Reduced basis set for the gold atom in cluster complexes

To extend the metal cluster size used in interfacing between bulk metals and molecules in ab initio studies of molecular electronics and chemisorption, a reduced size atomic orbital basis set for the gold atom has been generated. Based on the SKBJ relativistic effective core potential set, the three component 5d Gaussian orbital basis set is completely contracted. Comparisons between the full and reduced basis set in Au atom clusters and cluster complexes for geometry, bond distances, dipole moments, atomic charges, spin, bond dissociation energies, lowest energy harmonic frequencies, electron affinities, ionization energies, and density of states distributions show the contracted set to be a viable replacement for the full basis set. This result is obtained using both the B3LYP and BPW91 exchange-correlation potentials in density functional theory.     

Atomistic Model of Uranium

The electronic state and potential data of U₂ molecules are performed by first principle calculations with B3LYP hybrid exchange-correlation functional, the valence electrons of U atom are treated with the (5s4p3d4f)/[3s3p2d2f] contraction basis sets, and the cores are approximated with the relativistic effective core potential. The results show that the ground electronic state is X⁹∑⁺_g . The pair potential data are fitted with a Murrell-Sorbie analytical potential function. The U-U embedded atom method (EAM) interatomic potential is deter-mined based on the generalized gradient approximation calculation within the framework of the density functional theory using Perdew-Burke-Ernzerhof exchange-correlation functional at the spin-polarized level. The physical properties, such as the cohesive energy, the lattice constant, the bulk modulus, the shear modulus, the sc/fcc relative energy, the hcp/fcc rela-tive energy, the shear modulus and the monovacancy formation energy are used to evaluate the EAM potential parameters. The U-U pair potential determined by the first principle calculations is in agreement with that defined by the EAM potential parameters. The EAM calculated formation energy of the monovacancy in the fcc structure is also found to be in close agreement with DFT calculation.     

Design-atom approach for the quantum mechanical/molecular mechanical covalent boundary: a design-carbon atom with five valence electrons

A critical issue underlying the accuracy and applicability of the combined quantum mechanical/molecular mechanical (QM/MM) methods is how to describe the QM/MM boundary across covalent bonds. Inspired by the ab initio pseudopotential theory, here we introduce a novel design atom approach for a more fundamental and transparent treatment of this QM/MM covalent boundary problem. The main idea is to replace the boundary atom of the active part with a design atom, which has a different number of valence electrons but very similar atomic properties. By modifying the Troullier-Martins scheme, which has been widely employed to construct norm-conserving pseudopotentials for density functional calculations, we have successfully developed a design-carbon atom with five valence electrons. Tests on a series of molecules yield very good structural and energetic results and indicate its transferability in describing a variety of chemical bonds, including double and triple bonds.     

Criteria for aromaticity of mesoionic heterocycles

The quantum chemical calculations of the basic criteria for aromaticity (nucleus-independent chemical shift (NICS), aromatic stabilization energy (ASE), and parameters of harmonic oscillator model of aromaticity (HOMA), and geometric indices (I ₅)) of 54 mesoionic heterocycles in the 6–31G* split-valence basis set were performed in terms of the density functional theory (DFT) with the B3LYP exchange-correlation hybrid functional. The aromatic nature of the mesoionic heterocycles containing the pyridinium N atom was shown.     

Comparative theoretical investigation of the vertical excitation energies and the electronic structure of [MoVOCl4]-: influence of basis set and geometry

The electronic structures, geometries, and vibration frequencies of the open-shell molybdenum(V) ion, [MoOCl(4)](-), have been calculated at the extended Hückel, semiempirical ZINDO/1, ZINDO/S, and PM3(tm), as well as ab initio and DFT theoretical levels. Electronic structure calculations suggest that the expected metal-fold orbital order can be satisfied only at the DFT level. The time-dependent density functional theory (TDDFT) approach has been used for the calculation of the vertical excitation energies in the UV-vis region with different basis sets, starting geometries, and exchange-correlation functionals. A good agreement between the predicted and the experimental electronic absorption and MCD spectra of the complex, [MoOCl(4)](-), was observed when the B3LYP and B3P86 exchange-correlation functionals were used with a full electron valence double-zeta with polarization basis set for the molybdenum and 6-311G(d) for all other atoms. Similar results were obtained when the LANL2DZ effective core potential for molybdenum atom and 6-31G(d) for all other atoms were used. The best absolute deviation of 0.13 and mean deviation of 0.01 eV were calculated for the bands in the UV-vis region by B3P86, while the results for the B3LYP exchange-correlation functional were less satisfactory. Compared to polarization functions, the inclusion of diffuse functions resulted in little improvement. The calculated excitations energies and charge-transfer band intensities are found to be sensitive to the Mo=O distance and O-Mo-Cl angle.     

Importance of selecting proper basis set in quantum mechanical studies of potential energy surfaces of carbohydrates

An extensive quantum mechanical study of a water dimer suggests that the introduction of a diffuse function into the basis set, which significantly reduces the basis set superposition error (BSSE) in the hydrogen bonding energy calculation, is the key to better calculations of the potential energy surfaces of carbohydrates. This article examines the potential energy surfaces of selected d -aldo- and d -ketohexoses (a total of 82 conformers) by quantum mechanics (QM) and molecular mechanics (MM) methods. In contrast to the results with a smaller basis set (B3LYP/6-31G** 5d), we found at the higher level calculation (B3LYP/6-311++G(2d,2p)//B3LYP/6-31G** 5d) that, in most cases, the furanose forms are less stable than the pyranose forms. These discrepancies are mainly due to the fact that intramolecular hydrogen bonding energies are overestimated in the lower level calculations. The higher level QM calculations of the potential energy surfaces of d -aldo- and d -ketohexoses now are more comparable to the MM3 results. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1593–1603, 1999     

Generalized hybrid orbital for the treatment of boundary atoms in combined quantum mechanical and molecular mechanical calculations using the semiempirical parameterized model 3 method

The application of combined quantum mechanical (QM) and molecular mechanical methods to large molecular systems requires an adequate treatment of the boundary between the two approaches. In this article, we extend the generalized hybrid orbital (GHO) method to the semiempirical parameterized model 3 (PM3) Hamiltonian combined with the CHARMM force field. The GHO method makes use of four hybrid orbitals, one of which is included in the QM region in self-consistent field optimization and three are treated as auxiliary orbitals that do not participate in the QM optimization, but they provide an effective electric field for interactions. An important feature of the GHO method is that the semiempirical parameters for the boundary atom are transferable, and these parameters have been developed for a carbon boundary atom consistent with the PM3 model. The combined GHO-PM3/CHARMM model has been tested on molecular geometry and proton affinity for a series of organic compounds.Acknowledgement We thank the National Institutes of Health for support of this research.Contribution to the Jacopo Tomasi Honorary Issue     

Grid‐based density functional calculations of many‐electron systems

Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many‐electron systems in the 3D cartesian coordinate grid (CCG). The atom‐centered localized gaussian basis set, electronic density, and the two‐body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange‐correlation potential, while Hay‐Wadt‐type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, and atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom‐centered grid as well as the grid‐free calculation. Results for three atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many‐electron systems. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

A theoretical study of the mechanism of the nucleotidyl transfer reaction catalyzed by yeast RNA polymerase II

The mechanism of the nucleotidyl transfer reaction catalyzed by yeast RNA polymerase II has been investigated using molecular mechanics and quantum mechanics methods.Molecular dynamics(MD) simulations were carried out using the TIP3 water model and generalized solvent boundary potential(GSBP) by CHARMM based on the X-ray crystal structure.Two models of the ternary elongation complex were constructed based on CHARMM MD calculations.All the species including reactants,transition states,intermediates,and products were optimized using the DFT-PBE method coupled with the basis set DZVP and the auxiliary basis set GEN-A2.Three pathways were explored using the DFT method.The most favorable reaction pathway involves indirect proton migration from the RNA primer 3’-OH to the oxygen atom of-phosphate via a solvent water molecule,proton rotation from the oxygen atom of-phosphate to the-phosphate side,the RNA primer 3’-O nucleophilic attack on the-phosphorus atom,and P-O bond breakage.The corresponding reaction potential profile was obtained.The rate limiting step,with a barrier height of 21.5 kcal/mol,is the RNA primer 3’-O nucleophilic attack,rather than the commonly considered proton transfer process.A high-resolution crystal structure including crystallographic water molecules is required for further studies.     

醋酸铀酰负离子气相分解反应的密度泛函理论研究

采用密度泛函理论(DFT), 选择杂化密度泛函TPSSh和TZVP基组, 对一个UO₂(CO₃)₃^4-负离子的结构进行优化, 理论计算所得结果(键长等参数)与实验数据一致. 应用TPSSh/TZVP(ECP)方法对醋酸铀酰负离子UO₂(CH₃COO)₃^-的气相分解反应进行了理论计算, 成功地解释了含+5价铀的气相自由基负离子的稳定性, 并对2个负离子(CH₃COO)UO₂CH₃^-和CH₃UO₂OH^-分别与水的复分解反应进行了理论计算, 所得数据与质谱的实验结果较好地吻合.     

A quantum mechanical/molecular dynamics/mean field study of acrolein in aqueous solution: analysis of H bonding and bulk effects on spectroscopic properties

A novel molecular dynamics methodology recently proposed by our group [Rega et al., Chem. Phys. Lett. 422, 367 (2006)], which is based on an integrated hybrid potential rooted in high level quantum mechanical methods using localized basis functions and nonperiodic boundary conditions, has been applied to study acrolein in aqueous solution. The solute structural rearrangement and its hydrogen-bonding pattern due to the interactions with water have been analyzed in some detail. Moreover, the solvent effects on the UV n-->pi* vertical transition and on the NMR 13C and 17O shielding constants of acrolein have been investigated theoretically by performing a posteriori quantum mechanical calculations on a statistically significant number of snapshots extracted from both gas-phase and aqueous solution simulations. Results show that such effective computational strategy can be successfully used to improve our understanding, at atomic level, of important spectroscopic observables.     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

Quantum crystallography applied to crystalline maleic anhydride

Quantum crystallography (QCr) is a term that concerns techniques for using crystallographic information to enhance quantum mechanical calculations and the information derived from them. In our approach to QCr, we use molecular orbitals and a single‐determinant density matrix formalism to develop a quantum mechanical model. Our initial application to a test material, crystalline maleic anhydride, involved the adjustment of the elements in the density (projector) matrix and some others in the quantum mechanical model. The purpose was to optimize the fit between the experimental structure factor magnitudes and the values of those magnitudes obtained from the quantum mechanical model. The adjustment of the projector matrix preserved the idempotency and normalization properties of the matrix. In this application, it was also found that it was necessary to correct the X‐ray diffraction data for systematic errors. An effective statistical method for doing this was developed from quantum mechanical theory. There were a number of special features of this investigation that emerged as it progressed. The mirror plane in maleic anhydride, for example, was quite useful because, in the absence of significant interactions between the molecules in the crystal, charge distributions on both sides of the mirror plane should be essentially the same. Deviations raised questions that resulted in improved procedures. The quality of theoretical results as a function of basis set and mode of calculation is also part of this investigation. One result of the information obtained from various aspects of this study is the potential for greater efficiency in the procedures and calculations. The calculations for maleic anhydride based on its structure concern the number of electrons per atom, various energies, and electron density contours. Related theoretical calculations based on geometry optimization were also made. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 439–450, 1999     

On effective potentials in classical mechanical systems

A classical mechanical variational method for computing effective potentials due to exact, first order and adiabatic constraints is presented. The effective potential can be used to envision in configuration space the restricted motion imposed by the constraints relative to the full potential. It can locate effective equilibrium structures and transition barriers and saddles and can be used when combined with semi-classical ideas to delineate regions of quantum packet flow and stationary state localization. The latter gives information on energy flow in a system and on the nature of basis sets needed for full quantum calculations. The advantage of the method is that is does not involve the solution of any equations of motion. The ideas are illustrated by some examples coming from the area of atomic and molecular dynamics.     

An efficient methodology to study cyclodextrin clusters: application to α-CD hydrated monomer, dimer, trimer and tetramer

The hydrated α-cyclodextrin (α-CD) clusters resulting from the following process: nα-CD + n(H₂O)₆ → α-CD_n · 6nH₂O, with n = 1, 2, 3, 4, have been investigated using semiempirical (PM3), ab initio Hartree-Fock and Density Functional Theory (BLYP functional) levels of theory. The largest structure containing 576 atoms and 5,760 contracted basis functions (6-31G(d,p) basis set) poses as a considerable hard task for quantum chemical calculations. As the number of basis function increases rapidly with the cluster size, an alternative procedure to make the calculations feasible is certainly welcome, in order to perform BLYP calculations with an adequate basis set. Through the aid of a computer program that we developed, it became of practical use the selection of atom by atom basis sets, using the common chemical sense, enabling quantum mechanical calculations to be performed for very large molecular interacting systems (inclusion complexes), at an affordable computational cost. In this article we show how an appropriate selection of basis functions, leaving the CH_n groups with a minimal basis set and the oxygen atoms (and OH groups) with a better quality basis set, lower considerably the computational cost with no significant loss in the calculated interaction energies. A regular pattern is observed for α-CD hydrated monomer, dimer, trimer and tetramer, therefore adding support to the use of this procedure when studying larger hydrogen bonded clusters where electron correlation effects are important. We show that the procedure reported here enables DFT calculations for hydrated cyclodextrin using basis set up to the 6-311++G(3df,3pd) triple zeta quality .     

The exchange-correlation potential in ab initio density functional theory

From coupled-cluster theory and many-body perturbation theory we derive the local exchange-correlation potential of density functional theory in an orbital dependent form. We show the relationship between the coupled-cluster approach and density functional theory, and connections and comparisons with our previous second-order correlation potential [OEP-MBPT(2) (OEP-optimized effective potential)] [I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, J. Chem. Phys. 116, 4415 (2002)]. Starting from a general theoretical framework based on the density condition in Kohn-Sham theory, we define a rigorous exchange-correlation functional, potential and orbitals. Specifying initially to second-order terms, we show that our ab initio correlation potential provides the correct shape compared to those from reference quantum Monte Carlo calculations, and we demonstrate the superiority of using Fock matrix elements or more general infinite-order semicanonical transformations. This enables us to introduce a method that is guaranteed to converge to the right answer in the correlation and basis set limit, just as does ab initio wave function theory. We also demonstrate that the energies obtained from this generalized second-order method [OEP-MBPT2-f] and [OEP-MBPT2-sc] are often of coupled-cluster accuracy and substantially better than ordinary Hartree-Fock based second-order MBPT=MP2.     

Quantum mechanical polarizable force field (QMPFF3): refinement and validation of the dispersion interaction for aromatic carbon

The authors have recently introduced a general, polarizable force field QMPFF fitted solely to high-level quantum mechanical data for simulations of biomolecular systems. Here the authors demonstrate using an advanced version QMPFF3 how the problem of insufficient accuracy of the MP2-based training set for the aromatic carbon atom type can be effectively solved by a simple model correction using state-of-the-art CCSD(T) data. The approach demonstrates excellent transferability, which is confirmed for three phases of matter by accurate calculations of the second virial coefficient for benzene vapor and various properties of liquid benzene and polyaromatic hydrocarbon crystals.