Showing papers in "Journal of Computational Chemistry in 1992"

SETTLE: an analytical version of the SHAKE and RATTLE algorithm for rigid water models

Abstract: An analytical algorithm, called SETTLE, for resetting the positions and velocities to satisfy the holonomic constraints on the rigid water model is presented. This method is still based on the Cartesian coordinate system and can be used in place of SHAKE and RATTLE. We implemented this algorithm in the SPASMS package of molecular mechanics and dynamics. Several series of molecular dynamics simulations were carried out to examine the performance of the new algorithm in comparison with the original RATTLE method. It was found that SETTLE is of higher accuracy and is faster than RATTLE with reasonable tolerances by three to nine times on a scalar machine. Furthermore, the performance improvement ranged from factors of 26 to 98 on a vector machine since the method presented is not iterative. © 1992 by John Wiley & Sons, Inc.

The weighted histogram analysis method for free-energy calculations on biomolecules. I: The method

Abstract: The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built-in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free-energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.

Automated docking with grid-based energy evaluation

Abstract: The ability to generate feasible binding orientations of a small molecule within a site of known structure is important for ligand design. We present a method that combines a rapid, geometric docking algorithm with the evaluation of molecular mechanics interaction energies. The computational costs of evaluation are minimal because we precalculate the receptor-dependent terms in the potential function at points on a three-dimensional grid. In four test cases where the components of crystallographically determined complexes are redocked, the «force field» score correctly identifies the family of orientations closest to the experimental binding geometry

Validation of the general purpose QUANTA 3.2/CHARMm force field

Abstract: An evaluation of the CHARMm force field for small molecules is described. Using different force field conditions and computational techniques, a wide variety of compounds are analyzed. rms deviations of Cartesian coordinates for 49 diverse organic molecules taken from the Cambridge Crystallographic Data Base and internal coordinate geometries for 28 other molecules are reported. Results are described with different dielectrics, dihedral constraints, and crystal packing to allow analysis of deviations from experimental data and give precise statements of the reliability of the parameters used in the force field. Torsional barriers (rms = 0.4) and conformational energy differences (rms = 0.4) are examined and comparisons made to other force fields such as MM2, Tripos, and DREIDING. The results confirm that CHARMm is an internally consistent all purpose force field with energy terms for bonds, angles, dihedrals, and out-of-plane motions, as well as nonbonded electrostatic and van der Waals interactions. Reported CHARMm results (rms = 0.006 A for bonds, rms = 1.37° for angles, and rms = 3.2° for dihedrals) are in excellent agreement with high quality electron diffraction data. © 1992 by John Wiley & Sons, Inc.

Molecular docking using shape descriptors

Abstract: Molecular docking explores the binding modes of two interacting molecules. The technique is increasingly popular for studying protein‐ligand interactions and for drug design. A fundamental problem problem with molecular docking is that orientation space is very large and grows combinatorially with the number of degrees of freedom of the interacting molecules. Here, we describe and evaluate algorithms that improve the efficiency and accuracy of a shape‐based docking method. We use molecular organization and sampling techniques to remove the exponential time dependence on molecular size in docking calculations. The new techniques allow us to study systems that were prohibitively large for the original method. The new algorithms are tested in 10 different protein‐ligand systems, including 7 systems where the ligand is itself a protein. In all cases, the new algorithms successfully reproduce the experimentally determined configurations of the ligand in the protein.

Microscopic models for quantum mechanical calculations of chemical processes in solutions: LD/AMPAC and SCAAS/AMPAC calculations of solvation energies

Abstract: Our previously developed approaches for integrating quantum mechanical molecular orbital methods with microscopic solvent models are refined and examined. These approaches consider the nonlinear solute–solvent coupling in a self‐consistent way by incorporating the potential from the solvent dipoles in the solute Hamiltonian, while considering the polarization of the solvent by the potential from the solute charges. The solvent models used include the simplified Langevin Dipoles (LD) model and the much more expensive surface constrained All Atom Solvent (SCAAS) model, which is combined with a free energy pertubation (FEP) approach. Both methods are effectively integrated with the quantum mechanical AMPAC package and can be easily combined with other quantum mechanical programs. The advantages of the present approaches and their earlier versions over macroscopic reaction field models and supermolecular approaches are considered. A LD/MNDO study of solvated organic ions demonstrates that this model can yield reliable solvation energies, provided the quantum mechanical charges are scaled to have similar magnitudes to those obtained by high level ab initio methods. The incorporation of a field‐dependent hydrophobic term in the LD free energy makes the present approach capable of evaluating the free energy of transfer of polar molecules from non polar solvents to aqueous solutions. The reliability of the LD approach is examined not only by evaluating a rather standard set of solvation energies of organic ions and polar molecules, but also by considering the stringent test case of sterically hindered hydrophobic ions. In this case, we compare the LD/MNDO solvation energies to the more rigorous FEP/SCAAS/MNDO solvation energies. Both methods are found to give similar results even in this challenging test case. The FEP/SCAAS/AMPAC method is incorporated into the current version of the program ENZYMIX. This option allows one to study chemical reactions in enzymes and in solutions using the MNDO and AM1 approximations. A special procedure that uses the EVB method as a reference potential for SCF MO calculations should help in improving the reliability of such studies.

The solution of adsorption integral equations by means of the regularization method

Abstract: An overall adsorption quantity for a heterogeneous solid is usually expressed by an integral equation, which contains a distribution function that describes heterogeneous properties of this solid. The calculation of this distribution function is an ill-posed problem. The current article shows that the difficulties arising from the ill-posed nature of an adsorption equation can be overcome with the regularization method. This work presents general principles of regularization for solving the ill-posed problems without detailed mathematical considerations. The application of the regularization method to calculate a distribution function from any overall adsorption functions is illustrated with both simulated and experimental adsorption isotherms.

Conformational analysis of flexible ligands in macromolecular receptor sites

Abstract: A computational method for exploring the orientational and conformational space of a flexible ligand within a macromolecular receptor site is presented. The approach uses a variant of the DOCK algorithm [Kuntz et al., J. Mol. Biol., 161, 288 (1982)] to determine orientations of a fragment of the ligand within the site. These positions then form the basis for exploring the conformational space of the rest of the ligand, using a systematic search algorithm. The search incorporates a method by which the ligand conformation can be modified in response to interactions with the receptor. The approach is applied to two test cases, in both of which the crystallographically determined structures are obtained. However, alternative models can also be obtained that differ significantly from those observed experimentally. The ability of a variety of measures of the intermolecular interaction to discriminate among these structures is discussed.

Ab initio prediction of possible crystal structures for general organic molecules

Abstract: The performance of a new crystal packing procedure for the ab initio prediction of possible molecular crystal structures is presented. The method is based upon only molecular information, i.e., no unit cell parameters are assumed to be known. The search for the global crystal energy minimum and all local minima inside an energy window is derived from Monte Carlo simulated annealing methods and has been applied to various organic molecules containing heteroatoms and polar groups. A systematic evaluation of the search method and of the quality of the potential energy function has been established. It is demonstrated that the packing of general organic molecules is possible even with standard force fields like CHARMM provided that the charges defining the electrostatic interactions are based upon physical models rather than transferable empirical parameters. Concepts of crystal packing that were based till now upon assumptions and speculations could be proved or disproved by solving directly the extended global optimization problem related to crystal packing. Crystal structures of molecules as complex as those treated in this article have not been, till now, predicted by a computational approach. In one case, a disagreement between the predicted and experimental structure was evident and, based upon the computations, we suspect that the published structure is the wrong one. © 1992 by John Wiley & Sons, Inc.

PM3-SM3: a general parameterization for including aqueous solvation effects in the PM3 molecular orbital model

Abstract: Our recently proposed scheme for including aqueous solvation free energies in parameterized NDDO SCF models is extended to the Parameterized Model 3 semiempirical Hamiltonian. The solvation model takes accurate account of the hydrophobic effect for hydrocarbons, as well as electric polarization of the solvent, the free energy of cavitation, and dispersion interactions. Eight heteroatoms are included (along with H and C), and the new model is parameterized accurately for the water molecule itself, which allows meaningful treatments of specifically hydrogen bonded water molecules. The unphysical partial charges on nitrogen atoms predicted by the Parameterized Model 3 Hamiltonian limit the accuracy of the predicted solvation energies for some compounds containing nitrogen, but the model may be very useful for other systems, especially those for which PM3 is preferred over AM1 for the solute properties of the particular system under study. © 1992 by John Wiley & Sons, Inc.

MSEED: a program for the rapid analytical determination of accessible surface areas and their derivatives

Abstract: An algorithm for the rapid analytical determination of the accessible surface areas of solute molecules is described. The accessible surface areas as well as the derivatives with respect to the Cartesian coordinates of the atoms are computed by a program called “MSEED,” which is based in part on Connolly's analytical formulas for determining surface area. Comparisons of the CPU time required for MSEED, Connolly's numerical algorithm DOT, and a program for surface area determination (ANA) based on Connolly's analytical algorithm, are presented. MSEED is shown to be as much as 70 times faster than ANA and up to 11 times faster than DOT for several proteins. The greater speed of MSEED is achieved partially because nonproductive computation of the surface areas of internal atoms is avoided. A sample minimization of an energy function, which included a term for hydration, was carried out on MET‐enkephalin using MSEED to compute the solvent‐accessible surface area and its derivatives. The potential employed was ECEPP/2 plus an empirical potential for solvation based on the solvent‐accessible surface area of the peptide. The CPU time required for 150 steps of minimization with the potential that included solvation was approximately twice as great as the CPU time required for 150 steps of minimization with the ECEPP/2 potential only.

Fast geometry optimization in self-consistent reaction field computations on solvated molecules

Abstract: The free energy gradient or Hessian of a molecule interacting with a liquid represented by a dielectric continuum is derived in the self-consistent reaction field formalism. An ellipsoidal approximation of the cavity is proposed with an algorithm to automatically define the ellipsoid from the nuclear coordinates of the atoms. With this approximation, geometry optimization of the solvated molecule becomes very fast. This method has been implemented in some standard ab initio or semiempirical computational codes. As a first test of the method, full geometry optimization of formamide in a high dielectric constant medium reveals that the CPU time needed for one optimization cycle is less than 3% longer for a solvated species than for the corresponding free molecule.

Ab initio computed molecular structures and energies of the conformers of glucose

Abstract: Ab initio computations indicate the existence of several stable and some unstable conformers in isolated α and β glucose molecules All of the lower-energy conformers exhibit a strikingly regular pattern of internal hydrogen bonding Five such stable structures have been identified for each of the α and β anomers, differing primarily in the orientation of the CH 2 OH group In each conformer, the α anomer is predicted to be lower in energy than the corresponding conformers of β anomer The difference is about 2 kcal/mol in the 4-31G basis but only 04 kcal/mol in the 6-31G * basis

Study of hydrogen bonding interactions relevant to biomolecular structure and function

Abstract: Ab initio molecular orbital calculations were used to study hydrogen bonding interactions and interatomic distances of a number of hydrogen bonded complexes that are germane to biomolecular structure and function. The calculations were carried out at the STO-3G, 3-21G, 6-31G * , and MP2/6-31G * levels (geometries were fully optimized at each level). For anionic species, 6-31+G * and MP2/6-31+G * were also used. In some cases, more sophisticated calculations were also carried out. Whenever possible, the corresponding enthalpy, entropy, and free energy of complexation were calculated

Analysis of a large data base of electrostatic potential derived atomic charges

Abstract: A large data base of 6-31G*, MNDO, AM1, and PM3 electrostatic potential (ESP) derived point charges of amino acids and monosaccharides is analyzed. We find that MNDO correlates well with 6-31G* ESP derived point charges, while AM1 and PM3 do so quite poorly. Furthermore, scaling MNDO ESP derived point charges enhances the ability of MNDO to reproduce 6-31G* results. We used our data base to attempt to derive a 6-31G* transferable charge model at an atom-by-atom level. We find that it is simple to derive a transferable model for monosaccharides, but for the amino acids statistical difficulties make this a less attractive approach. The transferable charge model for the monosaccharides is slightly better than MNDO, but scaled MNDO charges perform significantly better than the transferable model. We also carried out a QMD simulation on the alanine dipeptide to assess the fluctuations that would be expected in atomic point charges during the course of an MD simulation. Relatively large charge fluctuations are observed and their impact on molecular simulation is addressed. © 1992 by John Wiley & Sons, Inc.

Solving the finite-difference non-linear Poisson-Boltzmann equation

Abstract: The Poisson–Boltzmann equation can be used to calculate the electrostatic potential field of a molecule surrounded by a solvent containing mobile ions. The Poisson–Boltzmann equation is a non-linear partial differential equation. Finite-difference methods of solving this equation have been restricted to the linearized form of the equation or a finite number of non-linear terms. Here we introduce a method based on a variational formulation of the electrostatic potential and standard multi-dimensional maximization methods that can be used to solve the full non-linear equation. © 1992 by John Wiley & Sons, Inc.

Ab initio calculation of magnetic properties by the “Direct” IGLO method

Abstract: A direct method for the ab initio calculation of the magnetic susceptibility and chemical shielding tensors based on the individual gauge for localized molecular orbitals (IGLO) formalism is introduced. “Direct” in this context means we avoid storing the two-electron repulsion integrals in favor of recalculating them whenever necessary. In conjunction with the Direct-SCF package TURBOMOLE Direct IGLO (DIGLO) permits calculation of magnetic second-order properties for large molecules by minimizing peripheral disc storage requirements. The size of the molecules to be treated is limited only by the amount of CPU time available. The performance of DIGLO is demonstrated for some selected examples.

NDDO fragment self-consistent field approximation for large electronic systems

Abstract: A semi-empirical NDDO method, generalized from a similar scheme at the CNDO/2 level developed previously, is presented to treat very large molecules. The extended molecular system is divided into a relatively small subsystem where substantial chemical changes take place and an environment remaining more-or-less unperturbed during the process. Expanding the wave function on an atomic hybrid basis an SCF procedure is performed for the subsystem in the field of the iteratively determined electronic distribution of the environment. A computer program has been written for the IBM RISC System/6000 530 computer and several test calculations were done for a variety of large classical molecules, like substituted aliphatic hydrocarbons, water oligomers, and a heptapeptide. Protonation energies, proton transfer potential curves, rotational barriers, atomic net charges, and HOMO and LUMO energies, as computed by the exact version of the NDDO method, are fairly well reproduced by our approximation if the subsystem is appropriately defined. © 1992 by John Wiley & Sons, Inc.

Conformational analysis of trehalose disaccharides and analogues using MM3

Abstract: Energy surfaces for the relative orientations of the pyranosyl rings of α,α‐, α,β‐, and β,β‐trehalose and analogues were generated with MM3. Sixteen starting conformations of the rotatable side groups of α,β‐trehalose were considered, while only 10 conformations were needed for α,α‐ and β,β‐trehalose because of molecular symmetry. Energies were calculated at 20° increments of the two torsional angles of the glycosidic linkage, but otherwise the molecules were fully relaxed. The structure at the overall minimum for α,α‐trehalose agrees well with that found in crystal structures, and also agrees with interpretations of NMR and optical rotation data. The energy surfaces for the three trehaloses differ greatly from each other, but are each similar to those for the corresponding three 2‐(6‐methyltetrahydropyran‐2‐yloxy)6‐methyltetrahydropyrans. This suggests that linkage type (axial or equatorial) is more important than exocyclic substituents in determining trehalose conformations. A comparison with surfaces from the corresponding 5a‐carba trehalose analogues illustrates that the exo‐anomeric effect is important in determining disaccharide conformation.

Conformational dependence of electrostatic potential derived charges of a lipid headgroup: glycerylphosphorylcholine

Abstract: Atomic monopoles are routinely determined through a least squares fit to molecular electrostatic potentials We report studies of the variation in atomic monopoles with variation in conformation for the zwitterionic polar head group of lecithins, a common class of lipid The monopole of one atom, a relatively buried carbon, varied by 13 electron units between different conformers “Exterior” atoms, as seen previously, showed smaller changes in charge and smaller estimated standard deviations The total charge of local groups of atoms varied less than the charge of individual atoms, indicating that shifts in charge occurred mostly between neighboring atoms This effect might be reflected in the high correlations seen between charges of many neighboring atoms These correlations, while present for many logical groupings of atoms (such as within methylene and methyl groups), are curiously absent between some bonded atoms Monopoles were fit to multiple conformations simultaneously to provide a charge set that could optimally reproduce the electrostatic potential of all the conformers as a means of generating monopoles for molecular dynamics simulations or other studies where conformation varies In some cases, the charges on chemically equivalent atoms (eg, the hydrogen atoms in a methyl group) were different by more than their estimated error of fit These studies lead to the suggestion that a minimum error in reported charges is on the order of 10% All conformations show that the positive charge of the trimethylalkyl ammonium group is carried by the methyl hydrogens; the total charge on the nine hydrogens is over 2 electron units, counterbalanced by negative monopoles on the carbons The presence of this diffuse cloud of substantial charge would appear to be a disindicator of the use of a “united” atoms approach for these methyl groups The effects of the charge variation on intermolecular interactions is also examined

Derivation of fluorine and hydrogen atom parameters using liquid simulations

Abstract: Simulations of periodic boxes of tetrafluoromethane and trifluoromethane were run to determine van der Waals parameters for fluorine and for hydrogen attached to a fluorine-bearing carbon. The simulations of CF4 were performed first to determine the optimal van der Waals radius R* and well depth e for fluorine by adjusting these parameters to reproduce the experimental molar volume and enthalpy of vaporization of CF4. The best values of R* and e were determined to be 1.75 A and 0.061 kcal/mol. Using these fluorine parameters, the simulations of CHF3 were then performed to determine if the hydrogen of this molecule required a smaller R* than that used for the “normal” hydrocarbon hydrogen determined by Spellmeyer and Kollman (results in preparation). That R* was determined by running Monte Carlo simulations on methane, ethane, propane, and butane and adjusting R* and e for carbon and hydrogen to reproduce the experimental molar volume and enthalpy of vaporization. It was found that an Re of 1.21 A was optimal, significantly smaller than the R* = 1.49 A found by Spellmeyer for “normal” hydrocarbon hydrogens. This value of R* is in good agreement with the R* for the hydrogen in CHF3 derived independently using ab initio calculations and molecular mechanics on F3CH… OH2 by Veenstra et al. © 1992 by John Wiley & Sons, Inc.

Extension of SINDO1 to transition metal compounds

Abstract: The semiempirical MO method SINDO1, originally suitable for first- and second-row atoms, is extended to transition metals from scandium to zinc. The core Hamiltonian elements in a symmetrically orthogonalized atomic orbital (OAO) basis set are modified and the parameters are optimized to reproduce the experimental geometries, heats of formation, and ionization potentials. An application of the method to a selected number of molecules, as well as a comparison between calculated and experimental data is reported.

Polynomial path for the calculation of liquid state free energies from computer simulations tested on liquid water

Abstract: as well as its range of appli- cability in conjunction with Monte Carlo computer simulations using thermodynamic integration based on Gaussian quadratures. The technique employed is compared with the slow growth method (an other vari- ant of thermodynamic integration), with the perturbation method and with the use of the grand-canonical ensemble. INTRODUCTION AND BACKGROUND The calculation of the free energy, long recognized as a computationally exacting task, is of special importance due to the role of the free energy in determininig chemical equilibria. As reviewed recently, 1 4 free energy simulation techniques are characterized by the path selected that connects the two systems in the configuration space (e.g. the choice of the coupling parameter, vide infra) and by the quantity chosen whose Boltzmann average is related to the free energy — with the exception of calculations in the grand-canonical ensemble where the chemical potential is fixed at the outset. The various choices of the coupling parameter, described in detail in ref. 2, fall into two distinct classes:

Highly accurate diatomic centrifugal distortion constants for high orders and high levels

Abstract: The problem of the computation of the Centrifugal Distortion Constants (CDC) related to a diatomic potential is considered. The analytical expressions obtained from a reformulation of the Rayleigh-Shrodinger perturbation theory are used. These are e n+1 = - Σ n m=1 e m where R =1/r 2 , Φ 0 = Ψ v is the vibrational wave function (corresponding to the given energy E v = e 0 ) and Φ 1 , Φ 2 , ..., are the rotational corrections to Φ 0 , solutions of the rotational (nonhomogeneous Shrodinger equations. These equations are integrated by using a recent integrator powerful local control allowing (for Φ 0 ) a high accuracy. The integrals are computed by using another powerful technique tailored for matrix elements between numerical wave functions. This numerical treatment is applied to the model Lennard-Jones potential and to the RKR potential of the I 2 ground state

Theoretical studies of organometallic compounds. I: All electron and pseudopotential calculations of Ti(CH 3 ) n Cl 4- n ( n =0-4)

Abstract: The performance of effective core potentials (ECP) and model potentials (MP) has been studied by calculating the geometries and reaction energies of isodesmic reactions for the molecules Ti(CH3)nCl4 − n (n = 0–4) at the Hartree–Fock level of theory. The results are compared with data from all electron calculations and experimental results as far as available. The all electron calculations were performed with a 3-21G basis set from Hehre and a (53321/521/41) basis set from Huzinaga. For the ECP calculations the potentials developed by Hay and Wadt, and for the MP calculations, the model potentials developed by Sakai and Huzinaga, are employed. © 1992 by John Wiley & Sons, Inc.

Conformational sampling and ensemble generation by molecular dynamics simulations: 18-Crown-6 as a test case

Abstract: Using the crown ether 18-crown-6 as a test system, molecular dynamics has been evaluated as a technique for conformational searching and thermodynamic ensemble generation. By running a series of 200 ps and 2 ns simulations, an “optimum” temperature range for conformational searching, i.e., the temperature at which one finds the largest number of low energy structures, was demonstrated to be dependent on the time interval at which one examines the structure. By considering conformational degeneracy and entropy with the rigid rotor harmonic oscillator approximation we have been able to demonstrate that the ensemble generated approaches thermodynamic equilibrium in about 6 ns of simulation. To our knowledge this is the first time this has been demonstrated for a complex organic molecule and it highlights the power and usefulness of molecular dynamics as a method for thermodynamic ensemble generation and conformational searching.

Electrostatic energy calculations by a finite-difference method: rapid calculation of charge-solvent interaction energies

Abstract: Finite-difference Poisson–Boltzmann (FDPB) methods allow a fast and accurate calculations of the reaction field (charge–solvent) energies for molecular systems. Unfortunately, the energy in the FDPB calculations includes the self-energies and the finite-difference approximation to the Coulombic energies as well as the reaction field energy. A second finite-difference calculation, in a uniform dielectric, is therefore necesssary to eliminate these contributions. In this article we describe a rapid and accurate method to calculate the self energy and finite-difference Coulombic energies in a uniform dielectric thus eliminating the need for a second finite-difference calculation. The computational savings for this method range from a factor of 4 for a typical protein to a factor of 103 for small molecules. © 1992 by John Wiley & Sons, Inc.

Atomic charge calculations for quantitative structure-property relationships

Abstract: A previously published empirical charge scheme has been adapted for use in studies of quantitative structure-property relationships. New parameters have been developed to allow the inclusion of nitrates, nitriles, sulfides, thiols, thiophenes, and sulfoxides. No changes have been made to the original scheme, thus preserving all previous results. A few simple additions to the program have made it possible to calculate atomic charges in a variety of ionic structures containing a formally positive nitrogen or a formally negative oxygen. The results obtained for ions are consistent with a number of concepts surrounding the familiar inductive and resonance effects.

Precision of free energies calculated by molecular dynamics simulations of peptides in solution

Abstract: Errors in free energies for molecular replacement and for conformation change of a small model peptide have been determined empirically by repeated simulations from different starting points. All calculations have been done using thermodynamic integration, in which the system's potential energy is coupled to a parameter λ, that is increased or decreased by a small amount at each step of the simulation. The effects of several factors that may alter the precision are evaluated. These factors include: the length of the simulation, the dependence of the potential energy on λ, the use of conformational restraints, and their magnitude and form. The methods used for restraint and conformational forcing are described in detail. The free energy change, calculated as the mean from several successive simulations with alternately increasing and decreasing λ, is found to be independent of the length of the simulations. As expected, longer simulations produce more precise results. The variation of the calculated free energies is found to consist of two parts, a random error and a systematic hysteresis, i.e., a dependence on the direction in which λ changes. The hysteresis varies as the inverse of the length of the simulation and the random error as the inverse square root The advantage of the use of a different (nonlinear) dependence of the attractive and repulsive parts of the nonbonded potential energy on the coupling parameter when “creating” particles in solution is found to be very large. This nonlinear coupling was found to be superior to the use of linear coupling and a nonlinear change of the coupling parameter with the simulation time. The hysteresis in conformational free energy calculations is found to increase markedly if too weak a forcing restraint is chosen. It is shown how to deconvolute the contribution of a torsional restraint from the dependence of the free energy on a torsion angle.

Extended Koopmans' theorem: approximate ionization energies from MCSCF wave functions

Abstract: The extended Koopmans' theorem has been implemented using multiconfigurational self-consistent field wave functions calculated with the GAMESS, HONDO, and SIRIUS programs. The results of illustrative calculations are presented for the molecules HF, H2O, NH3, CH4, N2, CO, HNC, HCN, C2H2, H2CO, and B2H6. The lowest extended Koopmans' theorem ionization potentials agree well within the experimental values and the ionization potentials representing excited states of the ions show some improvements over the Koopmans' theorem values in most cases. The extended Koopmans' theorem is easily implemented and the time required to calculate the ionization energies is insignificant compared to the time required to calculate the wave function of the un-ionized molecule. © 1992 by John Wiley & Sons, Inc.