Approximate Methods Hybrid Force Fields

The frequencies of the fundamental transitions within the the VPT2 approach can be written as 

Avj (K, co) is the so called anharmonic shift of the fundamental frequency of mode k, the computationally most demanding part of the calculations, requiring the evaluation of the numerical third and fourth derivatives of the PES and the treatment of the Fermi resonances. The anharmonic shifts can be seen as corrections with respect to the harmonic frequencies, in most cases not exceeding 5%, but are very important when vibrational frequencies need to be computed with a high accuracy, or even for a qualitative analysis for example, for a C-H stretching mode typically at about 3000 cm , an anharmonic correction 

Regardingthe intensities, the transition dipole moment for a generic fundamental transition (Eq. 10.27) can be split into a doubly harmonic term (i.e., depending only on and co) and an anharmonic shift (depending also on and K), 

Using this definition of the transition dipole moments, for IR spectra, the Djp can be written as 

3) In addition, when resonance-free schemes such as the DCPT2 and the HDCPT2 are employed and the identification of the resonances is not a required step, the set of co is still necessary for the evaluation of the anharmonic matrix. 

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In recent years, there have been many attempts to combine the best of both worlds. Continuum solvent models (reaction field and variations thereof) are very popular now in quantum chemistry but they do not solve all problems, since the environment is treated in a static mean-field approximation. The Car-Parrinello method has found its way into chemistry and it is probably the most rigorous of the methods presently feasible. However, its computational cost allows only the study of systems of a few dozen atoms for periods of a few dozen picoseconds. Semiempirical cluster calculations on chromophores in solvent structures obtained from classical Monte Carlo calculations are discussed in the contribution of Coutinho and Canuto in this volume. In the present article, we describe our attempts with so-called hybrid or quantum-mechanical/molecular-mechanical (QM/MM) methods. These concentrate on the part of the system which is of primary interest (the reactants or the electronically excited solute, say) and treat it by semiempirical quantum chemistry. The rest of the system (solvent, surface, outer part of enzyme) is described by a classical force field. With this, we hope to incorporate the essential influence of the in itself uninteresting environment on the dynamics of the primary system. The approach lacks the rigour of the Car-Parrinello scheme but it allows us to surround a primary system of up to a few dozen atoms by an environment of several ten thousand atoms and run the whole system for several hundred thousand time steps which is equivalent to several hundred picoseconds. 

Where quantum chemical methods have been used to study problems in medicinal chemistry and drug design, it has usually been combined with a continuum approximation [90,107-112], rather than explicit simulation, for the solvent effect. As noted, molecular simulations with an explicit solvent are traditionally performed using classical force fields. The reason for this is obvious quantum mechanical calculations are too time consuming. The coupling of QM with continuum approximations has therefore become convenient. However, the so-called hybrid quantum mechanical and... 

Harvey et al. proposed a hybrid method for calculating the effective gradients (Eqs. [98] and [99]) by approximating the difference gradients at lower level of theory from the evaluation of the energy term. For the approximation to work, the force fields of the two states calculated at a higher level of theory must be equal to those calculated at a lower level of theory. In cases that Harvey et al. have examined, they have shown that the approximation is reliable. 

Direct dynamics calculations of the type just described, with all degrees of freedom included, are very expensive if the local quadratic approximations to the potential energy surface are obtained from an ab initio computation. In applications we have used a hybrid parameterized quantum-mechanical/force-field method, designed to simulate the CASSCF potential for ground and covalent excited states. A force field is used to describe the inert molecular a-framework, and a parameterized Heisenberg Hamiltonian is used to represent the CASSCF active orbitals in a valence bond space. Applications include azulene and benzene excited state decay dynamics. 

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