Analytic energy derivatives

One way around the slow convergence of single-center expansions is a multi-center multipole expansion [225-229], Several workers have explored the utility ofDME within the SCRF framework [112, 164, 171], Of course, when the multipoles do not reside at atomic positions, it is clear that calculation of such quantities as analytic energy derivatives will become more difficult. 

R. J. Bartlett and J. Noga, The expectation value coupled-cluster method and analytical energy derivatives. Chem. Phys. Lett. 150, 29-36 (1988). 

With the development of analytical energy derivative methods135 l67, the calculation of vibrational frequencies (second derivatives of the energy with regard to atomic coordinates) and infrared absorption intensities (derivatives of the energy with regard to components of electronic field and atomic coordinates, i.e. dipole moment derivatives) both at the HF and correlation corrected levels has become routine168. There are six (two a " + four e)... 

V. Dillet, D. Rinaldi, J. Bertran, and J. L. Rivail, Analytical energy derivatives for a realistic continuum model of solvation application to the analysis of solvent effects on reaction paths, J. Chem. Phys., 104 (1996) 9437. 

Salter EA, Trucks GW, Bartlett RJ (1989) Analytic energy derivatives in many-body methods. I. First derivatives. J Chem Phys 90 1752-1766... 

E. A. Salter, G. W. Trucks, and R. J. Bartlett,/. Chem. Phys., 90, 1752 (1989). Analytic Energy Derivatives in Many-Body Methods. I. First Derivatives. 

J. F. Stanton and J. Gauss,/. Chem. Phys., 101,8938 (1994). Analytic Energy Derivatives fot Ionized States Described hy the Equation-of-Motion Coupled-Cluster Method. 

M. Waldman and B. B. Masek, /. Comput. Chem., 10, 856 (1989). Analytical Energy Derivatives and Normal Modes in Force Fields Employing Lone-Pair Pseudoatoms. 

Since the late 1970s, significant attention has been devoted to the evaluation of analytical energy derivatives (gradients and hessians) with respect to atomic... 

Analytic energy derivatives are as important as the energies themselves. One needs first derivatives for geometry optimizations, reaction path following, dynamics simulations, and (if analytic second derivatives are not available) second derivatives via finite differencing. Second derivatives are necessary for the computation of vibrational frequencies and, subsequently, thermodynamic properties via the appropriate partition functions. 

One of the most significant advances made in applied quantum chemistry in the past 20 years is the development of computationally workable schemes based on the analytical energy derivatives able to determine stationary points, transition states, high-order saddle points, and conical intersections on multidimensional PES. The determination of equilibrium geometries, transition states, and reaction paths on ground-state potentials has become almost a routine at many levels of calculation (SCF, MP2, DFT, MC-SCF, CCSD, Cl) for molecular systems of chemical interest. 

Analytic gradient methods became widely used as a result of their implementation for closed-shell self-consistent field (SCF) wavefunctions by Pulay, who has reviewed the development of this topic. Since then, these methods have been extended to deal with all types of SCF wavefunctions, - as well as multi-configuration SCF (MC-SCF), - " configuration-interaction (Cl) wavefunctions, and various non-variational methods such as MoUer-Plesset (MP) perturbation theory - - and coupled-cluster (CC) techniques. - In short, it is possible to obtain analytic energy derivatives for virtually all the standard ab initio approaches. The main use of analytic gradient methods is, and will remain, the location of stationary points on a potential energy siuface, to obtain equilibrium and transition-state geometries. However, there is a specialized use in the calculation of quantities such as dipole derivatives. 

It is important to note that analytic energy derivatives are the key to molecular structure optimizations and also to the calculation of molecular properties. While the latter issue will be discussed in chapter 15, the former is considered in this section. The major advantage of basis-set-expansion methods is that any kind of derivative can be taken analytically. In fully numerical methods — such as those discussed in the preceding chapter — any kind of gradient would have to be evaluated numerically by separate single-point calculations for given distorted values of the variable under consideration. 

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