Molecular crystals computations

Solids can be crystalline, molecular crystals, or amorphous. Molecular crystals are ordered solids with individual molecules still identihable in the crystal. There is some disparity in chemical research. This is because experimental molecular geometries most often come from the X-ray dilfraction of crystalline compounds, whereas the most well-developed computational techniques are for modeling gas-phase compounds. Meanwhile, the information many chemists are most worried about is the solution-phase behavior of a compound. 

In 1985 Car and Parrinello invented a method [111-113] in which molecular dynamics (MD) methods are combined with first-principles computations such that the interatomic forces due to the electronic degrees of freedom are computed by density functional theory [114-116] and the statistical properties by the MD method. This method and related ab initio simulations have been successfully applied to carbon [117], silicon [118-120], copper [121], surface reconstruction [122-128], atomic clusters [129-133], molecular crystals [134], the epitaxial growth of metals [135-140], and many other systems for a review see Ref. 113. 

Due to their demanding synthesis, diamondoids are helpful models to study structure-activity relationships in carbocations and radicals, to develop empirical computational methods for hydrocarbons, and to investigate orientational disorders in molecular crystals as well [5,32]. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

However, It has been found that in many cases, simple models of the properties of atomic aggregates (monocrystals, poly crystals, and glasses) can account quantitatively for hardnesses. These models need not contain disposable parameters, but they must be tailored to take into account particular types of chemical bonding. That is, metals differ from covalent crystals which differ from ionic crystals which differ from molecular crystals, including polymers. Elaborate numerical computations are not necessary. 

Investigations of the conformational properties of the flavan-3-ols and oligomeric proanthocyanidins have hitherto involved a variety of molecular mechanics and molecular orbital computations in combination with crystal structures, time-resolved fluorescence, as well as and NMR methods. Representative references to all these techniques may be found in the papers listed in Refs. 241-247, 250. These NMR papers incidentally also represent the major contributions regarding the conformation of proanthocyanidins, and may be summarized in a conformational context by reference to the significant contributions of Hatano and Hemingway. 

These are invariant to translation and rotation of a stereomodel. Most experimental chemists are familiar with internal coordinates from crystal structure analyses and the employment of molecular modelling computer programs. With regard to fundamental concepts of stereochemistry, internal coordinates are of prime importance as they allow clear definitions of terms to be formulated. ... 

Currently the problems involved in calculating the electronic band structures of molecular crystals and other crystalline solids centre around the various ways of solving the Schrodinger equation so as to yield acceptable one-electron solutions for a many-body situation. Fundamentally, one is faced with an appropriate choice of potential and of coping with exchange interactions and electron correlation. The various computational approaches and the many approximations and assumptions that necessarily have to be made are described in detail in the references cited earlier. 

The first computational consideration is that of obtaining the solutions of the unperturbed problem, Eq. (15), and the approach taken in the present study is to utilize the Crystal program [1] as it has been successfully used for studies in molecular crystals [10-12,15], A given crystalline orbital, (k,r), such as that required for the matrix elements necessary given by the integral in Eq. (16), is expressed as a linear combination of Bloch functions, a ,(k) and atomic orbitals, (k,r) [1]... 

The crystal and molecular structure of l,3-dimethyl-8-azaxanthine monohydrate has been determined by X-ray diffraction. The compound exists as the N-8-H tautomer in the solid state, and hydrogen-bonded dimers are formed. Molecular orbital computations have been performed for this... 

The first discovered solid phase of fullerenes C6o represents typical molecular crystal. Later it was established that high pressure applied to solid C6o at high temperature induces polymerization of C6o [1-2]. Using the computer modeling methods allows confirming the existence of at least three different planar polymerized structures of fullerene Cgo with coordination numbers 2, 4, 6, and besides the values 4 and 6 are more probable ones. 

Fujii et al.30 have reported experimental evidence for the molecular dissociation process in Br2 near 80 GPa. This transition, which is coincident with the onset of pressure-induced metallization, was first discovered in molecular/metallic iodine.3 A diatomic molecular crystal loses its molecular character in the limit when the intermolecular distance becomes equal to the intramolecular bond length. Fujii et al.30 applied the Herzfeld criterion to I2 and Br2 and estimated that the molar reffactivity reaches the atomic limit around 20 GPa in I2 and 80 GPa in B12. In both cases, the computed pressure coincides with that for molecular dissociation accompanied by metallization. 

Clydesdale, G., Roberts, K. J. and Docherty, R. (1994fl). Computational studies of the morphology of molecular crystals through solid-state intermolecular force... 

Gdanitz, R. J. (1997). Ab initio prediction of possible molecular crystal stmctures. In Theoretical aspects and computer modeling of the molecular solid state (ed. A. Gavezzotti), pp. 185-99. Wiley, Chichester. [182]... 

Legrand, J. R, Lajzerowicz, J., Lajzerowicz-Bonneteau, J. and Capiomont, A. (1982). Ferroelastic and ferroelectric phase transition in a molecular crystal tanane. 3.-From ab initio computation of the intermolecular forces to statistical mechanics of the transition. J. Phys., 43, 1117-25. [202]... 

Willcock, J. D., Price, S. L., Leslie, M. and Catlow, C. R. A. (1995). The relaxation of molecular crystal structures using a distributed multipole electrostatic model. J. Comput. Chem., 16, 628. [183]... 

The Raman spectra of solids have a more or less prominent collision-induced component. Rare-gas solids held together by van der Waals interactions have well-studied CILS spectra [656, 657]. The face-centered, cubic lattice can be grown as single crystals. Werthamer and associates [661-663] have computed the light scattering properties of rare-gas crystals on the basis of the DID model. Helium as a quantum solid has received special attention [654-658] but other rare-gas solids have also been investigated [640]. Molecular dynamics computations have been reported for rare-gas solids [625, 630, 634]. 

Distance geometry provides sets of 3-D structures of a protein or nucleic acid that fulfill the constraints. The combination of distance geometry, for generation of molecular starting points, with molecular dynamics computations can yield 3-D models of small proteins with precision equal to X-ray crystallography. This combination of NMR, molecular mechanics, and molecular dynamics can be used to provide a three-dimensional protein structure in a situation where the protein cannot be crystallized or the crystals are not appropriate for X-ray crystallography. 

Clydesdale, G. Docherty, R. Roberts, K.J. HABIT-a program for predicting the morphology of molecular crystals. 161. Comput. Phys.Commun. 1991, 64, 311-328. 

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