On the Energetics of nh3 Adsorption and Decomposition on nb(100) Surface : a ubi-qep Study

The energetics of the adsorption and decomposition of ammonia on Nb(100) surface was investigated by the method of unity bond index-quadratic exponential potential (UBI-QEP). The experimental as well as theoretically derived atomic heats of adsorptions were used as the input data and the results were compared with the findings of local density functional theory (LDFT) and non-local density functional theory (NLDFT). The method was capable of correctly predicting the fragmentation of ammonia on 4-fold hollow sites on the surface of Nb(100) and magnitudes of the heats of adsorptions and activation energies were more realistic.     

Computation of affinity and selectivity: Binding of 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors to dihydrofolate reductases

Binding energy calculations for complexes of mutant and wild-type human dihydrofolate reductases with 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors are reported. Quantitative insight into binding energetics of these molecules is obtained from calculations based on force field energy evaluation and thermal sampling by molecular dynamics simulations. The calculated affinity of methotrexate for wild-type and mutant enzymes is reasonably well reproduced. Truncation of the methotrexate glutamate tail results in a loss of affinity by several orders of magnitude. No major difference in binding strength is predicted between the pteridines and the quinazolines, while the N-methyl group present in methotrexate appears to confer significantly stronger binding. The recent improvement, which is used here, of our linear interaction energy method for binding affinity prediction, as well as problems with treating charged and flexible ligands are discussed. This approach should be suitable in a drug discovery context for prediction of binding energies of new inhibitors prior to their synthesis, when some information about the binding mode is available.     

Electrostatics of ligand binding: parametrization of the generalized Born model and comparison with the Poisson-Boltzmann approach

An accurate and fast evaluation of the electrostatics in ligand-protein interactions is crucial for computer-aided drug design. The pairwise generalized Born (GB) model, a fast analytical method originally developed for studying the solvation of organic molecules, has been widely applied to macromolecular systems, including ligand-protein complexes. However, this model involves several empirical scaling parameters, which have been optimized for the solvation of organic molecules, peptides, and nucleic acids but not for energetics of ligand binding. Studies have shown that a good solvation energy does not guarantee a correct model of solvent-mediated interactions. Thus, in this study, we have used the Poisson-Boltzmann (PB) approach as a reference to optimize the GB model for studies of ligand-protein interactions. Specifically, we have employed the pairwise descreening approximation proposed by Hawkins et al.(1) for GB calculations and DelPhi for PB calculations. The AMBER all-atom force field parameters have been used in this work. Seventeen protein-ligand complexes have been used as a training database, and a set of atomic descreening parameters has been selected with which the pairwise GB model and the PB model yield comparable results on atomic Born radii, the electrostatic component of free energies of ligand binding, and desolvation energies of the ligands and proteins. The energetics of the 15 test complexes calculated with the GB model using this set of parameters also agrees well with the energetics calculated with the PB method. This is the first time that the GB model has been parametrized and thoroughly compared with the PB model for the electrostatics of ligand binding.     

Monte Carlo and UBI–QEP Modeling of the Coverage-Dependent Binding Energy for Atomic Adsorbates on the (111) and (100) Transition Metal Surfaces

Using the unity bond index–quadratic exponential potential (UBI–QEP) formalism and the Monte Carlo method, functions are obtained that describe the dependence of the binding energies of atomic adsorbates on the single crystal surface coverage for the models of random adsorption, models with a site choice and site preference, models with neighbor exclusion, and models with diffusion assistance.     

First principle study of hydrogen storage on the graphene-like aluminum nitride nanosheet

Employing density functional calculations including an empirical dispersion term, we investigated the hydrogenation of an aluminum nitride nanosheet (h-AlN) with atomic and molecular hydrogen. It was found that atomic H prefers to be adsorbed on an N atom rather than Al, releasing energy of 21.1 kcal/mol. The HOMO/LUMO energy gap of the sheet is dramatically reduced from 107.9 to 44.5 kcal/mol, upon the adsorption of one hydrogen atom. The adsorption of atomic H on the h-AlN presents properties which are promising for nanoelectronic applications. The molecular H₂ was found to be adsorbed collinearly on an N atom and dissociated to two H atoms on Al–N bond. Calculated barrier and adsorption energies for this dissociation process are about +18.9 and ?1.9 kcal/mol. We predict that each nitrogen atom in an AlN sheet can adsorb two hydrogen molecules on opposite sides of the sheet, and thus the gravimetric density for hydrogen storage on AlN sheet is evaluated to be about 8.9 wt%.     

On the transferability of hydration-parametrized continuum electrostatics models to solvated binding calculations

Using molecular mechanics force field partial atomic charges, we show the nonuniqueness of the parametrization of continuum electrostatics models with respect to solute atomic radii and interior dielectric constant based on hydration (vacuum-to-water transfer) free energy data available for small molecules. Moreover, parameter sets that are optimal and equivalent for hydration free energy calculations lead to large variations of calculated absolute and relative electrostatic binding free energies. Hence, parametrization of solvation effects based on hydration data, although a necessary condition, is not sufficient to guarantee its transferability to the calculation of binding free energies in solution.     

Multiconfigurational time-dependent Hartree calculations for dissociative adsorption of H2 on Cu(100)

The efficiency of the multiconfigurational time-dependent Hartree (MCTDH) method for calculating the initial-state selected dissociation probability of H(2)(v=0,j=0) on Cu(100) is investigated. The MCTDH method is shown to be significantly more efficient than standard wave packet methods. A large number of single-particle functions is required to converge the initial-state selected reaction probability for dissociative adsorption. Employing multidimensional coordinates in the MCTDH ansatz (mode combination) is found to be crucial for the efficiency of these MCTDH calculations. Perspectives towards the application of the MCTDH approach to study dissociative adsorption of polyatomic molecules on surfaces are discussed.     

Probing the structural and electronic factors affecting the adsorption and reactivity of alkenes in acidic zeolites using DFT calculations and multivariate statistical methods

Quantum mechanical (QM) cluster calculations have been performed on a model of ZSM-5 at DFT and MP2 levels. We investigated how the adsorption energies and the energetics of alkoxide intermediate formation of six different alkene substrates, ethene, propene, 1-butene, cis/trans butene, and isobutene, vary in this zeolite model. An analysis of the DFT geometric, electronic, and energetic parameters of the zeolite-substrate complexes, transition states, and alkoxide intermediates is performed using principal components analysis (PCA) and partial least squares (PLS). These deliver an insight into the correlated changes that occur between molecular structure and energy along the reaction coordinate between the physisorbed and chemisorbed species within the zeolite. To the best of our knowledge, this is the first occasion multivariate techniques such as PCA or PLS have been employed to profile the changes in electronics, distances, and angles in QM calculations of catalytic systems such as zeolites. We find the calculated adsorption and the alkoxide intermediate energies correlate strongly with the absolute charge on the substrate and the length of the substrate double bond. The transition states' energies are not affected by the zeolite framework as modeled, which explains why they correlate strongly with the gas-phase substrate protonation energy. Our cluster results show that for ethene, propene, 1-butene, and isobutene, the relative energetics associated with the formation of the alkoxide intermediate in ZSM-5 follow the same trends as calculations where the effects of the framework are included.     

Spectral-product methods for electronic structure calculations

Progress is reported in development, implementation, and application of a spectral method for ab initio studies of the electronic structure of matter. In this approach, antisymmetry restrictions are enforced subsequent to construction of the many-electron Hamiltonian matrix in a complete orthonormal spectral-product basis. Transformation to a permutation-symmetry representation obtained from the eigenstates of the aggregate electron antisymmetrizer is seen to enforce the requirements of the Pauli principle ex post facto, and to eliminate the unphysical (non-Pauli) states spanned by the product representation. Results identical with conventional use of prior antisymmetrization of configurational state functions are obtained in applications to many-electron atoms. The development provides certain advantages over conventional methods for polyatomic molecules, and, in particular, facilitates incorporation of fragment information in the form of Hermitian matrix representatives of atomic and diatomic operators which include the non-local effects of overall electron antisymmetry. An exact atomic-pair expression is obtained in this way for polyatomic Hamiltonian matrices which avoids the ambiguities of previously described semi-empirical fragment-based methods for electronic structure calculations. Illustrative applications to the well-known low-lying doublet states of the H₃ molecule in a minimal-basis-set demonstrate that the eigensurfaces of the antisymmetrizer can anticipate the structures of the more familiar energy surfaces, including the seams of intersection common in high-symmetry molecular geometries. The calculated H₃ energy surfaces are found to be in good agreement with corresponding valence-bond results which include all three-center terms, and are in general accord with accurate values obtained employing conventional high-level computational-chemistry procedures. By avoiding the repeated evaluations of the many-centered one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices in the antisymmetric basis states commonly employed in conventional calculations, and by performing the required atomic and atomic-pair calculations once and for all, the spectral-product approach may provide an alternative potentially efficient ab initio formalism suitable for computational studies of adiabatic potential energy surfaces more generally. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Kramers' restricted hartree—fock method for polyatomic molecules using ab initio relativistic effective core potentials with spin—orbit operators

A two-component Kramers' restricted Hartree–Fock method (KRHF) has been developed for the polyatomic molecules with closed shell configurations. The present KRHF program utilizes the relativistic effective core potentials with spin–orbit operators at the Hartree–Fock (HF) level and produces molecular spinors obeying the double group symmetry. The KRHF program enables the variational calculation of spin–orbit interactions at the HF level. KRHF calculations have been performed for the HX, X₂, XY(X, Y = I, Br), and CH₃I molecules. It is demonstrated that the orbital energies from KRHF calculations are useful for the interpretation of spin-orbit splittings in photoelectron spectra. In all molecules studied, bond lengths are only slightly expanded, harmonic vibrational frequencies are reduced, and bond energies are significantly decreased by the spin–orbit interactions.     

Bond dissociation energies in second-row compounds

Heats of formation at 0 and 298 K are predicted for PF3, PF5, PF3O, SF2, SF4, SF6, SF2O, SF2O2, and SF4O as well as a number of radicals derived from these stable compounds on the basis of coupled cluster theory [CCSD(T)] calculations extrapolated to the complete basis set limit. In order to achieve near chemical accuracy (+/-1 kcal/mol), additional corrections were added to the complete basis set binding energies based on frozen core coupled cluster theory energies: a correction for core-valence effects, a correction for scalar relativistic effects, a correction for first-order atomic spin-orbit effects, and vibrational zero-point energies. The calculated values substantially reduce the error limits for these species. A detailed comparison of adiabatic and diabatic bond dissociation energies (BDEs) is made and used to explain trends in the BDEs. Because the adiabatic BDEs of polyatomic molecules represent not only the energy required for breaking a specific bond but also contain any reorganization energies of the bonds in the resulting products, these BDEs can be quite different for each step in the stepwise loss of ligands in binary compounds. For example, the adiabatic BDE for the removal of one fluorine ligand from the very stable closed-shell SF6 molecule to give the unstable SF5 radical is 2.8 times the BDE needed for the removal of one fluorine ligand from the unstable SF5 radical to give the stable closed-shell SF4 molecule. Similarly, the BDE for the removal of one fluorine ligand from the stable closed-shell PF3O molecule to give the unstable PF2O radical is higher than the BDE needed to remove the oxygen atom to give the stable closed-shell PF3 molecule. The same principles govern the BDEs of the phosphorus fluorides and the sulfur oxofluorides. In polyatomic molecules, care must be exercised not to equate BDEs with the bond strengths of given bonds. The measurement of the bond strength or stiffness of a given bond represented by its force constant involves only a small displacement of the atoms near equilibrium and, therefore, does not involve any reorganization energies, i.e., it may be more appropriate to correlate with the diabatic product states.     

Approximating coupled cluster level vibrational frequencies with composite methods

An extensive study of the harmonic frequencies of a large set of small polyatomic closed-shell molecules computed at both single level ab initio and composite approximations is presented here. Using various combinations of basis sets, composite methods are capable of predicting single level ab initio CCSD(T) harmonic frequencies to within 5 cm(-1) on average, which suggests a computationally affordable means of obtaining highly accurate vibrational frequencies compared to the CCSD(T) level. A general approach for calculating the composite level equilibrium geometries and harmonic frequencies for polyatomic systems that uses the Collin's method of interpolating potential energy surfaces is also described here. This approach is further tested on tetrafluoromethane, and an estimation of the potential CPU time savings that may be obtained is also presented. It is envisaged that the findings here will enable theoretical studies of fundamental frequencies and energetics of significantly larger molecular systems.     

Molecular electronegativity in density functional theory (VI)

Based on the density functional theory and partitioning the molecular electron density ρ (r) into atomic electronic densities and bond electronic densities, the expressions of the total molecular energy and the “effective electronegativity” of an atom or a bond in a molecule are obtained. The atom-bond electronegativity equalization model is then proposed for the direct calculation of the total molecular energy and the charge distribution of large molecules. Practical calculations show that the atom-bond electronegativity equalization model can reproduce the correspondingab initio values of the total molecular energies and charge distributions for a series of large molecules with a very satisfactory accuracy.     

First Principles Investigation of Noncovalent Complexation: A [2.2.2]‐Cryptand Ion‐Binding Selectivity Study

A first principles methodology, aimed at understanding the roles of molecular conformation and energetics in host–guest binding interactions, is developed and tested on a system that pushes the practical limits of ab initio methods. The binding behavior between the [2.2.2]‐cryptand host (4,7,13,16,21,24‐hexaoxa‐1,10‐diaza‐bicyclo[8.8.8]hexacosane) and alkali metal cations (Li⁺, Na⁺, and K⁺) in gas, water, methanol, and acetonitrile is characterized. Hartree–Fock and density functional theory methods are used in concert with crystallographic information to identify gas phase, energy‐minimized conformations. Gas phase free energies of binding, with vibrational contributions, are compared to solution‐state binding constants through relative binding selectivity analysis. Calculated relative binding free energies qualitatively correlated with solution state experiments only after gas phase metal desolvation is considered. The B3LYP exchange–correlation functional improves theoretical correlations with experimental relative binding free energies. The relevance of gas phase calculations towards understanding binding in condensed phases is discussed. Natural bond orbital methods highlights previously unidentified intramolecular and intermolecular M⁺(222) chemistries, such as an intramolecular n′_O→σ*_CH hydrogen bond.     

Binding energies of first row diatomics in the light of the interacting quantum atoms approach

Binding energies of first row diatomics are revisited within the interacting quantum atoms (IQA) approach. This is a formalism in chemical bonding theory based upon the quantum theory of atoms in molecules. It is characterized by the preservation of the energetic identity of atoms within molecules. Quantum mechanically computed binding energies are recovered in IQA as a sum of small atomic deformation energies and large pairwise interaction terms. We show how this partition responds faithfully to chemical intuition, and how the different evolution of deformations and interactions accounts in a unified manner for the subtle variations of the binding energy of these molecules.     

A distance-dependent parameterization of the extended Hubbard model for conjugated and aromatic hydrocarbons derived from stretched ethene

The Hubbard model, which is widely used in physics but is mostly unfamiliar to chemists, provides an attractive yet simple model for chemistry beyond the self consistent field molecular orbital approximation. The Hubbard model adds an effective electron-electron repulsion when two electrons occupy the same atomic orbital to the familiar Hückel Hamiltonian. Thus it breaks the degeneracy between excited singlet and triplet states and allows an explicit treatment of electron correlation. We show how to evaluate the parameters of the model from high-level ab initio calculations on two-atom fragments and then to transfer the parameters to large molecules and polymers where accurate ab initio calculations are difficult or impossible. The recently developed MS-RASPT2 method is used to generate accurate potential energy curves for ethene as a function of carbon-carbon bond length, which are used to parameterize the model for conjugated hydrocarbons. Test applications to several conjugated/aromatic molecules show that even though the model is very simple, it is capable of reasonably accurate predictions for bond lengths, and predicts molecular excitation energies in reasonable agreement with those from the MS-RASPT2 method.     

Calculation of absolute binding free energies for charged ligands and effects of long-range electrostatic interactions

A recently proposed molecular dynamics method for estimating binding free energies is applied to the complexation of two charged benzamidine inhibitors with trypsin. The difficulties with calculations of absolute binding energies for charged molecules, associated with long-range electrostatic contributions, are discussed and it is shown how to deal with these effectively. In particular, energetic effects caused by the trunction of dipole-dipole interactions in the medium surrounding the charged ligand are examined and found to be significant. Calculations of the absolute binding energy for benzamidine using the free energy perturbation approach are also reported. These simulations illustrate the typical problems associated with annihilation transformations of molecules bound inside proteins. © 1996 by John Wiley & Sons, Inc.     

Polyatomic,anharmonic, vibrational–rotational analysis. Application to accurate ab initio results for formaldehyde

A computer program SURVIB is described for calculating vibrational anharmonicity constants for polyatomic molecules. The program requires as input a grid of calculated energies in the vicinity of a stationary point. This grid is fit, in a least squares sense, to a polynomial function of the internal coordinates. This analytic representation of the energy surface is employed in a normal mode analysis, and the energy is reexpanded as a polynominal function of the normal mode coordinates (expressed as vectors in the mass-weighted atomic Cartesian coordinate space). The resulting coefficients are used in a second-order perturbation theory analysis to obtain the vibrational anharmonicity constants. Also reported is an application of this program to formaldehyde employing ab initio, RHF , MP 2, MP 3, and RHF -CI calculations. The spectroscopic constants obtained for H₂CO are in good agreement with experimentally derived values recently reported by Reisner.