Classical quantum force field

Monard G, M Loos, V Thery, K Baka, and JL Rivail (1996) Hybrid classical quantum force field for modeling very large molecules. Int. J. Quantum Chem. 58 (2) 153-159... 

In practice, the localized orbital is extracted from a model small molecule computed with the same semi-empirical method and incorporated into the QM/MM scheme. This is the basis of the Local Self-Consistent Field [37] which consists in solving the Hartree-Fock equations relative to the quanffim subsystem in which the electronic interactions with the electrons of the localized bond as well as the classical point charges are included. The adaptation of the PM3 semi-empirical scheme [38] to the AMBER force-field [9] and the analytical expression of the energy derivatives and changes of coordinates led to the so-called classical-quantum force-field (CQFF) [39]. In this force-field, the first atom belonging to the classical part and linked to the quanffim part by means of the... 

CQFF = classical quantum force field CTC = charge transfer complex LSCF = local self-consistent field SLO = strictly localized orbitals. 

Therefore the energy derivatives can be computed analytically and a full classical quantum force field (CQFF) is defined. It can be used like the purely classical force fields but does not require the existence of well defined bonds in the quantum subsystem and can be used to study reactive processes. 

Figure 10 Transition state obtained by the combined classical quantum force field in a study of a peptide hydrolysis reaction catalyzed by theimolysin...

As an example of application to a reaction involving a macromolecule, we indicate below the transition state obtained by the combined classical quantum force field in a study of the peptide hydrolysis reaction catalyzed by thermolysin. The subsystem is limited to the substrate, a water molecule, a zinc atom, the side chains of His 143, Glul66, the whole glutamic acid and the histidine 146 moieties (see Figure 10). The transition state represented here corresponds to the proton transfer from Glul43 to the nitrogen atom of the peptidic bond before the breaking of the bond. 

Hybrid Classical Quantum Force Field for Modeling Very Large Molecules. 

Finally, it must be remembered that DFT and AIMD can be incorporated into the so-called mixed quantum mechanical/molec-ular mechanical (QM/MM) hybrid schemes [12, 13]. In such methods, only the immediate reactive region of the system under investigation is treated by the quantum mechanical approach -the effects of the surroundings are taken into account by means of a classical mechanical force field description. These DFT/MM calculations enable realistic description of atomic processes (e.g. chemical reactions) that occur in complex heterogeneous envir-... 

The exponential increase in computer power and the development of highly efficient algorithms has distinctly expanded the range of structures that can be treated on a first-principle level. Using parallel computers, AIMD simulations of systems with few hundred atoms can be performed nowadays. This range already starts to approach the one relevant in biochemistry. Indeed, some simulations of entire biomolecules in laboratory-realizable conditions (such as crystals or aqueous solutions) have been performed recently [25-28]. For most applications however, the systems are still too large to be treated fully at the AIMD level. By combining AIMD simulations with a classical MD force field in a mixed quantum mechanical/molecular mechanical fashion (Hybrid-AIMD) the effects of the protein environment can be explicitly taken into account and the system size can be extended. 

Molecular geometries may be calculated by means of quantum-chemical semi-empirical valence electron theories, such as Dewar s MINDO/3 , MNDO " or AMl procedures, or by classical molecular force-field methods, such as Allinger s MM2 procedure. Alternatively, inirio Hartree-Fock SCF MO methods allow, by virtue of analytical gradient evaluations , the determination of molecular geometries independent of experimentally adjusted integral values. 

In the case of intersubsystem junction represented by classical bonding terms an important question arises which terms should be included and which should not The most popular way is to include classical bonded force fields when at least one MM atom is involved in it [33,34]. At the same time it does not allow to avoid double counting of interactions computed quantum mechanically. To smooth this inconsistence the authors of Ref. [124] proposed to calculate only those classical bonding force fields where at least one central atom is from the MM subsystem or in the case of improper dihedral terms only those with both outer atoms from the MM subsystem. 

Fig. 7 ID-Free energy profile of the dihydroxylated compound IV as a single function of P from classical (GAFF force field) and quantum simulations (CPMD) in A vacuum, B explicit water.

Macromolecules are very diverse in composition and function and they occur in many fields of chemistry and biochemistry. The usual applications of synthetic polymers mainly deal with their physical properties molecular weight, conformations, van des Waals interactions... which don t require detailed knowledge of the electronic structure and can be approached by classical computational force fields which are at the basis of what one usually calls molecular mechanics. Nevertheless, one may be interested in the chemical reactivity of some region of the polymer, such as structural defects, and a quantum computation may be the only way to get the reliable chemical information. The other, very important class of macromolecules contains the innumerable biomacromolecules polypeptides, enzymes, nucleic acids. The understanding of their role in life usually requires the knowledge of the electronic structure and often the reactivity of at least well defined parts of the large system they constitute. This knowledge can only be reached by means of quantum chemical computations. 

A 7ab = Ua U-q, all of which can be evaluated using quantum-chemical methods, classical polarizable force-fields, or quantum-classical hybrids as discussed in the following sections. Various generalizations of this expression to quantum-mechanical modes have been derived [81-84]. 

Available methods are based on either classical mechanics (force field methods) or quantum mechanics. Force fields are important in the context of quantum mechanics/molecular mechanics (QM/MM) procedures and hence were described in detail in Chapter 10. A short mention will be made here in the paragraph on... 

Aqvist, J., Warshel, A. Simulation of enzyme reactions using valence bond force fields and other hybrid quantum/classical approaches. Chem. Rev. 93... 

Aqvist J and A Warshel 1993. Simulation of Enzyme Reactions Using Valence Bond Force Fields a Other Hybrid Quantum/Classical Approaches. Chemical Reviews 93 2523-2544. 

The force constants in the equations are adjusted empirically to repro duce experimental observations. The net result is a model which relates the "mechanical" forces within a stmcture to its properties. Force fields are made up of sets of equations each of which represents an element of the decomposition of the total energy of a system (not a quantum mechanical energy, but a classical mechanical one). The sum of the components is called the force field energy, or steric energy, which also routinely includes the electrostatic energy components. Typically, the steric energy is expressed as... 

Figure 1 Schematic diagram depicting the partitioning of an enzymatic system into quantum and classical regions. The side chains of a tyrosine and valine are treated quantum mechanically, whereas the remainder of the enzyme and added solvent are treated with a classical force field.

Finally, the parametrization of the van der Waals part of the QM-MM interaction must be considered. This applies to all QM-MM implementations irrespective of the quantum method being employed. From Eq. (9) it can be seen that each quantum atom needs to have two Lennard-Jones parameters associated with it in order to have a van der Walls interaction with classical atoms. Generally, there are two approaches to this problem. The first is to derive a set of parameters, e, and G, for each common atom type and then to use this standard set for any study that requires a QM-MM study. This is the most common aproach, and the derived Lennard-Jones parameters for the quantum atoms are simply the parameters found in the MM force field for the analogous atom types. For example, a study that employed a QM-MM method implemented in the program CHARMM [48] would use the appropriate Lennard-Jones parameters of the CHARMM force field [52] for the atoms in the quantum region. 

Figure 2 A glutamate side chain partitioned into quantum and classical regions. The terminal CH2C02 group IS treated quantum mechanically, and the backbone atoms are treated with the molecular mechanics force field.

A classical description of M can for example be a standard force field with (partial) atomic charges, while a quantum description involves calculation of the electronic wave function. The latter may be either a semi-empirical model, such as AMI or PM3, or any of the ab initio methods, i.e. HF, MCSCF, CISD, MP2 etc. Although the electrostatic potential can be derived directly from the electronic wave function, it is usually fitted to a set of atomic charges or multipoles, as discussed in Section 9.2, which then are used in the actual solvent model. 

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