Ab initio correlation corrections to the Hartree-Fock quasi band-structure of periodic systems employing Wannier-type orbitals

A size-consistent ab initio formalism to calculate correlation corrections to ionization potentials as well as electron affinities of periodic systems is presented. Our approach is based on a Hartree-Fock scheme which directly yields local orbitals without any a posteriori localization step. The use of local orbitals implies non-zero off-diagonal matrix elements of the Fock operator, which are treated as an additional perturbation and give rise to localization diagrams. Based on the obtained local orbitals, an effective Bloch Hamiltonian is constructed to second order of perturbation theory with all third-order localization diagrams included. In addition, the summation of certain classes of diagrams up to infinite order in the off-diagonal Fock elements as well as the Epstein-Nesbet partitioning of the full Hamiltonian are discussed. The problem of intruder states, frequently encountered in many-body perturbation theory, is dealt with by employing the theory of intermediate Hamiltonians. As model systems we have chosen cyclic periodic structures up to an oligoethylene ring in double-zeta basis; however, the theory presented here straightforwardly carries over to infinite periodic systems. Received: 30 April 1998 / Accepted: 27 July 1998 /  Published online: 7 October 1998     

Adsorption of styrene on micron-sized, monodisperse, cross-linked polymer particles in a snowman-shaped state by utilizing the dynamic swelling method

Polystyrene/styrene–divinylbenzene copolymer composite particles with different cross-linking densities were produced by seeded copolymerization for (styrene/divinylbenzene)-swollen polystyrene particles prepared by utilizing the dynamic swelling method (DSM) which was proposed by the authors in 1991. Using the cross-linked, composite particles as seeds, styrene-adsorbed (swollen) composite particles having snowman shapes were prepared by the DSM. With a decrease in the cross-linking density in the composite particles, the volume of the composite particle which was embedded in a spherical styrene phase in the snowman-shaped, styrene-adsorbed particle increased and the contact angle of the styrene phase on the composite particle decreased. In the DSM process, the absorption stage of styrene in the composite particles and the adsorption stage thereon were clearly observed. This suggests that the cross-linking density of the composite particles greatly affects the morphology of the snowman-shaped particles. Received: 13 December 2000 Accepted: 14 March 2001     

Adsorption of neutral polymers on negatively charged liposomes. A novel quantitative method to measure the rate of polymer adsorption on the liposomal surface

We studied the adsorption of two neutral polymers [poly(vinyl pyrrolidone) and poly(vinyl alcohol) (PVA)] on negatively charged liposomes composed of 25:2:3 (molar ratio) soy lecithin/dicetyl phosphate/cholesterol.The liposomes were prepared in buffered solution at pH 7.4 and were mixed with the solution of the polymers in the desired polymer/lipid ratios. Adsorption was measured by determination of the equilibrium bulk concentration of the polymer. Protamine hydrochloride was used to aggregate the liposomes with polymers adsorbed on their surface and to facilitate their separation from the equilibrium bulk solution. In the case of PVA, quantitative adsorption measurements with a specific reagent were possible. Adsorption isotherms were recorded at 25 ± 0.2 °C. It was concluded that adsorbed and nonadsorbed PVA molecules are in equilibrium even at low polymer/lipide ratios. The results were confirmed by dynamic laser light scattering, X-ray diffraction and thermal activity monitoring experiments. Received: 13 October 2000 Accepted: 8 March 2001     

Effect of amorphous precipitated silica on the properties and structure of poly(p-phenylene sulfide)

Using a precipitation technique, silicas were obtained from sodium metasilicate solution employing an acidic agent. Alcohol solutions were used in the process of production of highly dispersed silicas, which resulted in partial blocking of the silica surface silanol groups. Moreover, studies on morphology and microstructure using transmission electron microscopy and scanning electron microscopy were performed. The size distributions of primary particles and aggregate and agglomerate structures were determined using a ZetaPlus instrument using the dynamic light scattering method. The structure and molecular dynamics of the nanocomposite, consisting of poly (p-phenylene sulfide) (PPS) and of the precipitated silica, were studied using atomic force microscopy and nuclear magnetic resonance. It was proved that during annealing the fragmentation of PPS agglomerates takes place. This phenomena probably resulted from repulsion forces existing between agglomerates and aggregates. Fragmentation in the polymer network probably resulted from repulsion forces between agglomerates and smaller aggregates. Received: 7 November 2000 Accepted: 5 April 2001     

Cyanovinyl radical: an illustration of the poor performance of unrestricted perturbation theory and density functional theory procedures in calculating radical stabilization energies

Stabilization energies for the 1-cyanovinyl radical (CH₂=CCN) have been calculated using a variety of conventional ab initio (M?ller–Plesset, quadratic configuration interaction and coupled-cluster) and density functional theory (B-LYP, B3-LYP) procedures, as well as with a range of compound methods. Compared with a high-level benchmark value (that predicts a stabilization energy of 17.1 kJ mol⁻¹), UMP2 and UMP4 give the wrong sign and magnitude of the stabilization energy (both methods predicting desta- bilization instead of stabilization), while B-LYP and B3-LYP overestimate the degree of stabilization. The RMP2, RMP4, QCISD(T) and CCSD(T) techniques, and several, but not all, variants of G2 and CBS theories give radical stabilization energies in good agreement with the benchmark value. Received: 15 June 1998 / Accepted: 19 August 1998 /  Published online: 15 February 1999     

Efficient electronic structure calculations for systems of one-dimensional periodicity with the restricted Hartree–Fock–linear combination of atomic orbitals method implemented in Fourier space

 Formulas are presented for restricted Hartree–Fock (RHF) calculations on systems with periodicity in one dimension using a basis set of contracted spherical Gaussians. Applying Fourier-space and Ewald-type methods, all lattice sums appearing in the formulation have been brought to forms exhibiting accelerated convergence. Calculations have been carried out for infinite chains of Li₂ molecules and a poly(oxymethylene) chain. The methods used here yield results that are far more precise than corresponding direct-space calculations and for the first time show the vanishing of the RHF density of states at the Fermi level for situations of partial band occupancy. Our initial computational implementation was about 5 times slower than the fastest direct-space RHF code, but improvements in special-function evaluations and numerical integrations over the Brillouin zone are shown to remove this disparity in computing speed. Received: 20 August 1999 / Accepted: 17 January 2000 / Published online: 5 June 2000     

Radial electron-pair densities in momentum space and shell structure of atoms

 The radial electron-pair intracule (relative motion) H(u) and extracule (center-of-mass motion) D(R) densities in position space were known to reveal four types of maxima which are related to the four inner electron shells, K, L, M, and N, of atoms. The corresponding radial electron-pair intracule Hˉ(v) and extracule Dˉ(P) densities in momentum space are studied for the 102 atoms from He (atomic number Z=2) to Lr (Z=103). The densities Hˉ(v) and Dˉ(P) are found to have either one maximum or two maxima, and the numbers of maxima in Hˉ(v) and Dˉ(P) are the same for 98 atoms. For these atoms, the locations υ _max and P _max and the heights Hˉ _max and Dˉ _max of the corresponding maxima satisfy the approximate relations υ _max ≅ 2P _max and Hˉ _max ≅Dˉ _max /2. On the basis of their Z-dependence, the maxima in Hˉ(v) and Dˉ(P) of the 102 atoms are classified into five types. Shell-pair decompositions of the radial densities show that these maxima reflect five outer electron shells of atoms. Received: 24 January 2001 / Accepted: 12 March 2001 / Published online: 13 June 2001     

Structure and stabilities of (HA1NH)n (n = 2–4)

Ab initio molecular electronic structure methods have been used to study the relative stability of the planar inorganic ring (HAlNH)_n (n = 2–4) during homodesmotic and monomer polymerization reactions. Optimized geometries, frequencies and energies through restricted Hartree-Fock/6-31G* are reported, and energies at the self-consistent field optimized geometries including M?ller-Plesset fourth perturbation theory with single, double and quadruple excitation (MP4SDQ) corrections are also reported for both reactions. Homodesmotic reactions with MP4SDQ −28.5 kcal/mol for (AlN)₂, 1.9 kcal/mol for (AlN)₃ and −0.97 kcal/mol for (AlN)₄. On analysing a π-molecular orbitals diagram, only one, three and three strongly bonding π-molecular orbitals exist for the planar four-, six- and eight-membered AlN rings, respectively. Received: 9 March 1998 / Accepted: 19 March 1998 / Published online: 23 June 1998     

The pellicular monolith: pore-surface functionalization and surface-phase construction in macroporous polymeric materials

We report synthesis and characterization of a macroporous polymeric material containing a covalently immobilized pore-surface phase of well-defined thickness, gel-phase porosity and organic functional group content. The pore surfaces of otherwise inert macroporous (32 μm mean pore size) ultrahigh-molecular-weight polyethylene (UHMWPE) are aminated throughout using a low-pressure flowing-discharge process to enable covalent immobilization of lightly cross-linked polymer colloid particles on all pore surfaces in the monolith. Solvent swelling and chemical derivitization of the covalently immobilized polymer colloid particles produce a pore-surface gel phase of well-defined thickness, organic amine content, and gel-phase porosity. The low degree of cross-linking in the polymer colloid particles prevents dissolution of the immobilized colloid in good solvents and enables the formation of pore-surface gel phases having high gel porosity on swelling in good solvents. The pore-surface amination introduced by the flowing discharge process varies by less than 17% through 5-mm thickness of the macroporous UHMWPE material. The properties of the pore-surface gel phase also vary by less than 17% through the cross section. The pore-surface immobilized polymer colloid particles swell by a factor of 10 in water and tetrahydrofuran after derivitization with polyethylene glycol. Received: 20 November 1998 Accepted in revised form: 21 January 1999     

The inclusion of electron correlation in intermolecular potentials: applications to the formamide dimer and liquid formamide

A test of the quality of the electrostatic properties and polarizabilities used in the nonempirical molecular orbital (NEMO) potential is carried out for formamide by calculating the molecular dipole moment and polarizability at the second-order M?ller–Plesset (MP2) level of theory. The molecular dipole moment is 11% lower at the MP2 level than at the Hartree–Fock (HF) level, whereas the isotropic part of the polarizability is increased by 36% by adding electron correlation and using a considerably larger basis set. The atomic charges, dipole moments and polarizabilities obtained at the HF level are rescaled to get the correct molecular properties at the MP2 level. The potential minimum for the cyclic dimer of formamide is −17.50 kcal/mol with the MP2-scaled properties and is significantly lower than other potentials give. Two intermolecular potentials are constructed and used in subsequent molecular dynamics simulations: one with the regular NEMO potential and the other with the rescaled MP2 properties. A damping of the electrostatic field at short intermolecular distances is included in the present NEMO model. The average energies for liquid formamide are lower for the MP2-scaled model and are in good agreement with experimental results. The lowering of the simulation energy for the MP2-scaled potential indicates the strong dispersive interactions in liquid formamide. Received: 20 March 2000 / Accepted: 18 April 2000 / Published online: 18 August 2000     

The performance of the rapid estimation of basis set error and correlation energy from partial charges method on new molecules of the G3/99 test set

Experimental enthalpies of formation have been approximated using single-point Hartree–Fock (HF)–self-consistent-field (SCF) total energies plus the rapid estimation of basis set error and correlation energy from partial charges (REBECEP) energy corrections. The energy corrections are calculated from the HF–SCF partial atomic charges and optimized atomic energy parameters. The performance of the method was tested on 51 closed-shell neutral molecules (50 molecules from the G3/99 thermochemistry database plus urea, composed of H, C, N, O, and F atoms). The predictive force of the method is demonstrated, because these larger molecules were not used for the optimization of the atomic parameters. We used the earlier RECEP-3 [HF/6-311+G(2d,p)] and REBECEP [HF/6-31G(d)] atomic parameter sets obtained from the G2/97 thermochemistry database (containing small molecules) together with natural population analysis and Mulliken partial charges. The best results were obtained using the natural population analysis charges, although the Mulliken charges also provide useful results. The root-mean-square deviations from the experimental enthalpies of formation for the selected 51 molecules are 1.15, 3.96, and 2.92 kcal/mol for Gaussian-3, B3LYP/6-11+G(3df,2p), and REBECEP (natural population analysis) enthalpies of formation, respectively (the corresponding average absolute deviations are 0.94, 7.09, and 2.27 kcal/mol, respectively). The REBECEP method performs considerably better for the 51 test molecules with a moderate 6-31G(d) basis set than the B3LYP method with a large 6-311+G(3df,2p) basis set. Received: 10 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001     

A variationally stable quasi-relativistic method: low-order approximation to the normalized elimination of the small component using an effective potential

A simple and variationally stable quasi-relativistic method based on a modified low-order (LO) approximation to the normalized elimination of the small component (NESC) method is presented. The modification of the original LO-NESC scheme implies the use of an energy-independent factor in the relativistic correction to the potential energy. This factor cuts off the potential energy at short distances from the nucleus and in this way restores the variational stability of LO-NESC. The new method, dubbed LO-NESC-effective potential (EP) was tested in calculations on one-, two- and many-electron atoms. The LO-NESC-EP can be easily implemented into the existing nonrelativistic quantum-chemical program codes because its Hamiltonian matrix can be expressed entirely in terms of the integrals appearing in a nonrelativistic calculation. Received: 1 April 2002 / Accepted: 23 June 2002 / Published online: 30 August 2002     

Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase

 A replica path method has been developed and extended for use in complex systems involving hybrid quantum/classical (quantum mechanical/molecular mechanical) coupled potentials. This method involves the definition of a reaction path via replication of a set of macromolecular atoms. An “important” subset of these replicated atoms is restrained with a penalty function based on weighted root-mean-square rotation/translation best-fit distances between adjacent (i±1) and next adjacent (i±2) pathway steps. An independent subset of the replicated atoms may be treated quantum mechanically using the computational engine Gamess-UK. This treatment can be performed in a highly parallel manner in which many dozens of processors can be efficiently employed. Computed forces may be projected onto a reference pathway and integrated to yield a potential of mean force (PMF). This PMF, which does not suffer from large errors associated with calculated potential-energy differences, is extremely advantageous. As an example, the QM/MM replica path method is applied to the study of the Claisen rearrangement of chorismate to prephenate which is catalyzed by the Bacillus subtilis isolated, chorismate mutase. Results of the QM/MM pathway minimizations yielded an activation enthalpy ΔH ^†† of 14.9 kcal/mol and a reaction enthalpy of −19.5 kcal/mol at the B3LYP/6-31G(d) level of theory. The resultant pathway was compared and contrasted with one obtained using a forced transition approach based on a reaction coordinate constrained repeated walk procedure (ΔH ^†† =20.1 kcal/mol, ΔH _rxn = −20.1 kcal/mol, RHF/4-31G). The optimized replica path results compare favorably to the experimental activation enthalpy of 12.7±0.4 kcal/mol. Received: 16 December 2001 / Accepted: 6 September 2002 / Published online: 8 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 22nd National Meeting of the American Chemical Society, 2001. Correspondence to: H.L. Woodcock e-mail: hlwood@ccqc.uga.edu Acknowledgements. The authors thank Eric Billings, Xiongwu Wu, and Stephen Bogusz for helpful discussions and related work. The authors also show grateful appreciation to The National Institutes of Health and The National Science Foundation for support of the current research.     

A new method for modelling spectator chemical groups in ab initio calculations: effective group potentials

 A new method for an increased numerical efficiency of ab initio calculations is proposed. It is based on the assumption that in most cases chemical properties of functional groups in molecules are mainly controlled by a few electrons. This statement allows one to distinguish between two classes of nuclei and electrons: active and inactive ones. The effective group potential (EGP) method presupposes that the effect of inactive electrons in a functional chemical group can be described by a pseudopotential, in the same way that core electrons are replaced by effective core potentials in atoms. It is shown that EGPs are able to predict chemical and structural features of the active part of a molecule and at a fraction of the ordinary computational cost. The preliminary results reported here concern the determination of EGPs for ammonia, the methyl radical and the cyclopendadienyl ligand, which represent different types of bonding. Received: 15 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Investigation of the S<Subscript>0</Subscript>S<Subscript>1</Subscript> excitation in bacteriorhodopsin with the ONIOM(MO:MM) hybrid method

 We have investigated the S₀ and S₁ electronic states in bacteriorhodopsin using a variety of QM/MM levels. The decomposition of the calculated excitation energies into electronic and electrostatic components shows that the interaction of the chromophore with the protein electric field increases the excitation energy, while polarization effects are negligible. Therefore, the experimentally observed reduction in excitation energy from solution phase to protein environment (the Opsin shift) does not come from the electrostatic interaction with the protein environment, but from either the interaction ofthe chromophore with the solvent or counter ion, or structural effects. Our high-level ONIOM(TD– B3LYP:Amber) calculation predicts the excitation energy within 8 kcal/mol from experiment, the discrepancy probably being caused by the neglect of polarization of the protein environment. In addition, we have shown that the level of optimization is extremely critical for the calculation of accurate excitation energies in bacteriorhodopsin. Received: 13 October 2001 / Accepted: 6 September 2002 / Published online: 3 February 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 222nd National Meeting of the American Chemical Society, 2001 Correspondence to: K. Morokuma e-mail: morokuma@emory.edu     

The fundamental nature and role of the electrostatic potential in atoms and molecules

 A variety of atomic and molecular properties can be expressed in terms of the electrostatic potential. These include energies, covalent and anionic radii, electronegativities (chemical potentials) and a variety of properties that depend upon noncovalent interactons. We present a survey of such relationships, which may be exact or approximate; they may involve the potential in three-dimensional space, along the axes between bonded atoms, at nuclei or on molecular surfaces. Thus, the electrostatic potential, which is rigorously related to the electronic density by Poisson's equation, can be regarded as, effectively, another fundamental determinant of atomic and molecular properties. Received: 6 March 2002 / Accepted: 15 May 2002 / Published online: 29 July 2002     

Isotope effect of hydrogen and lithium hydride molecules. Application of the dynamic extended molecular orbital method and energy component analysis

In order to explore the isotope effect including the nuclear–electronic coupling and nuclear quantum effects under the one-particle approximation, we apply the dynamic extended molecular orbital (DEMO) method and energy component analysis to the hydrogen and lithium hydride isotope molecules. Since the DEMO method determines both electronic and nuclear wave functions simultaneously by variationally optimizing all parameters embedded in the basis sets, the virial theorem is completely satisfied and guarantees the relation of the kinetic and potential energies. We confirm the isotope effect on internuclear distances, nuclear and electronic wave functions, dipole moment, the polarizability, and each energy component. In the case of isotopic species of the hydrogen molecule, the total energy decreases from the H₂ to the T₂ molecule due to the stabilization of the nuclear–electronic potential component, as well as the nuclear kinetic one. In the case of the lithium hydride molecule, the energy lowering by replacing ⁶Li with ⁷Li is calculated to be greater than that by replacing H with D. This is mainly caused by the small destabilization of electron–electron and nuclear–nuclear repulsion in ⁷LiH compared to ⁶LiH, while the change in the repulsive components from ⁶LiH to ⁶LiD increases. Received: 24 March 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999     

Role of twisting and sliding on the solvation of a stacked cytosine dimer: an ab initio study

Ab initio calculations with inclusion of correlation effects at the MP2/6-31G* level have been used to predict the interaction energy of stacked cytosine dimer (C/C) as a function of twisting and sliding in the gas phase. Systematic calculations have also been carried out on the solvation free energies of various rotated and translated C/C dimers using a polarized continuum model approach at the HF/6-31G* level with a view to probe the role of various degrees of freedom on the free energy of solvation of the C/C dimer. The interaction energy of the C/C dimer decreases upon changing from a parallel to an antiparallel conformation in the gas phase. The 180°-rotated conformation has been found to be the most stable arrangement when compared to other rotated positions. The rotated and translated dimers exhibit lower solvation free energy than the parallel conformation. The decrease in the dipole moment upon rotation from the parallel to the antiparallel conformation indicates the cancellation of charge distribution upon rotation in the z direction of one cytosine base with respect to the other. The calculation reveals that the present approach could not yield association energy, ΔΔG _Asso, in a solvent medium. This may be due to the fact that in the case of floppy molecules the contribution from translational, rotational and vibrational free energies plays a significant role in the calculation of ΔΔG _Asso. Received: 13 December 2001 / Accepted: 25 March 2002 / Published online: 13 June 2002