The path of chemical reactions - the IRC approach
About: This article is published in Accounts of Chemical Research.The article was published on 1981-12-01. It has received 5052 citations till now. The article focuses on the topics: Path (graph theory).
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TL;DR: A description of the ab initio quantum chemistry package GAMESS, which can be treated with wave functions ranging from the simplest closed‐shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication.
Abstract: A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines. © John Wiley & Sons, Inc.
18,546 citations
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TL;DR: The “Activation‐strain TS interaction” (ATS) model of chemical reactivity is reviewed as a conceptual framework for understanding how activation barriers of various types of reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis.
Abstract: We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn–Sham molecular orbital (MO) theory, and illustrate the power of the Kohn–Sham MO model in conjunction with the ADF-typical fragment approach to quantitatively understand and predict chemical phenomena. We review the “Activation-strain TS interaction” (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time-dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 931–967, 2001
8,490 citations
TL;DR: In this article, a second order algorithm for finding points on a steepest descent path from the transition state of the reactants and products is presented. But 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 the gradient at each point is tangent to the path.
Abstract: 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.
5,487 citations
TL;DR: In this paper, a modified conjugate gradient algorithm for geometry optimization is presented for use with ab initio MO methods, where the second derivative matrix rather than its inverse is updated employing the gradients.
Abstract: 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.
3,373 citations
TL;DR: In this paper, the main emphasis is put on directed transport in so-called Brownian motors (ratchets), i.e. a dissipative dynamics in the presence of thermal noise and some prototypical perturbation that drives the system out of equilibrium without introducing a priori an obvious bias into one or the other direction of motion.
2,098 citations
References
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TL;DR: In this article, the Brester-Wigner theory of small vibrations when the potential energy is invariant under the rotation displacement group is developed, and it is shown that the use of these coordinates implies the use a particular (normal) system of rotating axes whose construction is given.
Abstract: The theory of small vibrations when the potential energy is invariant under the rotation-displacement group is developed. The results are compared with the Brester-Wigner theory of the normal coordinates, and it is shown that the use of these coordinates implies the use of a particular (normal) system of rotating axes whose construction is given. It is shown that when the motion of a normal molecule is referred to these axes, those terms of the Hamiltonian which are linear in the angular momenta will be especially small and of the same order of magnitude as the quadratic terms (Casimir's condition). When the amplitude of one or more of the normal vibrations becomes large, this is no longer true of the normal axes; this will always be the case when one of the normal frequencies is small compared to the others, as has been noted by other writers. The normal axes are not the principal axes of inertia of the instantaneous configuration of the system, and certain conclusions recently published by the author are wrong for that reason.
890 citations
TL;DR: In this article, a method of calculating the intrinsic reaction coordinate starting at a saddle point is proposed, which is used in combination with the analytical evaluation of the energy gradient for the calculation of the reaction coordinate on an ab initio potential energy surface.
Abstract: A practical method of calculating the intrinsic reaction coordinate starting at a saddle point is proposed. The method has been used in combination with the analytical evaluation of the energy gradient for the calculation of the reaction coordinate on an ab initio potential energy surface. The reaction coordinates are obtained for the HNC to HCN isomerization and the SN2 exchange reaction involving H−+CH4→CH4+H−.
748 citations
TL;DR: In this paper, a method for obtaining the secular equation for the vibration frequencies of a molecule directly in expanded form, i.e. as an algebraic rather than a determinantal equation, is described.
Abstract: A method is described for obtaining the secular equation for the vibration frequencies of a molecule directly in expanded form, i.e. as an algebraic rather than a determinantal equation. The force constants occur literally and the masses may occur either literally or numerically, as desired. The symmetry may be employed as usual to factor the secular equation. Several methods of obtaining approximate roots are described for which the expanded form is particularly suitable. Finally, an example, the nonlinear general triatomic molecule, is worked out algebraically.
651 citations
TL;DR: In this article, the authors derived an expression for the vibration-rotation Hamiltonian of a triatomic molecule using a curvilinear bending coordinate and two rectilinear stretching coordinates in such a way that the Hamiltonian obtained is applicable for any linear or bent, and allows for large displacements of the bending coordinate.
538 citations