Interpolation of diabatic potential energy surfaces

A method is presented for constructing diabatic potential energy matrices from ab initio quantum chemistry data. The method is similar to that reported previously for single adiabatic potential energy surfaces, but correctly accounts for the nuclear permutation symmetry of diabatic potential energy matrices and other complications that arise from the derivative coupling of electronic states. The method is tested by comparison with an analytic model for the two lowest energy states of H(3).     

Ab initio computed diabatic potential energy surfaces of OH-HCl

The two four-dimensional diabatic potential energy surfaces (DPESs) for OH-HCl are computed that correlate with the twofold degenerate (2)Pi ground state of the free OH radical. About 20 000 points on the surface are obtained by the ab initio coupled-cluster and multi-reference configuration interaction methods. Analytic forms for the diabatic potential energy surfaces are derived as expansions in complete sets of orthogonal functions depending on the three intermolecular angles. The numeric computation of the angular expansion coefficients is discussed. The distance-dependence of the angular coefficients is represented by the reproducing kernel Hilbert space method. It is checked that both diabatic potentials converge for large intermolecular separations to the values computed directly from the electrostatic multipole expansion. The final DPESs are discussed and illustrated by some physically meaningful one- and two-dimensional cuts through them.     

Nonadiabatic dynamics in multidimensional complex potential energy surfaces

Despite the continuous development of theoretical methodologies for describing nonadiabatic dynamics of molecular systems, there is a lack of approaches for processes where the norm of the wave function is not conserved, i.e., when an imaginary potential accounts for some irreversible decaying mechanism. Current approaches rely on building potential energy surfaces of reduced dimensionality, which is not optimal for more involving and realistic multidimensional problems. Here, we present a novel methodology for describing the dynamics of complex-valued molecular Hamiltonians, which is a generalisation of the trajectory surface hopping method. As a first application, the complex surface fewest switches surface hopping (CS-FSSH) method was employed to survey the relaxation mechanisms of the shape resonant anions of iodoethene. We have provided the first detailed and dynamical picture of the π*/σ* mechanism of dissociative electron attachment in halogenated unsaturated compounds, which is believed to underlie electron-induced reactions of several molecules of interest. Electron capture into the π* orbital promotes C C stretching and out-of-plane vibrations, followed by charge transfer from the double bond into the σ* orbital at the C–I bond, and, finally, release of the iodine ion, all within only 15 fs. On-the-fly dynamics simulations of a vast class of processes can be envisioned with the CS-FSSH methodology, including autoionisation from transient anions, core-ionised and superexcited states, Auger and interatomic coulombic decay, and time-dependent luminescence.

Despite the continuous development of methods for describing nonadiabatic dynamics, there is a lack of multidimensional approaches for processes where the wave function norm is not conserved. A new surface hopping variant closes this knowledge gap.     

Explorations on the multidimensional potential energy surface of a chiral stationary phase

The multidimensional potential energy surface for a soluble analog of a chiral phase is computed with MM2 and MNDO. Minimum energy conformations are located. The minimum energy reaction pathway between these forms is located, and the templating ability of these phases is described.     

On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory

A theoretical model is presented for deriving effective diabatic states based on ab initio valence bond self-consistent field (VBSCF) theory by reducing the multiconfigurational VB Hamiltonian into an effective two-state model. We describe two computational approaches for the optimization of the effective diabatic configurations, resulting in two ways of interpreting such effective diabatic states. In the variational diabatic configuration (VDC) method, the energies of the diabatic states are variationally minimized. In the consistent diabatic configuration (CDC) method, both the configuration coefficients and orbital coefficients are simultaneously optimized to minimize the adiabatic ground-state energy in VBSCF calculations. In addition, we describe a mixed molecular orbital and valence bond (MOVB) approach to construct the CDC diabatic and adiabatic states for a chemical reaction. Note that the VDC-MOVB method has been described previously. Employing the symmetric S(N)2 reaction between NH(3) and CH(3)NH(3)(+) as a test system, we found that the results from ab initio VBSCF and from ab initio MOVB calculations using the same basis set are in good agreement, suggesting that the computationally efficient MOVB method is a reasonable model for VB simulations of condensed phase reactions. The results indicate that CDC and VDC diabatic states converge, respectively, to covalent and ionic states as the molecular geometries are distorted from the minimum of the respective diabatic state along the reaction coordinate. Furthermore, the resonance energy that stabilizes the energy of crossing between the two diabatic states, resulting in the transition state of the adiabatic ground-state reaction, has a strong dependence on the overlap integral between the two diabatic states and is a function of both the exchange integral and the total diabatic ground-state energy.     

Quantum wave packet study of the H+ + D2 reaction on diabatic potential energy surfaces

The exact three-dimensional nonadiabatic quantum dynamics calculations were carried out for the title reaction by a time-dependent wave packet approach based on a newly constructed diabatic potential energy surface (Kamisaka et al. J. Chem. Phys. 2002, 116, 654). Three processes including those of reactive charge transfer, nonreactive charge transfer, and reactive noncharge transfer were investigated to determine the initial state-resolved probabilities and reactive cross sections. The results show that a large number of resonances can be observed in the calculated probabilities due to the deep well on adiabatic ground surface and the dominant process is the reactive noncharge-transfer process. Some interesting dynamical features such as v-dependent and j-dependent behaviors of the probabilities are also revealed. In addition, a good agreement has been achieved in the comparison between the calculated quantum cross sections from the ground rovibrational initial state and the experimental measurement data.     

The structural stability principle and branching points on multidimensional potential energy surfaces

The chemically interesting potential energy surfaces (PES) are considered on which the conditions underlying application of structural stability principle and Morse inequalities are violated. The possibility of treatment of singular branching points on a PES slope in terms of intrinsic reaction curves (IRC) is discussed.     

Theoretical study of the He-HF+ complex. II. Rovibronic states from coupled diabatic potential energy surfaces

The bound rovibronic levels of the He-HF+ complex were calculated for total angular momentum J=1/2, 3/2, 5/2, 7/2, and 9/2 with the use of ab initio diabatic intermolecular potentials presented in Paper I and the inclusion of spin-orbit coupling. The character of the rovibronic states was interpreted by a series of calculations with the intermolecular distance R fixed at values ranging from 1.5 to 8.5 A and by analysis of the wave functions. In this analysis we used approximate angular momentum quantum numbers defined with respect to a dimer body-fixed (BF) frame with its z axis parallel to the intermolecular vector R and with respect to a molecule-fixed (MF) frame with its z axis parallel to the HF+ bond. The linear equilibrium geometry makes the He-HF+ complex a Renner-Teller system. We found both sets of quantum numbers, BF and MF, useful to understand the characteristics of the Renner-Teller effect in this system. In addition to the properties of a "normal" semirigid molecule Renner-Teller system it shows typical features caused by large-amplitude internal (bending) motion. We also present spectroscopic data: stretch and bend frequencies, spin-orbit splittings, parity splittings, and rotational constants.     

Generalized electronic diabatic approach to structural similarity in two‐dimensional potential energy surfaces of various topologies

Active site properties in some proteins can be affected by conformational fluctuations of neighbor residues, even when the latter are not involved directly in the binding process. A local environment thus appears to alter the relevant potential energy surface and its reaction paths. Here, some aspects of this phenomenon are simulated within a generalized electronic diabatic (GED) scheme to study the geometry and structural similarity for a class of two‐dimensional (2D) energy surfaces. The electronic quantum state is a linear superposition of diabatic basis functions, each of which is taken to represent a single (pure) electronic state for the isolated material system. Here, we describe a model reaction of isomerization by shifts in amplitudes for three diabatic species (reactant, product, and an open‐shell transition state) coupled in an external field. The “effective” 2D energy surface in the field is characterized in terms of critical points, and the amplitudes along the main reaction paths. A new feature is the introduction of a phase diagram where all possible potential‐energy‐surface topologies (consistent with three‐state systems in two linear coordinates) are matched with actual model parameters. By varying the coupling strengths between diabatic states, we classify regions of this phase diagram in terms of electronic and structural similarities; some regions comprise models whose reaction paths have geometries that belong to the catchment region of the reactant, yet are electronically akin to the diabatic transition state or product. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Efficient generation of Heisenberg Hamiltonian matrices for VB calculations of potential energy surfaces

The spin‐Hamiltonian valence bond theory relies upon covalent configurations formed by singly occupied orbitals differing by their spin counterparts. This theory has been proven to be successful in studying potential energy surfaces of the ground and lowest excited states in organic molecules when used as a part of the hybrid molecular mechanics—valence bond method. The method allows one to consider systems with large active spaces formed by n electrons in n orbitals and relies upon a specially proposed graphical unitary group approach. At the same time, the restriction of the equality of the numbers of electrons and orbitals in the active space is too severe: it excludes from the consideration a lot of interesting applications. We can mention here carbocations and systems with heteroatoms. Moreover, the structure of the method makes it difficult to study charge‐transfer excited states because they are formed by ionic configurations. In the present work we tackle these problems by significant extension of the spin‐Hamiltonian approach. We consider (i) more general active space formed by n ± m electrons in n orbitals and (ii) states with the charge transfer. The main problem addressed is the generation of Hamiltonian matrices for these general cases. We propose a scheme combining operators of electron exchange and hopping, generating all nonzero matrix elements step‐by‐step. This scheme provides a very efficient way to generate the Hamiltonians, thus extending the applicability of spin‐Hamiltonian valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

A topological stochastic approach to the study of multidimensional potential energy surfaces of chemical reactions

In this article we propose a new approach for investigating the properties of multidimensional potential energy surfaces in chemical reactions, based on relations of each multidimensional surface to its one-dimensional image which is the chemical reaction tree. This approach makes it possible to find a common number of independent channels in chemical reactions for complex systems and to construct the probable models.     

Quenching of Li (2P) by H2: potential energy surfaces, conical intersection seam, and diabatic bases

The quenching of Li (1s ²2p; ²P) to Li (1s ²2s; ²S) by H₂ is considered using coupled-cluster and multireference configuration-interaction techniques. C _{2 v} (²A₁, ²B₂) and C _{∞ v} (²Π,²Σ⁺) sections of the 1²A^′ and 2²A^′ potential energy surfaces are determined. The C _{2 v} portion of the 1²A^′−2²A^′ seam of conical intersection is studied. Perhaps the most significant finding is a surprising trifurcation of this seam into a portion with only C _s symmetry and the aforementioned C _{2 v} portion. The adiabatic-to-diabatic state transformation is considered in the vicinity of the seam of conical intersection using both perturbation theory and the dipole moment operator. The ²B₂ section of the 2²A^′ potential energy surface exhibits an exciplex in the general vicinity of the seam of conical intersection. The ²Π section of the 2²A^′ potential energy surface possesses a global minimum lying 1.86kcal/mol below the Li (²P)+H₂ asymptote. A van der Waals-like minimum with C _{∞ v} symmetry was found on the 1²A^′ potential energy surface. Received: 14 August 1998 / Accepted: 20 August 1998 / Published online: 11 November 1998     

Ab initio treatment of the chemical reaction precursor complex Cl(2P)-HF. 1. Three-dimensional diabatic potential energy surfaces

The three adiabatic potential surfaces of the Cl(2P)-HF complex that correlate with the 2P ground state of the Cl atom were calculated with the ab initio RCCSD(T) method (partially spin-restricted coupled cluster theory including single and double excitations and perturbative correction for the triples). With the aid of a geometry-dependent diabatic mixing angle, calculated by the complete active space self-consistent field (CASSCF) and multireference configuration-interaction (MRCI) methods, these adiabatic potential surfaces were converted to a set of four distinct diabatic potential surfaces required to define the full 3 x 3 matrix of diabatic potentials. Each of these diabatic potential surfaces was expanded in terms of the appropriate spherical harmonics in the angle theta between the HF bond axis r and the Cl-HF intermolecular axis R. The dependence of the expansion coefficients on the Cl-HF distance R and the HF bond length r(HF) was fit to an analytic form. The strongest binding occurs for the hydrogen-bonded linear Cl-HF geometry, with D(e) = 676.5 cm(-1) and R(e) = 6.217 a0 when r(HF) = r(e) = 1.7328 a0. This binding energy D(e) depends strongly on r(HF), with larger r(HF) causing stronger binding. An important contribution to the binding energy is provided by the interaction between the quadrupole moment of the Cl(2P) atom and the dipole of HF. In agreement with this electrostatic picture, the ground state of linear Cl-HF is a 2-fold degenerate electronic Pi state. For the linear Cl-FH geometry the states are in opposite order, i.e., the Sigma state is lower in energy than the Pi state. The following paper in this issue describes full three-dimensional computations of the bound states of the Cl-HF complex, based on the ab initio diabatic potentials of this paper.     

One- and multidimensional conformational free energy simulations

A new thermodynamic integration approach to conformational free energy simulations is presented. The method is applicable both to one-dimensional cases (reaction coordinates) and multidimensional situations (free energy surfaces). Analysis of the properties of the thermodynamic integration algorithm is used to formulate methods of calculating multidimensional free energy gradients. The method is applied to calculate the free energy profile for rotation around the central C—C bond of n-butane in the gas and liquid phase and to generate maps of the 18-dimensional free energy gradient with respect to all nine ϕ and nine ψ dihedrals of the decaalanine and deca-α-methylalanine peptides in vacuum. For n-butane essentially no change in the gauche–trans equilibrium between the gas and liquid is predicted within the CHARMM explicit hydrogen model, with the thermodynamic integration, thermodynamic perturbation, and direct simulation methods yielding free energy profiles that are identical within errors. For the decapeptides the right-handed helical region of conformational space is investigated. For decaalanine a minimum on the free energy surface is found in the vicinity of (ϕ, ψ) = (-64.5°, -42.5°) in the α-helix region; no minimum exists for 3₁₀-helix-type conformers. For deca-α-methylalanine free energy minima corresponding to both the α-helix at ( - 55.5°, - 51.5°) and the 3₁₀-helix at ( - 54°, - 29°) are found; the α-helix state is favored by about 4 kcal/mol and the barrier for the concerted 3₁₀-helix → α-helix transition is about 3 kcal/mol. The α-methylation also considerably increases the rigidity of the α-helix with respect to deformations. The computational efficiency, ease of generalization to calculations of multidimensional gradients, and analytical capability due to component analysis of free energy differences make the method a novel, powerful tool to improve the basic understanding of conformational equilibria of flexible molecules in condensed phases. A related scheme for energy minimization in the presence of holonomic constraints is also presented, allowing generation of adiabatic energy surfaces in constrained systems. © 1996 by John Wiley & Sons, Inc.     

Comparison of line search minimization algorithms for exploring topography of multidimensional potential energy surfaces: Mg+Arn case

The most robust numerical algorithms for unconstrained optimization that involve a line search are tested in the problem of locating stable structures and transition states of atomic microclusters. Specifically, the popular quenching technique is compared with conjugate gradient and variable metric algorithms in the Mg⁺Ar_n clusters. It is found that the variable metric method BFGS combined with an approximate line minimization routine is the most efficient, and it shows global convergence properties. This technique is applied to find a few hundred stationary points of Mg⁺Ar₁₂ and to locate isomerization paths between the two most stable icosahedral structures found for Mg⁺Ar₁₂. The latter correspond to a solvated and a nonsolvated ion, respectively. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 :1011–1022, 1997