Semiempirical methods hybrid approaches

Double Hybrid Functionals Incorporation of the unoccupied Kohn-Sham orbitals to create fifth-rung methods has been difficult. The one approach that has seen some application to organic chemistry is the semiempirical double hybrid approach of Grimme. The approach begins with a hybrid (jGA functional of the form... 

Semiempirical methods are the middle ground between highly accurate ab initio methods and completely empirical molecular mechanical (MM) methods [155]. For the treatment of very large biomolecules, hybrid approaches have been developed where the reactive center is described by a semiempirical method and the inert rest of the molecule by a classical force field [3,156,157], This technique can also be applied for the description of solvent effects. The solvent molecules are then described by the MM method. If an even higher accuracy is required for the reactive center of the system, a hybrid approach of three different methods can be applied, e.g., in the ONIOM model by Vreven and Morokuma [158], Here the center is described at DFT or post-HF level, the nearest-neighbor atoms at semiempirical level, and the outer surrounding at MM level. There also exist hybrid schemes between semiempirical and DFT methods only [159],... 

In this chapter, we will first discuss some of the important features of dynamical methods that purport to treat multiple electronic states, that is, beyond the Born-Oppenhe-imer approximation which separates electronic and nuclear motion. Then we will discuss the various possibilities for representing the PESs and their couplings, from ab initio to semiempirical and hybrid quantum mechanical and molecular mechanical methods. In both of these discussions, the emphasis will be on approaches that are suited to simultaneous solution of the dynamics and electronic structime problems. Finally, we illustrate with several example applications. 

A comprehensive discussion of hybrid methods and their application is beyond the scope of this article, and we refer the reader to recent reviews in this field [186, 222-224] and to other methodological papers [225-228] for more detailed information. In the following we focus on the use of semiempirical methods in QM/MM approaches and on some conceptual issues. One typical example for the use of hybrid methods is the study of solvent effects through explicit solvation models (see Section III.C). In this case there is an obvious partitioning between the QM part (solute) and the MM part (solvent) of the system, with well-known QM/MM interactions. The effective Hamiltonian is written as the sum of three terms [186,227] ... 

Hybrid approaches combining ab-initio or DFT and semiempirical approaches have become popular. As an example, we can refer to LEDO (hmited expansion of differential overlap) densities application to the density-functional theory of molecules [262]. This LEDO-DFT method should be well suited to the electronic-structure calculations of large molecules and in the anthors opinion its extension to Bloch states for periodic structures is straightforward. In the next sections we discuss the extension of CNDO and INDO methods to periodic stmctures - models of an infinite crystal and a cyclic cluster. 

The work described in Refs. 5 and 17 indicated that hybrid potentials could describe reaction processes in solution. However, it is only with the work of Gao that the real utility of this approach has become apparent. He and his co-workers have developed a hybrid potential that combines the AMI/MNDO semiempirical method with a force field similar to the OPLS force field of Jorgensen and with it they have studied a very wide range of solution phenomena in combination with Monte Carlo simulation techniques. As Gao has recently published two excellent reviews of hybrid potentials which include discussion of his own work only a few brief details will be given here. 

AMI AMBER A Program for Simulation of Biological and Organic Molecules CHARMM The Energy Function and Its Parameterization Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Divide and Conquer for Semiempirical MO Methods Electrostatic Catalysis Force Fields A General Discussion Force Fields CFF GROMOS Force Field Hybrid Methods Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) Methods Mixed Quantum-Classical Methods MNDO MNDO/d Molecular Dynamics Techniques and Applications to Proteins OPLS Force Fields Parameterization of Semiempirical MO Methods PM3 Protein Force Fields Quantum Mechanical/Molecular Mechanical (QM/MM) Coupled Potentials Quantum Mecha-nics/Molecular Mechanics (QM/MM) SINDOI Parameterization and Application. 

Smooth COSMO solvation model. We have recently extended our smooth COSMO solvation model with analytical gradients [71] to work with semiempirical QM and QM/MM methods within the CHARMM and MNDO programs [72, 73], The method is a considerably more stable implementation of the conventional COSMO method for geometry optimizations, transition state searches and potential energy surfaces [72], The method was applied to study dissociative phosphoryl transfer reactions [40], and native and thio-substituted transphosphorylation reactions [73] and compared with density-functional and hybrid QM/MM calculation results. The smooth COSMO method can be formulated as a linear-scaling Green s function approach [72] and was applied to ascertain the contribution of phosphate-phosphate repulsions in linear and bent-form DNA models based on the crystallographic structure of a full turn of DNA in a nucleosome core particle [74],... 

Another way of performing calculations using the cluster model is the use of a hybrid method. It is a theoretical method, which uses different approaches for different parts of the molecular system. The ONIOM method is one of the hybrid methods developed quite recently to facilitate accurate ab initio calculations of large chemical species. The ONIOM method (n-layered integrated molecular orbital and molecular mechanics approach) [29] is a multi-level extrapolation method, in which the studied molecular system is divided into two or more parts or layers. The most important part of the system from the chemical point of view (the inner part, IP) is treated at a high" level of theory (the HL method - a high level of ab initio molecular orbital method) and the rest of the system is described by a computationally less demanding method (the LL method - the lowest ab initio approximation or even semiempirical or molecular mechanic approximations) [30]. 

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