximation, which is widely used in molecular dynamic simulations for the energy-entropy decomposition of a free energy potential, can lead to a significant error.

The effect of gas heating in laboratory sputter magnetrons is investigated by means of numerical modeling. The model is two-dimensional in the coordinate space and three-dimensional in the velocity space based on the particle-in-cellMonte Carlo collisions technique. It is expanded in a way that allows the inclusion of the neutral plasma particles (fast gas atoms and sputtered atoms), which makes it possible to calculate the gas temperature and its influence on the discharge behavior in a completely self-consistent way. The results of the model are compared to experimental measurements and to other existing simulation results. The results show that gas heating is pressure dependent (rising with the increase in the gas pressure) and should be taken into consideration at pressures above 10 mTorr.

A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing N(state) coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a least-squares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a least-squares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the 1 (2)A(1) and 1 (2)E states of the 1-propynyl radical, CH(3)CC.

Sampling of small-scale and large-scale motions is important in various computational tasks, such as protein-protein docking and ligand binding. Here, we report further development and applications of the activation-relaxation technique for internal coordinate space trajectories (ARTIST). This method generates conformational moves of any complexity and size by identifying and crossing well-defined saddle points connecting energy minima. Simulations on two all-atom proteins and three protein complexes containing between 70 and 300 amino acids indicate that ARTIST opens the door to the full treatment of all degrees of freedom in dense systems such as protein-protein complexes.

A recently developed method for determining avoided surface crossings using analytic gradient techniques is used to locate an actual crossing seam for the 1 1A’ and 2 1A’ potential energy surfaces of the He–H2 system. This seam is not related to any high symmetry nuclear configurations. The computational procedure, which is based on the minimization of ΔEIJ(R)2≡[EI(R)−EJ(R)]2, &(R)]2, uses different density matrices to simplify the construction of the energy difference gradient, the most costly step in the procedure. The actual crossing seam, R(r), is specified by the ordered triple R(r)≡[R(r), γ(r),r] for which ΔEIJ(R)=0. It is exoergic with respect to the He–H2(B 1Σ+u) asymptote for r≊[2.60, 5.70]. Here r≡R(H2), R=R(He–H2) and γ is the He–H2 angle. This seam defines a region nuclear coordinate space near which helium can efficiently quench H2(B 1Σ+u).

A method is presented to depict the intramolecular dynamics of resonantly coupled vibrations, starting from the experimental overtone and combination spectrum. The nonlinear least‐squares fit of the spectrum is used to obtain a semiclassical phase space Hamiltonian via the Heisenberg correspondence principle. This integrable Hamiltonian, corresponding to quasiperiodic motion, is used to generate a classical trajectory in phase space for each energy level in a resonance polyad. Polyad phase space profiles are shown to have complete mutual consistency starting from a fit in either the local or normal representation. It is argued that the best way to depict the phase space profile is on a spherical surface called the polyad phase sphere. Represented in this way, the local and normal mode phase spaces are seen to be a single entity, manifestly equivalent by a 90° rotation. The phase space trajectories can be converted into a coordinate space representation. This gives an easily visualized picture of the semiclassical intramolecular dynamics corresponding to each energy level. The polyad phase spheres from the fits of the experimental stretching spectra of H2O, O3 and SO2 are displayed. H2O and O3 are seen to be molecules with a local to normal modes transition, while SO2 is seen to be very near the pure normal modes limit. The experimentally determined phase space dynamics of H2O seen on the phase sphere are compared with the dynamics determined by Lawton and Child from trajectory calculations on the Sorbie–Murrell potential surface. The coordinate space trajectories corresponding to the phase spheres are compared with wave functions from the fit of the spectrum.

An ab initio approach to the theoretical description of centrifugal distortions in molecules is presented. The method is based on the calculation of the electronic energy changes and gradients accompanying rotationally induced distortions. A centrifugal distortion pathway in nuclear coordinate space is defined. Results are presented at the HF/6‐31G** level for NH3, CH4, BF3, and SF6, and at the Guillemin–Zener level for H+2. Quartic centrifugal distortion parameters are computed for each molecule, with distortion anisotropies presented in the form of tensor coefficients. Centrifugally induced electric dipole moment coefficients are presented for CH4 and BF3 together with dipole moment changes for NH3. Agreement with experiment and with conventional theoretical descriptions is generally quite satisfactory, particularly for the tensor coefficients representing the cubic anisotropy in the distortions of the spherical tops CH4 and SF6.

A revised assignment of vibrational fundamentals is developed for trans‐diazene (HN=NH) and its −d1 and −d2 modifications that is consistent with all of the published spectra. The fundamental frequencies (in cm−1) for trans‐diazene are: (Ag) 3128, 1583, 1529; (Au) 1286; (Bu) 3120, 1322. A seven‐parameter, general valence type potential function is fit to the 18 observed frequencies of the three isotopic species with an average frequency error of 6.6 cm−1. When transformed into internal coordinate space, the theoretical potential function calculated by Peric, Buenker, and Peyerimhoff compares favorably with the empirical function. From empirical potential functions of trans‐methyldiazene, trans‐diazene, and cis‐methyldiazene, a potential function for cis‐diazene is constructed and used to predict the vibrational frequencies of this elusive substance.

Recently Ablowitz and Haberman have shown that, in three spatial dimensions, the nonlinear 3‐wave evolution equation results from the compatibility condition between two well‐defined first‐order linear differential 3×3 systems having common solutions. We construct inversionlike integral equations (I.E.) associated with both these two linear differential systems so that the solutions of the I.E. embody their compatibility conditions. The scalar kernels of these I.E. depend upon three independent variables in such a way that there exist degenerate kernels confined in the three‐dimensional coordinate space. Consequently we exhibit, for the nonlinear 3‐wave evolution equations, an infinite number of solutions which, at fixed time, are confined in the three‐dimensional coordinate space.

A recent paper established technical conditions for the construction of a class of induced representations of the nonrelativistic current group SΛK, where S is Schwartz’s space of rapidly decreasing C∞ functions, and K is a group of C∞ diffeomorphisms of Rs. Bose and Fermi N‐particle systems were recovered as unitarily inequivalent induced representations of the group by lifting the action of K on an orbit Δ⊆S′ to its universal covering space δ. For s⩾3, δ is the coordinate space for N particles, which is simply connected. In two‐dimensional space, however, the coordinate space is multiply connected, implying induced representations other than those describing the usual Bose or Fermi statistics; these are explored in the present paper. Likewise the Aharonov–Bohm effect is described by means of induced representations of the local observables, defined in a nonsimply connected region of Rs. The vector potential plays no role in this description of the Aharonov–Bohm effect.

We develop a coordinate‐space model for dynamical correlations in an inhomogeneous electron gas. The model treats opposite‐spin and same‐spin pairs separately, and it also accounts properly for correlation contributions to the kinetic energy. Furthermore, it gives identically zero correlation energy in the case of one‐electron systems. Applications to the uniform electron gas and to the atoms H through Ar are reported.

Invariant submanifolds of the linear representation space C4m of the physical symmetry group SU(2,2)×SU(m) and its subgroup P×SU(m) are studied in some detail. It is shown that there exists only one such manifold admitting unique projection onto Minkowski space. The structure of this manifold is investigated by using proper local coordinate systems.