Accuracy of energy extrapolation in multireference configuration interaction calculations

The accuracy of extrapolation procedures in conjunction with energy-based configuration selection in CI calculations is examined. The normally high accuracy of such extrapolation can deteriorate in multireference CI calculations when configuration functions of low weight are included in the root (reference) set. This is due to the inadequacy of second-order energy contribution estimates for the very large number of discarded low-contribution functions generated as single and double excitations from the minor members of the root set. The problem may be overcome by increasing the number of configurations included in the zero-order function used for the energy contribution estimation process. Illustrative results are presented for excited states of the H₂O molecule and the H₂O⁺ ion.     

Calculating zeros: Non-equilibrium free energy calculations

Free energy calculations on three model processes with theoretically known free energy changes have been performed using short simulation times. A comparison between equilibrium (thermodynamic integration) and non-equilibrium (fast growth) methods has been made in order to assess the accuracy and precision of these methods. The three processes have been chosen to represent processes often observed in biomolecular free energy calculations. They involve a redistribution of charges, the creation and annihilation of neutral particles and conformational changes. At very short overall simulation times, the thermodynamic integration approach using discrete steps is most accurate. More importantly, reasonable accuracy can be obtained using this method which seems independent of the overall simulation time. In cases where slow conformational changes play a role, fast growth simulations might have an advantage over discrete thermodynamic integration where sufficient sampling needs to be obtained at every λ-point, but only if the initial conformations do properly represent an equilibrium ensemble. From these three test cases practical lessons can be learned that will be applicable to biomolecular free energy calculations.     

Lattice match in density functional calculations: ice Ih vs. beta-AgI

Density functional optimizations of the crystal parameters of ice Ih and beta-AgI imply lattice mismatches of 4.2 to 7.9%, in a survey of eight common, approximate (non-hybrid) functionals, too large to allow a meaningful contribution from Density Functional Theory to the discussion of the significance of lattice match in ice nucleation.     

Basic ingredients of free energy calculations: A review

Methods to compute free energy differences between different states of a molecular system are reviewed with the aim of identifying their basic ingredients and their utility when applied in practice to biomolecular systems. A free energy calculation is comprised of three basic components: (i) a suitable model or Hamiltonian, (ii) a sampling protocol with which one can generate a representative ensemble of molecular configurations, and (iii) an estimator of the free energy difference itself. Alternative sampling protocols can be distinguished according to whether one or more states are to be sampled. In cases where only a single state is considered, six alternative techniques could be distinguished: (i) changing the dynamics, (ii) deforming the energy surface, (iii) extending the dimensionality, (iv) perturbing the forces, (v) reducing the number of degrees of freedom, and (vi) multi‐copy approaches. In cases where multiple states are to be sampled, the three primary techniques are staging, importance sampling, and adiabatic decoupling. Estimators of the free energy can be classified as global methods that either count the number of times a given state is sampled or use energy differences. Or, they can be classified as local methods that either make use of the force or are based on transition probabilities. Finally, this overview of the available techniques and how they can be best used in a practical context is aimed at helping the reader choose the most appropriate combination of approaches for the biomolecular system, Hamiltonian and free energy difference of interest. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Lattice relaxation and electric-field-gradient calculations in impurity-doped single ionic crystals

The lattice-relaxation parameters in several ionic crystals doped with monovalent impurity ions are calculated by energy minimization, taking into account the Coulomb, overlap-repulsive, and three-body potential energies. The displaced 256 ions around one substitutional impurity ion are taken into consideration and the results are utilized to calculate the electric-field gradients at sites similar to the (1,0,0), (1,1,0), and (1,1,1) sites relative to the impurity at (0,0,0), by using two different models for three-body potentials.     

Lattice energy estimation for inorganic ionic crystals

An empirical method based on chemical bond theory for the estimation of the lattice energy for ionic crystals has been proposed. The lattice energy contributions have been partitioned into bond dependent terms. For an individual bond, the lattice energy contribution made by it has been separated into ionic and covalent parts. Our calculated values of lattice energies agree well with available experimental and theoretical values for diverse ionic crystals. This method, which requires detailed crystallographic information and elaborate computation, might be extended and possibly yield further insights with respect to bond properties of materials.     

Correlation energy calculations for infinite systems

A survey is given of ab initio calculations for solids and polymers, which start from an SCF calculation and treat correlations by using local operators. The theory is formulated by employing a projection method. As regards applications, special attention is paid to elemental semiconductors and to polymers like polyethylene and polyacetylene. With the help of reduced Hamiltonians, insight can be gained into various correlation effects. This is demonstrated by a discussion of the problem of dimerization in polyacetylene. Finally, a formalism is described that allows for treating the effects of correlations on energy bands of solids. It is shown that qualitative new aspects of correlations enter when a quasiparticle in, e.g., a semiconductor is considered. The theory is applied to a calculation of the energy bands of silicon.     

Single-sweep methods for free energy calculations

A simple, efficient, and accurate method is proposed to map multidimensional free energy landscapes. The method combines the temperature-accelerated molecular dynamics (TAMD) proposed in [L. Maragliano and E. Vanden-Eijnden, Chem. Phys. Lett. 426, 168 (2006)] with a variational reconstruction method using radial-basis functions for the representation of the free energy. TAMD is used to rapidly sweep through the important regions of the free energy landscape and to compute the gradient of the free energy locally at points in these regions. The variational method is then used to reconstruct the free energy globally from the mean force at these points. The algorithmic aspects of the single-sweep method are explained in detail, and the method is tested on simple examples and used to compute the free energy of the solvated alanine dipeptide in two and four dihedral angles.     

CNDO calculations of ring puckering potential energy

The ring puckering potential energy functions are calculated for 2,3-dihydrofuran, 2,5-dihydrofuran, cyclopentene and cyclopent-3-enone using the standard CNDO/2 method. The equilibrium conformations are discussed and the ring puckering force constants as well as the dipole moments are evaluated. A more detailed analysis of the influence of angular deformations on the potential function of the cyclopentene molecule is performed.     

Tseng's calculations of low energy pair production

We review the theoretical work 1971–1997 of H.K. Tseng on low energy pair production. In this work numerical calculations were performed in independent particle approximation in a screened self-consistent central potential, expanding the S-matrix element in partial waves and multipoles. Sampling techniques in partial waves and multipoles were used to extend the calculations to higher energies (up to 10 Mev). Total cross sections, the positron energy spectrum, the positron angular distributions, and the positron–photon polarization correlations were studied. Agreement was obtained with most experiments, although some anomalies remained at the lowest energies (particularly at 1082 keV). Atomic screening of the nuclear charge decreases cross sections at higher energies, as described by a form factor in the momentum transfer to the nucleus. In an intermediate energy regime point Coulomb results in a shifted energy spectrum may be used. At low energies screening increases cross sections, and this is characterized in terms of a normalization screening factor which describes the change in magnitude of electron and positron wave functions at small distances. In this low energy regime angular distribution shapes and polarization correlations are independent of screening.     

Simple technique to obtain correlated energy curves: LiH calculations

The possibility of applying the half-projected Hartree–Fock method together with the Coulomb hole model to obtain cofrelated potential-energy curves is investigated. Here we report calculations performed on the LiH molecule. The results show that this combined technique can provide potential curves very near to the experimental ones with a similar effort to that involved in the Hartree–Fock calculations.     

Lattice energies: calculations from pressure—volume data,and uncertainties in the results

A method of calculating lattice energies is developed, which reproduces directly the observed pressure—volume curve of some simple ionic solids. The results in general are close to the experimental values, and show deviations usually between 5 and 10 kJ mole^?1. The calculated values are not systematically too high or too low. Some estimates are made of the effect of errors in the P–V curve on the calculated lattice energies.     

Conformational energy analysis of substituted diphenylethanes: Part II. Empirical energy calculations on stilbene dihalogenides

The geometry and energy of the stable conformations of the isomeric forms of 1,2-halogeno-1,2-diphenylethanes have been obtained by means of empirical energy functions. A minimization of the conformational energy with respect to the torsion angles and the valence angles around the asymmetrically substituted carbon atoms has been carried out. The evaluated populations of the stable conformations showed good agreement with available experimental data. CNDO/2 calculations on the low-energy conformations of the isomeric forms of 1,2-difluoro-, 1,2-fluorochloro-, and 1,2-dichlorodiphenylethane have been carried out. These yielded improved estimates of the dipole moments for the dichloro isomers.     

Multipole electrostatics in hydration free energy calculations

Hydration free energy (HFE) is generally used for evaluating molecular solubility, which is an important property for pharmaceutical and chemical engineering processes. Accurately predicting HFE is also recognized as one fundamental capability of molecular mechanics force field. Here, we present a systematic investigation on HFE calculations with AMOEBA polarizable force field at various parameterization and simulation conditions. The HFEs of seven small organic molecules have been obtained alchemically using the Bennett Acceptance Ratio method. We have compared two approaches to derive the atomic multipoles from quantum mechanical calculations: one directly from the new distributed multipole analysis and the other involving fitting to the electrostatic potential around the molecules. Wave functions solved at the MP2 level with four basis sets (6-311G*, 6-311++G(2d,2p), cc-pVTZ, and aug-cc-pVTZ) are used to derive the atomic multipoles. HFEs from all four basis sets show a reasonable agreement with experimental data (root mean square error 0.63 kcal/mol for aug-cc-pVTZ). We conclude that aug-cc-pVTZ gives the best performance when used with AMOEBA, and 6-311++G(2d,2p) is comparable but more efficient for larger systems. The results suggest that the inclusion of diffuse basis functions is important for capturing intermolecular interactions. The effect of long-range correction to van der Waals interaction on the hydration free energies is about 0.1 kcal/mol when the cutoff is 12?, and increases linearly with the number of atoms in the solute/ligand. In addition, we also discussed the results from a hybrid approach that combines polarizable solute with fixed-charge water in the HFE calculation.     

Semi-empirical models for auger electron energy calculations

Three approaches to the semi-empirical calculation of Auger electron energies developed by Shirley et al., Larkins and Hoogewijs et al. respectively are critically discussed using a common notation.     

Zero-point energy constraint in quasi-classical trajectory calculations

A method to constrain the zero-point energy in quasi-classical trajectory calculations is proposed and applied to the Henon-Heiles system. The main idea of this method is to smoothly eliminate the coupling terms in the Hamiltonian as the energy of any mode falls below a specified value.     

Guidelines for the analysis of free energy calculations

Journal of Computer-Aided Molecular Design - Free energy calculations based on molecular dynamics simulations show considerable promise for applications ranging from drug discovery to prediction of...     

Lead optimization mapper: automating free energy calculations for lead optimization

Alchemical free energy calculations hold increasing promise as an aid to drug discovery efforts. However, applications of these techniques in discovery projects have been relatively few, partly because of the difficulty of planning and setting up calculations. Here, we introduce lead optimization mapper, LOMAP, an automated algorithm to plan efficient relative free energy calculations between potential ligands within a substantial library of perhaps hundreds of compounds. In this approach, ligands are first grouped by structural similarity primarily based on the size of a (loosely defined) maximal common substructure, and then calculations are planned within and between sets of structurally related compounds. An emphasis is placed on ensuring that relative free energies can be obtained between any pair of compounds without combining the results of too many different relative free energy calculations (to avoid accumulation of error) and by providing some redundancy to allow for the possibility of error and consistency checking and provide some insight into when results can be expected to be unreliable. The algorithm is discussed in detail and a Python implementation, based on both Schrödinger’s and OpenEye’s APIs, has been made available freely under the BSD license.