# Van der Waals energy calculations

The results of the calculations for the three systems were averaged and are displayed in Fig. 2. For unbound cAPK as well for cAPK complexed with ATP or PKI, the total conformational free energies increase monotonically in the sequence closed - intermediate - open . Binding is an interplay of opposing effects of unfavourable Poisson free energy of hydration that favors the solvation of buried protein groups, and the favourable van der Waals energy and coulombic energy that favour association of both domains. [c.70]

At best, van der Waals interactions are weak and individually contribute 0.4 to 4.0 kj/mol of stabilization energy. ITowever, the sum of many such interactions within a macromolecule or between macromolecules can be substantial. For example, model studies of heats of sublimation show that each methylene group in a crystalline hydrocarbon accounts for 8 k[, and each C—IT group in a benzene crystal contributes 7 k[ of van der Waals energy per mole. Calculations indicate that the attractive van der Waals energy between the enzyme lysozyme and a sugar substrate that it binds is about 60 k[/mol. [c.15]

For each atom type there are two parameters to be determined, the van der Waals radius and the atom softness, Rq and, It should be noted that since the van der Waals energy is calculated between pairs of atoms, but parameterized against experimental data, the derived parameters represent an effective pair potential, which at least partly includes many-body contributions. [c.22]

The van der Waals energy is the interaction between the electron clouds surrounding the nuclei. In the above treatment the atoms are assumed to be spherical. There are two instances where this may not be a good approximation. The first is when one (or both) of the atoms is hydrogen. Hydrogen has only one electron, which is always involved in bonding to the neighbouring atom. For this reason the electron distribution around the hydrogen nucleus is not spherical, rather the electron distribution is displaced towards the other atom. One way of modelling this anisotropy is to displace the position which is used in calculating vdw inwards along the bond. MM2 and MM3 use this approach with a scale factor of 0.92, i.e. the distance which enter vdw is calculated between points located 0.92 times the X-H bond distance, as shown in Figure 2.11. [c.22]

The function of thermodynamics is to provide phenomenological relationships whose validity has the authority of the laws of thermodynamics themselves. One may proceed further, however, if specific models or additional assumptions are made. For example, the use of the van der Waals equation of state allows an analysis of how P - p in Eq. III-40 should vary across the interface Tolman [36,37] made an early calculation of this type. There has been a high degree of development of statistical thermodynamics in this field (see Ref. 47 and the General References and also Sections XV-4 and XVI-3). A great advantage of this approach is that one may derive thermodynamic properties from knowledge of the intermolecular forces in the fluid. Many physical systems can be approximated with model interaction potential energies a widely used system comprises attractive hard spheres where rigid spheres of diameter b interact with an attractive potential energy, att( )- [c.61]

Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances [c.240]

Face-centered cubic crystals of rare gases are a useful model system due to the simplicity of their interactions. Lattice sites are occupied by atoms interacting via a simple van der Waals potential with no orientation effects. The principal problem is to calculate the net energy of interaction across a plane, such as the one indicated by the dotted line in Fig. VII-4. In other words, as was the case with diamond, the surface energy at 0 K is essentially the excess potential energy of the molecules near the surface. [c.264]

The starting point of an MD simulation is an initial set of coordinates, which may originate from X-ray crystallographic or NMR investigations. To remove bad contacts and initial strain (usually van der Waals overlap of non-bonded atoms), whidi may disturb the subsequent MD simulation, the structure is normally geometry-optimized using the same potential energy function. After assigning velocities v, which typically represent a low-temperature Maxwell distribution, the simulation is started by calculating the acceleration for every atom i according to Newton s law ai, written as in Eq. (33). [c.361]

The computer time required for a molecular dynamics simulation grows with the square of the number of atoms in the system, because of the non-bonded interactions defined in the potential energy function (Eq. (32)). They absolutely dominate the time necessary for performing a single energy evaluation and therefore the whole simulation. The easiest way to speed up calculations is to reduce the number of non-bonded interactions by the introduction of so-called cutoffs. They can be ap-phed to the van der Waals and electrostatic interactions by simply defining a maximum distance at which two atoms are allowed to interact through space. If the distance is greater than this, the atom pair is not considered when calculating the non-bonded interactions. Several cutoff schemes have been introduced, from a simple sphere to switched or shifted cutoffs, which all aim to reduce the distortions in the transition region that are possibly destabilizing the simulation. [c.362]

DFT calculations offer a good compromise between speed and accuracy. They are well suited for problem molecules such as transition metal complexes. This feature has revolutionized computational inorganic chemistry. DFT often underestimates activation energies and many functionals reproduce hydrogen bonds poorly. Weak van der Waals interactions (dispersion) are not reproduced by DFT a weakness that is shared with current semi-empirical MO techniques. [c.390]

A nonlinear relationship has been found between the lipophilicity of esters of norethindrone and levonorgestrel (177). The lipophilicity is expressed in terms of high performance Hquid chromatography (hplc) retention times. It has been proposed that the rate of release and dissolution of the esters, as well as partitioning through biological membranes, not in vivo ester hydrolysis, are the rate-determining steps in obtaining biologically active dmg. A pilot study has attempted to find a relationship between the calculated lipophilicity and steric effects of a 13P-substituent and progestational potency. The activity of the 13P-ethyl and 13P-acetyl pregnanes have been measured by the subcutaneous Clauberg assay (178). Binding energies of progesterone analogues, calculated from thek binding affinities for the rabbit uterine progesterone receptor, have been used to draw conclusions about receptor—ligand interactions. Binding is attributed to hydrogen bonds involving the C-3 and C-20 carbonyls, and van der Waals interactions at C-2, C-4, C-7, C-9, C-12, C-18, and C-19. A greater distance between the ligand and the receptor occurs at C-6, C-11, C-14, C-15, C-16, and C-21. An extensive discussion of stmcture and binding affinity correlations has been presented (179). A successful QSAR has been obtained for affinity to the progesterone receptor for 55 progesterone derivatives using the minimal steric, ie, topological, method (180). [c.220]

Van der Waals or Lennard-Jones contributions to empirical force fields are generally considered to be of less importance than the electrostatic term in contributing to the nonbond interactions in biological molecules. This view, however, is not totally warranted. Studies have shown significant contributions from the VDW term to heats of vaporization of polar-neutral compounds, including over 50% of the mean interaction energies in liquid NMA [67], as well as in crystals of nucleic acid bases, where the VDW energy contributed between 52% and 65% of the mean interaction energies [18]. Furthermore, recent studies on alkanes have shown that VDW parameters have a significant impact on their calculated free energies of solvation [29,63]. Thus, proper optimization of VDW parameters is essential to the quality of a force field for condensed phase simulations of biomolecules. [c.20]

A molecular dynamics force field is a convenient compilation of these data (see Chapter 2). The data may be used in a much simplified fonn (e.g., in the case of metric matrix distance geometry, all data are converted into lower and upper bounds on interatomic distances, which all have the same weight). Similar to the use of energy parameters in X-ray crystallography, the parameters need not reflect the dynamic behavior of the molecule. The force constants are chosen to avoid distortions of the molecule when experimental restraints are applied. Thus, the force constants on bond angle and planarity are a factor of 10-100 higher than in standard molecular dynamics force fields. Likewise, a detailed description of electrostatic and van der Waals interactions is not necessary and may not even be beneficial in calculating NMR strucmres. [c.257]

For all except the very simplest systems the potential energy is a complicated, multidimensional function of the coordinates. For example, the energy of a conformation of ethane is a function of the 18 internal coordinates or 24 Cartesian coordinates that are required to completely specify the structure. As we discussed in Section 1.3, the way in which the energy varies with the coordinates is usually referred to as the potential energy burface (sometimes called the hypersurface). In the interests of brevity all references to energy should be taken to mean potential energy for the rest of this chapter, except where explicitly stated otherwise. For a system with N atoms the energy is thus a function of 3N — 6 internal or 3N Cartesian coordinates. It is therefore impossible to visualise the entire energy surface except for some simple cases where the energy is a function of just orie or two coordinates. For example, the van der Waals energy of two argon atoms (as might be modelled using the Lennard-Jones potential function) depends upon just one coordinate the interatomic distance. Sometimes we may wish to visualise just a part of the energy surface. For example, suppose we take an extended conformation of pentane and rotate the two central carbon-carbon bonds so that the torsion angles vary from 0 to 360 , calculating the energy of each structure generated. The energy in this case is a function of just two variables and can be plotted as a contour diagram or as an isometric plot, as shown in Figure 5.1. [c.271]

Calculated torsional angles of minimum energy (method HMO-NBI), 15 and 20°, respectively (7. iMU040i). "Two independent molecules in the unit cell. The calculated dihedral angle corresponding to the conformation of minimum intramolecular van der Waals energy was 60° (82CJC97). [c.210]

Despite the recent successes of ab initio calculations, many of the most accurate potential energy surfaces for van der Waals interactions have been obtained by fitting to a combination of experimental and theoretical data. The fiitiire is likely to see many more potential energy surfaces obtained by starting with an ab initio surface, fitting it to a fimctional fonn and then allowing it to vary by small amounts so as to obtain a good fit to many experimental properties simultaneously see, for example, a recent study on morphing an ab initio potential energy surface for Ne-FIF [93]. [c.200]

The two principal methods of expansion used in perturbation theories are the high-temperature 1. expansion of Zwanzig [72], and the y expansion introduced by Henuuer [73]. In the Z-expansion, the perturbation w, 2)1 is modulated by the switching parameter X which varies between 0 and 1, thereby turning on the perturbation. The free energy is expanded in powers of I, and reduces to that of the reference system when 1 = 0. In the y expansion, the perturbation is long ranged of the fomi w r) = - y ( )( y r), and the free energy is expanded in powers of y about y = 0. In the limit as y—> 0, the free energy reduces to a mean-field van der Waals-like equation. The y expansion is especially usefiil in imderstandmg long-range perturbations, such as Coulomb and dipolar interactions, but difficulties in its practical implementation lie in the calculation of higher-order temis in the expansion. Another perturbation approach is the mode expansion of Andersen and Chandler [74], in which the configurational integral is expanded in temis of collective coordinates that are the Fourier transfomis of the particle densities. The expansion is especially useful for electrolytes and has been optimized and improved by adding the correct second virial coefficient. Combinations of the X and y expansions, the union of the X and virial expansions and other unprovements have also been discussed in the literature. Our discussion will be mainly confined to the X expansion and to applications of perturbation theory to detemiining free energy differences by computer simulation. We conclude the section with a brief discussion of perturbation theory of inhomogeneous fluids. [c.503]

CHARMM, which stands for Chemistry at HARvard Macromolecular Mechanics, is designed for macromolecular simulations including energy minimization, molecular dynamics simulations, and normal mode calculations. The development of the code was started and is coordinated by Martin Karplus (Cambridge, MA) and continues throughout the world with contributing developers in over 20 universities, research institutes, and companies. Originally described by Brooks et al. in 1983 [43] and Nilsson in 1986 [44], the energy function used an extended atom model, which treated all hydrogen atoms as part of the corresponding heavy atom [43]. Polar hydrogen atoms were included to better represent hydrogen bonds only by Coulomb and van der Waals interactions (CHARMM19 parameter set for proteins) [45]. Although the increase in computer power allowed the development of several all-atom parameter sets for proteins [46], lipids [47], and nucleic acids [48-50] (the version from July 2002 is named c30al), the united-atom implementation is stiU used for complex and time-consuming applications such as folding simulations or free energy calculations on model proteins [51]. Please note that CHARMM (with the last M a capital letter) refers to the academic version. The commercial, somewhat modified, counterpart is named CHARMm and is available [c.352]

Otlier groups have applied the linear response method to problems other than prot( ligand binding. A good problem for any new free energy approach is to predict the energies of hydration of small organic molecules. Accurate hydration data are avaih for a wide variety of systems, and the calculations can usually be run relatively quic One immediate problem with the two-parameter linear response method is that, as a d are both positive, it is not possible for any solute to have a positive hydration I energy (both the electrostatic and van der Waals interactions between solutes and wa give negative solute-solvent energies). To deal with this problem, Carlson and Jorgen introduced an additional term which was related to the penalty for forming a sol cavity [Carlsen and Jorgensen 1995]. This third term was proportional to the solv< accessible surface area [c.607]

Implementation of the two-region method requires calculation of the interaction between the ions in region 1 and region 2. For short-range potentials (e.g. the van der Waals contribution) it is only the inner part of region 2 that contributes significantly to the energy, E, and the forces on ions in region 1. Thus in current practical implementations of the method the outer region is subdivided into two regions, 2a and 2b (Figure 11.41). In region 1, an atomistic representation is used with full relaxation of the ions. Region 2a also contains expheit ions, whereas in region 2b it is assumed that the only effect of the defect is to change the polarisation of the ions. An iterative approach is used to identify the configuration in which the forces on the ions in region 1 are zero and the ions in region 2a are at equilibrium. The displacements of the ions in region 2a are commonly determined using just the electrostatic force from the defect species alone and equals the force due to any interstitial species less the force due to any vacancies (based on [c.640]

The first factor to note is that most software packages designed for elficient operation use integral accuracy cutoff s with ah initio calculations. This means that integrals involving distant atoms are not included in the calculation if they are estimated to have a negligible contribution to the final energy, usually less than 0.00001 Hartrees or one-hundredth the energy of a van der Waals interaction. In the literature, many of the graphs showing linear scaling DFT performance compare it to an algorithm that does not use integral accuracy cutoffs. Cases where the calculation runs faster without the linear scaling method are due to the integral accuracy cutoffs being more time-efficient than the linear scaling method. [c.44]

At a higher level molecular mechanics is ap plied quantitatively to strain energy calculations Each component of strain is separately described by a mathematical expression developed and refined so that It gives solutions that match experimental obser vations for reference molecules These empirically derived and tested expressions are then used to cal culate the most stable structure of a substance The various structural features are interdependent van der Waals strain for example might be decreased at the expense of introducing some angle strain tor sional strain or both The computer program searches for the combination of bond angles dis tances torsion angles and nonbonded interactions that gives the molecule the lowest total strain This procedure is called strain energy minimization and is based on the common sense notion that the most stable structure is the one that has the least strain [c.111]

Qualitatively the preference for an equatorial methyl group m methylcyclohexane is therefore analogous to the preference for the anti conformation m butane Quantitatively two gauche butane like structural units are present m axial methylcyclohexane that are absent m equatorial methylcyclohexane As we saw earlier m Figure 3 7 the anti con formation of butane is 3 3 kJ/mol (0 8 kcal/mol) lower m energy than the gauche There fore the calculated energy difference between the equatorial and axial conformations of methylcyclohexane should be twice that or 6 6 kJ/mol (16 kcal/mol) The expenmen tally measured difference of 7 1 kJ/mol (1 7 kcal/mol) is close to this estimate This gives us confidence that the same factors that govern the conformations of noncychc compounds also apply to cyclic ones What we call 1 3 diaxial repulsions m substituted cyclohex anes are really the same as van der Waals strain m the gauche conformations of alkanes Other substituted cyclohexanes are similar to methylcyclohexane Two chair con formations exist m rapid equilibrium and the one m which the substituent is equatonal IS more stable The relative amounts of the two conformations depend on the effective size of the substituent The size of a substituent m the context of cyclohexane confer matrons is related to the degree of branching at the atom connected to the ring A single [c.122]

Interactions. Solute—membrane interactions have been both measured and calculated. Liquid chromatography employing the membrane polymer as the column packing has been used to measure direcdy inorganic and organic solute—membrane interfacial parameters, such as equiHbrium distribution coefficients, Gibbs free energy, and surface excess for a large number of different polymers (7,58,59). Additionally, the SEPE model has been used to calculate solute—membrane interaction forces, coulombic or van der Waals (7,33,36), and interactions of organic solutes with polyhen2immida2o1e membranes have been characteri2ed using quantum chemistry calculations, Hquid chromatography, and ir spectroscopy (60). [c.150]

However, polymer stabilization is sensitive to the properties of the environment. This has been described in an eady calculation of polymer conformation at an interface (21). The fraction of adsorbed polymer was plotted as a function of its total adsorption energy (= number of adsorbing groups times their individual adsorption energy) at constant molecular weight, showing the range for usehd polymer stabilization to be extremely narrow. Adsorption energies lower than the optimal range (A, Fig. 10) give no adsorption of the polymer and no stabilization. At a higher adsorption energy (B, Fig. 10), the polymer adsorbs dat at the interface. Such an adsorption is also without stabilization effect because at short distances the van der Waals potential has already reached such large negative values that the potential well is too deep for the droplets to be deaggregated. Only in a limited range of adsorption energies, in which loops and tails are formed, does the polymer serve. In addition, the same phenomenon means that a minimum molecular weight is necessary to obtain stabiUty. [c.200]

Comparative Molecular Field Analysis Methods. Comparative molecular field analysis (CoMFA) (69,70) has been referred to as 3D-QSAR. CoMFA methodologies ate algorithms that relate the biological activities of a series of molecules to the steric (also known as van der Waals), and electrostatic energy fields calculated from their stmctural data. The CoMFA results are displayed three-dimension ally relative to the stmctures from which the energetics were originally calculated. As with QSAR, CoMFA has led to predictions of a molecule s biological activity after obtaining data from a series of stmcturaHy related compounds (71—73). For the CoMFA approach, a series of compounds that produces a specific biological response is identified, and three-dimensional stmctural models are constmcted. These stmctures are then superimposed upon one another and placed within a fixed lattice. A probe atom, with its own energetic values, is systematicaHy placed at each lattice poiat where it is used to calculate the steric and electrostatic potentials between itself and each of the superimposed stmctures. Again at each lattice poiat, these values ate stored along with each inhibitor s biological [c.327]

See pages that mention the term

**Van der Waals energy calculations**:

**[c.230] [c.42] [c.1874] [c.70] [c.347] [c.185] [c.204] [c.228] [c.244] [c.247] [c.249] [c.413] [c.592] [c.608] [c.616] [c.625] [c.727] [c.106] [c.87] [c.408] [c.23]**

Molecular modelling Principles and applications (2001) -- [ c.0 ]