Potential function parameters

Many times it is convenient to define a coupling parameter, X, that allows the smooth conversion of system 0 to 1. Then for many possible features i of the states, including geometrical and potential function parameters, equation (37) can be used to represent the mutation of state 0 to 1 as A goes from 0 to 1... 

Biochemistry and chemistry takes place mostly in solution or in the presence of large quantities of solvent, as in enzymes. As the necessary super-computing becomes available, molecular dynamics must surely be the method of choice for modeling structure and for interpreting biological interactions. Several attempts have been made to test the capability of molecular dynamics to predict the known water structure in crystalline hydrates. In one of these, three amino acid hydrates were used serine monohydrate, arginine dihydrate and homoproline monohydrate. The first two analyses were by neutron diffraction, and in the latter X-ray analysis was chosen because there were four molecules and four waters in the asymmetric unit. The results were partially successful, but the final comments of the authors were "this may imply that methods used currently to extract potential function parameters are insufficient to allow us to handle the molecular-level subtleties that are found in aqueous solutions" (39). 

Fig. 1. Molecule training set for fitting potential function parameters for the carbonate system. Red atoms are 02, black atoms are C4+, and pink atoms are H+. Bond lengths from C4+ to 02 are given in angstroms. Energies for transformations between the different species are given in kcal/mol.

G. Birnbaum and E. R. Cohen. Determination of molecular multipole moments and potential function parameters of non-polar molecules from far infrared spectra. Molec. Phys., 32 161, 1976. 

The initial description of the model is simple, as shown in Figure 3. The atomic coordinates of any suitable structure can serve as the input trial structure, even including a wrong monomer residue. The polar coordinates are calculated from the trial structure, adjusted and modified as necessary, and then subjected to refinement in accordance with the selected list of variables, limits and constraints. Any set of standard values and nonbonded potential function parameters can be used. Hydrogen bonds can be defined as desired, variables can be coupled, and the positions of solvent molecules can be individually refined. Single and multiple helices are equally easily handled, as are a variety of space groups. 

We can see from Eqs. (3.5) [see also Appendix in Ref. ] that the force constants F , F etc., are generally mass dependent quantities. To arrive at the iso-topically invariant potential function we must therefore express these quantities in terms involving mass independent valence force constants and to fit these to experimental spectra [cf. ]. For ammonia, this would represent a really formidable numerical problem. Taking into account the proposed limits of our model, the fact that we are mainly interested in the inversion—rotation structure of the spectra, we have overcome the above mentioned difficulties in the following way [see for details] (i) all the enharmonic force constants in Eq. (5.5) were neglected (ii) the p-dependent contributions to the harmonic force constants F [see Eq. (4.7)] were neglected (iii) the least squares fit of the double-minimum potential function parameters and the p-independent harmonic force constants were performed for light isotopes ( NHs, NHs) and heavy isotopes ( ND3, NTs) separately. 

In the non-rigid bender approximation, we solved the inverse eigenvalue problem described by Eq. (5.4), i.e. we determined the potential function parameters given in Table 3 for NX3 (X = H, D, T). We have used the experimental infrared frequencies of transitions from the ground state to the i>2,2 2 > 2. and 41 2 inversion states and the zero-order frequencies of vibrations (Table 4). The zero-order frequencies have been obtained from the observed fundamental frequencies of NH3 [Ref. >], ND3 [Ref. °>], NTg [Refs." and [Ref.- 3)] corrected for... 

We could of course attempt to adjust a potential function of ammonia using Eq. (5.4) in a least squares fit to the data extended to a set of energy levels with J = 0,k 0. However, it seems better to adjust a minimum number of potential function parameters using the vibration and inversion data alone and to check the validity of our model by comparing the calculated vibration—inversion—rotation transition frequencies with the observed data ... 

For NH2D and ND2H, only the rigid bender approximation has been used so far in the determination of the double-minimum potential function parameters ... 

Repulsive potential function Parameter in potential function... 

Quantitatively the MC simulations predict a 2.1-kcal/mol barrier between the contact and solvent-separated ion pairs, with the latter about 4 kcal/mol lower in free energy. These results should be considered preliminary on several counts. In particular, greater study of the dependence of the results on the cutoff procedure for the potential functions is desirable. Also, the constancy of the potential function parameters for between 2.5 and 7 A is a questionable approximation. However, some compensation in changes between the ion-ion and ion-water interactions is expected, that is, if the ion-ion interaction has a covalent component, the increased attraction would be somewhat offset by... 

As mentioned above, when a set of potential function parameters is to be used in molecular mechanics calculations on... 

Determines hydrogen-bonding energies Generates an energy vs. rotation angle plot Lists all atomic coordinates Allows modification of Lennard-Jones, nonbonded potential function parameters Lists all low energy conformers Performs multi-dimensional minimization Performs random type scan of conformational hyperspace... 

A STUDY OF POTENTIAL FUNCTION PARAMETERS FOR THE LENNARD-JONES /6-12/ MODEL USING THERMAL CONDUCTIVITY MEASUREMENTS. PH.D. THESIS. 

NAMD [227] is a more recent program which works with AMBER and CHARMM potential functions, parameters, and file formats, and it is specifically designed for high-performance simulatimi of large systems. The current version (2.9) is able to run on heterogeneous architectures made up of multiple CPUs and GPUs. 

IPAR PAR The pari file contains the potential function parameters and variables for the present calculation... 

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