Orientation-dependent potential

One of the simplest orientational-dependent potentials that has been used for polar molecules is the Stockmayer potential.48 It consists of a spherically symmetric Lennard-Jones potential plus a term representing the interaction between two point dipoles. This latter term contains the orientational dependence. Carbon monoxide and nitrogen both have permanent quadrupole moments. Therefore, an obvious generalization of Stockmayer potential is a Lennard-Jones potential plus terms involving quadrupole-quadrupole, dipole-dipole interactions. That is, the orientational part of the potential is derived from a multipole expansion of the electrostatic interaction between the charge distributions on two different molecules and only permanent (not induced) multipoles are considered. Further, the expansion is truncated at the quadrupole-quadrupole term. In all of the simulations discussed here, we have used potentials of this type. The components of the intermolecular potentials we considered are given by ... 

In the study of structural properties of fluids of particles interacting through orientation-dependent potentials, it is convenient to decompose the full pair-correlation function A(l,2) = h ri2,Qi, Q2) ... 

If now a magnetic field H is applied to a suspension of spherical particles of diameter d, the orientation-dependent potential energy Wh of a particle in this field is expressed as... 

Recently a more detailed, orientation-dependent PMF - the potential that depends on the relative orientation of the two amino acid chains (see Figure 15.6) - has been proposed. This potential between any two amino acid residues was derived from the statistical analysis of the experimental native structures deposited in the Protein Data Bank (PDB). In this model potential amino acid side-chains are represented by a single ellipsoidal of revolution. The PMF between two ellipsoidals of revolution was obtained by considering all the interacting sites in them. The site-site potentials were then calculated from the statistics of their distance of separation obtained from the crystal structures available in the PDB [11]. These site-site potentials were then summed up to obtain the distance and orientation-dependent potential between all amino acid residues. The PMFs so obtained show many interesting features. Two of the PMFs are shown in Figure 15.7. 

A. Mukherjee, P. Bhimalapuram, and B. Bagchi, Orientation-dependent potential of mean force for protein folding. J. Chem. Phys., 123 (2005), 014901. 

An alternative description of a molecular solvent in contact with a solute of arbitrary shape is provided by the 3D generalization of the RfSM theory (3D-RISM) which yields the 3D correlation functions of interaction sites of solvent molecules near the solute. It was first proposed in a general form by Chandler, McCoy, and Singer [22] and recently developed by several authors for various systems by Cortis, Rossky, and Friesner [23] for a one-component dipolar molecular liquid, by Beglov and Roux [24, 25] for water and a number of organic molecules in water, and by Hirata and co-workers for water [26, 27], metal-water [26, 28] and metal oxide-water [31] interfaces, orientationally dependent potentials of mean force between molecular ions in a polar molecular solvent [29], ion pairs in aqueous electrolyte [30], and hydration of hydrophobic and hydrophilic solutes alkanes [32], polar molecule of carbon monoxide [33], simple ions [34], protein [35], amino acids and polypeptides [36, 37]. It should be noted that accurate calculation of the solvation thermodynamics for ionic and polar solutes in a polar molecular liquid requires special corrections to the 3D-RISM equations to eliminate the electrostatic artifacts of the supercell treatment employed in the 3D-RISM approach [30, 34]. 

The chain relaxation time controls transient distribution of the chain end-to-end vectors in the system and the transient orientation distribution of chain segments. Time-dependent deformation rate and the chain relaxation introduce time- and orientation-dependent potential of cluster formation and the nucleation rate. The transient orientation-dependent potential of nucleation controls the orientation distribution of the critical cluster energy and the critical cluster size. 

Generate a set of k orientations 0 = oi, 02, , ot about the new center of mass for the forward move. Calculate the orientation dependent potential energy C/"(/) for each orientation in O. Note that henceforth, superscripts F and R will be used to denote corresponding quantities for the forward and reverse moves respectively. Evaluate the so-called Rosenbluth weight for the new position as follows... 

The first description of the nematic state was developed by Maier and Saupe. They considered the molecules as simple rigid rods with no internal degrees of freedom. In the nematic state the rods are aligned on average parallel to the nematic director. The orientation-dependent potential energy of one molecule in the field of its neighbors is taken in... 

In analyzing dielectric relaxation spectra in condensed matter, two different concepts of molecular dynamics are of great significance. The first, which is predominantly applicable to liquids, is to consider the liquid as a dense gas with very frequent collisions, the rate of which is so high that the reorientation of a molecule is completely controlled by the rate. Thus, in this case the rotational dynamics becomes similar to the Brownian translational diffusion and it is known as rotational diffusion. The second approach, which is more frequently used to describe dynamics in molecular crystals and intramolecular dynamics, emphasizes reorientation of a molecule in the presence of an orientation-dependent potential with well-defined minima. In this case, the molecule resides for finite time intervals in different potential wells, jumping between them from time to time. Since the time of jump is very short in comparison with the time of residence in the well, the concept is known as reorientation by instantaneous jumps. On infinite increase of the number of potential wells and the corresponding decrease of the angular distance between them, this approach reduces to rotational diffusion. ... 

Equations 10 and 11 indicate that the redox potential of the HQ/BQ couple is shifted in the negative direction when ti6-chemisorbed but shifted in the positive direction when 2,3-ti2-bonded. This orientation-dependent shift in redox potential is not unexpected by analogy with molecular organometallic compounds. For example, the redox potential for the reversible, one-electron reduction of duroquinone in acetonitrile is shifted from -0.90 V (vs. SCE) to -0.69 V in bis (duroquinone) Ni (0) and to -1.45 V in (1,5 — cyclooctadiene) (duroquinone)Ni (0) (22.) ... 

Rotationally mediated trapping is important. The coupling between rotational and kinetic energy arises from the orientational dependence of the attractive portion of the potential. 

One source of information on intermolecular potentials is gas phase virial coefficient and viscosity data. The usual procedure is to postulate some two-body potential involving 2 or 3 parameters and then to determine these parameters by fitting the experimental data. Unfortunately, this data for carbon monoxide and nitrogen can be adequately represented by spherically symmetric potentials such as the Lennard-Jones (6-12) potential.48 That is, this data is not very sensitive to the orientational-dependent forces between two carbon monoxide or nitrogen molecules. These forces actually exist, however, and are responsible for the behavior of the correlation functions and - In the gas phase, where orientational forces are relatively unimportant, these functions resemble those in Figure 6. On the other hand, in the liquid these functions behave quite differently and resemble those in Figures 7 and 8. 

The intermolecular potential consists of the sum of Eqs.(176) and (177). This simulation was done for 216 and 512 molecules. However, only the autocorrelation functions from the 512 molecules case are discussed here. The small dipole moment of carbon monoxide makes the orientational part of this potential so weak that molecules rotate essentially freely, despite the fact that this calculation was done at a liquid density. The results for the Stockmayer simulation serve the purpose of providing a framework for contrasting results from more realistic, stronger angular-dependent potentials. 

U(0) is the orientation dependent local potential energy and U (6) accounts for any anisotropy due to the local environment. For instance, if the sample were liquid crystalline, U (O) and U (rc) would represent the potential well associated with nematic or smectic director. In addition to local potentials it is clear that f(0) depends on the experimentally controllable quantities p, E, and T. The solution to equation 16 is the series expansion referred to as the third-order Langevin function L,3(p)... 

Nitric oxide exhibits a negative temperature coefficient for vibrational relaxation in self-collisions, below about 700° K. It has been suggested170 that this effect arises because the potential energy of the point of resonance, postulated by Nikitin, is strongly orientation dependent. (In this case the maximum depth of the potential minimum can be no greater than about 3 kcal. mole-1 which will not steepen the potential sufficiently to account for the observed relaxation rate, with l = 0.18 A.)... 

Consider a number n of stiff polymer components (here stiff is used to mean semiflexible ) and define orientation-dependent ideal and interacting response (n x n) matrices X0(Q, u, u ) and X(Q, u, u ) respectively. In this case, orientational correlations have to be included in addition to the usual isotropic ones. Doi et al. [36-38] have developed the theory for solutions of stiff homopolymers. Their formalism is applied in Appendices C and D to multicomponent blend mixtures of stiff polymers without and with the incompressibility condition respectively. The interaction potentials comprise anisotropic (also called nematic) contributions as well as the usual isotropic ones ... 

Kortemme T, Morozov AV, Baker D (2003) An orientation-dependent hydrogen bonding potential improves prediction of specificity and structure for proteins and protein-protein complexes, J Mol... 

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