A modified conjugate gradient algorithm for geometry optimization is outlined for use with ab initioMO methods. Since the computation time for analytical energy gradients is approximately the same as for the energy, the optimization algorithm evaluates and utilizes the gradients each time the energy is computed. The second derivative matrix, rather than its inverse, is updated employing the gradients. At each step, a one-dimensional minimization using a quartic polynomial is carried out, followed by an n-dimensional search using the second derivative matrix. By suitably controlling the number of negative eigenvalues of the second derivative matrix, the algorithm can also be used to locate transition structures. Representative timing data for optimizations of equilibrium geometries and transition structures are reported for ab initioSCF–MO calculations.

Optimization of equilibrium geometries and transition structures

We present an all atom potential energy function for the simulation of proteins and nucleic acids. This work is an extension of the CH united atom function recently presented by S.J. Weiner et al. J. Amer. Chem. Soc., 106, 765 (1984). The parameters of our function are based on calculations on ethane, propane, n−butane, dimethyl ether, methyl ethyl ether, tetrahydrofuran, imidazole, indole, deoxyadenosine, base paired dinucleoside phosphates, adenine, guanine, uracil, cytosine, thymine, insulin, and myoglobin. We have also used these parameters to carry out the first general vibrational analysis of all five nucleic acid bases with a molecular mechanics potential approach.

An all atom force field for simulations of proteins and nucleic acids.

AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules

The problem of determining which activated (and slow) transitions can occur from a given initial state at a finite temperature is addressed. In the harmonic approximation to transition state theory this problem reduces to finding the set of low lying saddle points at the boundary of the potential energy basin associated with the initial state, as well as the relevant vibrational frequencies. Also, when full transition state theory calculations are carried out, it can be useful to know the location of the saddle points on the potential energy surface. A method for finding saddle points without knowledge of the final state of the transition is described. The method only makes use of first derivatives of the potential energy and is, therefore, applicable in situations where second derivatives are too costly or too tedious to evaluate, for example, in plane wave based density functional theory calculations. It is also designed to scale efficiently with the dimensionality of the system and can be applied to very large systems when empirical or semiempirical methods are used to obtain the atomic forces. The method can be started from the potential minimum representing the initial state, or from an initial guess closer to the saddle point. An application to Al adatom diffusion on an Al(100) surface described by an embedded atom method potential is presented. A large number of saddle points were found for adatom diffusion and dimer/vacancy formation. A surprisingly low energy four atom exchange process was found as well as processes indicative of local hex reconstruction of the surface layer.

A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives

Before we start, we need a working definition for MOPAC. The following description has been used many times to describe MOPAC: MOPAC is a general-purpose, semiempirical molecular orbital program for the study of chemical reactions involving molecules, ions, and linear polymers. It implements the semiempirical Hamiltonians MNDO, AM 1, MINDO/3, and MNDOPM3, and combir_es the calculations of vibrational spectra, thermodynamic quantities, isotopic substitution effects, and force constants in a fully integrated program. Elements parameterized at the MNDO level include H, Li, Be, B, C, N, O, F, A1, Si, P, S, C1, Ge, Br, Sn, Hg, Pb, and I; at the PM3 level the elements H, C, N, O, F, A1, Si, P, S, C1, Br, and I are available. Within the electronic part of the calculation, molecular and localized orbitals, excited states up to sextets, chemical bond indices, charges, etc. are computed. Both intrinsic and dynamic reaction coordinates can be calculated. A transition-state location routine and two transition-state optimizing routines are available for studying chemical reactions.

MOPAC: A semiempirical molecular orbital program

Developpement d'un algorithme pour la marche automatisee sur une surface, en combinant l'approximation quadratique locale a la surface d'energie potentielle et une mise a l'echelle d'une coordonnee active

Walking on potential energy surfaces

numerical values of measured reactant and product concentrations during a MeMA BZ oscillator run are given. Since MeMA is in excess (0.28 M) compared to Br03ions (0.10 M), the stoichiometry of process 3 requires that 0.1 1 M MeMA should be left as deuterated or undeuterated species. This is exactly the result found in our experiment (Table I). Finally, we calculate the concentrations of BrMeMA and acetic acid. From the reacting MeMA (0.17 M), 0.10 M BrMeMA and 0.07 M CH,COOH should be found, when it is assumed that all bromate has reacted. Our observed values for BrMeMA and acetic acid are 0.09 and 0.06 M, respectively (see Table I), which are in fair agreement with the stoichiometric requirement of process 3.

Imposition of geometrical constraints on potential energy surface walking procedures

Studies of families of unusual species such as the double-Rydberg (DR) anions discussed in this review are of fundamental importance. These investigations expand our knowledge base and understanding of electronic structure and electronic dynamics. As science enters the 1990's. the search for new materials, new reaction pathways, and the design of materials with specified physical and chemical properties will require chemists to extend their conceptual understanding of chemical bonding and electronic structure and their relation to macroscopic behavior. It is the belief of the authors that any and all experience in which novel bonding situations or unusual electronic structures are encountered can contribute to the broadening of chemists' conceptual base. The class of anions treated here are unusual because (i) they are local minima on respective ground-state potential energy hypersurfaces where much more stable global minima exist, so rearrangement of the DR species via barrier tunneling is possible, (ii) they are electronically stable only because the motions of the outermost pair of electrons (Le., those that occupy the diffuse Rydberg-like orbitals) involve highly radially and angularly correlated motions (i.e., their electronic structures can not be viewed in the conventional 'electron pair occupying an orbital" picture), (iii) they possess a multitude of excited electronic

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Hugh Taylor

Papers

Walking on potential energy surfaces

Imposition of geometrical constraints on potential energy surface walking procedures

"Double-Rydberg" Molecular Anions

A different view of molecular electronic transitions