H. Bernhard Schlegel

An improved algorithm for reaction path following

A new algorithm is presented for obtaining points on a steepest descent path from the transition state of the reactants and products. In mass‐weighted coordinates, this path corresponds to the intrinsic reaction coordinate. Points on the reaction path are found by constrained optimizations involving all internal degrees of freedom of the molecule. The points are optimized so that the segment of the reaction path between any two adjacent points is given by an arc of a circle, and so that the gradient at each point is tangent to the path. Only the transition vector and the energy gradients are needed to construct the path. The resulting path is continuous, differentiable and piecewise quadratic. In the limit of small step size, the present algorithm is shown to take a step with the correct tangent vector and curvature vector; hence, it is a second order algorithm. The method has been tested on the following reactions: HCN→CNH, SiH2+H2→SiH4, CH4+H→CH3+H2, F−+CH3F→FCH3+F−, and C2H5F→C2H4+HF. Reaction paths calculated with a step size of 0.4 a.u. are almost identical to those computed with a step size of 0.1 a.u. or smaller.

Using redundant internal coordinates to optimize equilibrium geometries and transition states

A redundant internal coordinate system for optimizing molecular geometries is constructed from all bonds, all valence angles between bonded atoms, and all dihedral angles between bonded atoms. Redundancies are removed by using the generalized inverse of the G matrix; constraints can be added by using an appropriate projector. For minimizations, redundant internal coordinates provide substantial improvements in optimization efficiency over Cartesian and nonredundant internal coordinates, especially for flexible and polycyclic systems. Transition structure searches are also improved when redundant coordinates are used and when the initial steps are guided by the quadratic synchronous transit approach.

Potential energy curves using unrestricted Mo/ller–Plesset perturbation theory with spin annihilation

Unrestricted Hartree–Fock and unrestricted Mo/ller–Plesset perturbation theory are convenient methods to compute potential energy curves for bond dissociation, since these methods approach the correct dissociation limit. Unfortunately, a spin unrestricted wave function can contain large contributions from unwanted spin states that can distort the potential energy surface significantly. The spin contamination can be removed by projection or annihilation operators. As is well known, the spin project unrestricted Hartree–Fock bond dissociation curves have a large kink at the onset of the UHF/RHF instability, and a spurious minimum just beyond. However, the spurious minimum disappears and the kink is very much less pronounced at the unrestricted Mo/ller–Plesset level with spin projection. Bond dissociation potentials for LiH and CH4 were computed at the fourth order Mo/ller–Plesset level plus spin projection,4 and good agreement was found with full CI and MR‐CISD calculations.

Accurate reaction paths using a Hessian based predictor-corrector integrator

Central to the theoretical description of a chemical reaction is the reaction pathway. The intrinsic reaction coordinate is defined as the steepest descent path in mass weighted Cartesian coordinates that connects the transition state to reactants and products. In this work, a new integrator for the steepest descent pathway is presented. This method is a Hessian based predictor-corrector algorithm that affords pathways comparable to our previous fourth order method at the cost of a second order approach. The proposed integrator is tested on an analytic surface, four moderately sized chemical reactions, and one larger organometallic system.

Improved algorithms for reaction path following: Higher‐order implicit algorithms

Eight new algorithms for reaction path following are presented, ranging from third order to sixth order. Like the second‐order algorithm [J. Chem. Phys. 90, 2154 (1989)] these are implicit methods, i.e., they rely on the tangent (and in some cases the curvature) at the endpoint of the step. The tangent (and the curvature, if needed) are obtained by a constrained optimization using only the gradient. At most, only one Hessian calculation is needed per step along the path. The various methods are applied to the Muller–Brown surface and to a new surface whose reaction path is known analytically to test their ability to follow the reaction path and to reproduce the curvature along the path.

A direct method for the location of the lowest energy point on a potential surface crossing

Abstract We present a method, which avoids the use of Lagrange multipliers, for the optimisation of the lowest energy point of the intersection of two potential energy surfaces. The efficiency of this unconstrained algorithm is demonstrated for the n—2 intersection space of a conical intersection and the n—1 intersection space of the crossing of two states of different spin multiplicity.

Geometry optimization with QM/MM, ONIOM, and other combined methods. I. Microiterations and constraints

Hybrid energy methods such as QM/MM and ONIOM, that combine different levels of theory into one calculation, have been very successful in describing large systems. Geometry optimization methods can take advantage of the partitioning of these calculations into a region treated at a quantum mechanical (QM) level of theory and the larger, remaining region treated by an inexpensive method such as molecular mechanics (MM). A series of microiterations can be employed to fully optimize the MM region for each optimization step in the QM region. Cartesian coordinates are used for the MM region and are chosen so that the internal coordinates of the QM region remain constant during the microiterations. The coordinates of the MM region are augmented to permit rigid body translation and rotation of the QM region. This is essential if any atoms in the MM region are constrained, but it also improves the efficiency of unconstrained optimizations. Because of the microiterations, special care is needed for the optimization step in the QM region so that the system remains in the same local valley during the course of the optimization. The optimization methodology with microiterations, constraints, and step‐size control are illustrated by calculations on bacteriorhodopsin and other systems.

Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals

We propose and implement an alternative approach to the original Car–Parrinello method where the density matrix elements (instead of the molecular orbitals) are propagated together with the nuclear degrees of freedom. Our new approach has the advantage of leading to an O(N) computational scheme in the large system limit. Our implementation is based on atom-centered Gaussian orbitals, which are especially suited to deal effectively with general molecular systems. The methodology is illustrated by applications to the three-body dissociation of triazine and to the dynamics of a cluster of a chloride ion with 25 water molecules.

IDENTIFICATION AND TREATMENT OF INTERNAL ROTATION IN NORMAL MODE VIBRATIONAL ANALYSIS

A procedure that automatically identifies internal rotation modes and rotating groups during the normal mode vibrational analysis is outlined, and an improved approximation to the corrections for the thermodynamic functions is proposed. The identification and the characterization of the internal rotation modes require no user intervention and make extensive use of the information imbedded in the redundant internal coordinates. Rigid-rotor internal rotation modes are obtained by fixing stretching, bending, and out-of-plane bending motions and solving the vibrational problem for the constrained system. Normal vibrational modes corresponding to internal rotations are identified by comparing them with the constrained modes. The atomic composition of the rotating groups is determined automatically and the kinetic energy matrix for internal rotation is given by either the constrained Wilson-G matrix or the Kilpatrick and Pitzer protocol. The potential periodicity, the rotating tops’ symmetry numbers, and the we...

Ab initio molecular dynamics: Propagating the density matrix with Gaussian orbitals. III. Comparison with Born-Oppenheimer dynamics

In a recently developed approach to ab initio molecular dynamics (ADMP), we used an extended Lagrangian to propagate the density matrix in a basis of atom centered Gaussian functions. Results of trajectory calculations obtained by this method are compared with the Born–Oppenheimer approach (BO), in which the density is converged at each step rather than propagated. For NaCl, the vibrational frequency with ADMP is found to be independent of the fictitious electronic mass and to be equal to the BO trajectory result. For the photodissociation of formaldehyde, H2CO→H2+CO, and the three body dissociation of glyoxal, C2H2O2→H2+2CO, very good agreement is found between the Born–Oppenheimer trajectories and the extended Lagrangian approach in terms of the rotational and vibrational energy distributions of the products. A 1.2 ps simulation of the dynamics of chloride ion in a cluster of 25 water molecules was used as a third test case. The Fourier transform of the velocity–velocity autocorrelation function showed ...