The unrestricted natural orbital-restricted active space method: methodology and implementation

The full configuration interaction method in the space of fractionally occupied unrestricted natural orbitals (UNO-CAS method) is extended to excited states as well as to strongly correlated and reactive systems with large active spaces. This is accomplished by␣using restricted active space (RAS) wave functions introduced by Olsen et al. [(1988) J Chem Phys 89: 2185] and using the UNOs without the expensive orbital optimization step. In RAS, the space of active orbitals is subdivided into three groups: a group with essentially doubly occupied orbitals (RAS1), the usual CAS space (RAS2), and a space with weakly occupied active orbitals (RAS3). We select these spaces on the basis of the occupation numbers of the UNOs. All possible electron distributions are allowed in the usual CAS space, but the number of vacancies is limited in RAS1 and the number of electrons is limited in RAS3. We discuss an efficient algorithm for generating a RAS wave function. This is based on the Handy-Knowles determinantal expansion with an addressing scheme adopted for the restricted expansion. Results for both ground and excited states of azulene and free base porphyrin are presented. Received: 16 July 1998 / Accepted: 7 August 1998 / Published online: 19 October 1998     

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     

Gradient of the ZAPT2 energy

 An explicit expression for the analytical first derivative of the Z-averaged perturbation theory taken to second order energy, due to Lee and Jayatilaka, is presented for application to high-spin systems described by a restricted open-shell Hartree–Fock wavefunction. The use of frozen core orbitals is incorporated into the derivation. Received: 23 April 2001 / Accepted: 31 August 2001 / Published online: 9 January 2002     

Dressed coupled-electron-pair-approximation methods for periodic systems

 The techniques of matrix dressing for configuration-interaction (CI)-type or coupled-electron-pair-approximation (CEPA)-type correlation treatments are reviewed with respect to the application to periodic systems. All methods ranging from canonical second-order M?ller–Plesset perturbation theory over CI of single and double excitation, CEPA-0 or the averaged-coupled-pair-functional to self-consistent size-consistent CI can be formulated completely equivalently as an eigenvalue problem or as a solution to a system of linear equations. The size consistency of each method is obtained in a natural way, and invariance under orbital rotations is clearly assessible. A remark on the size consistency of the Davidson correction is presented. Additionally, the direct generation of localized Hartree–Fock orbitals as basic ingredients for the correlation calculations are addressed, as well as selected results on ring molecules, polymers, and 3D cubic beryllium as a model crystal. Received: 28 August 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000     

An overlap criterion for selection of core orbitals

 An overlap criterion is defined that connects the identification of core orbitals in a molecular system, which can be problematic, to that in isolated atoms, which is well defined. This approach has been tested on a variety of troublesome systems that have been identified in the literature, including molecules containing third-row main-group elements, and is shown to remove errors of up to 100 kcal/mol arising from an inconsistent treatment of core orbitals at different locations on a potential-energy surface. For some systems and choices of core orbitals, errors as large as 19 kcal/mol can be introduced even when consistent sets of orbitals are frozen, and the new method is shown to identify these cases of substantial core–valence mixing. Finally, even when there is limited core–valence mixing, the frozen-core approximation can introduce errors of more than 5 kcal/mol, which is much larger than the presumed accuracy of models such as G2 and CBS-QB3. The source of these errors includes interatomic core–core and core–valence dispersion forces. Received: 31 August 2001 / Accepted: 11 October 2001 / Published online: 9 January 2002     

Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 2002     

Electrochemical redox reactions studied in frozen tetrabutylammonium halide hydrates

The electrochemical redox reactions: Fe(CN)₆ ⁴⁻−e⁻↔ Fe(CN)₆ ³⁻, Ru(NH₃)₆ ³⁺+e⁻↔ Ru (NH₃)₆ ²⁺ and Fc(CH₂OH)₂−e⁻↔ Fc(CH₂OH)₂ ⁺ (Fc–ferrocene) were investigated in tetrabutylammonium halide hydrates at temperatures below and above the electrolyte melting point. They were studied by cyclic voltammetry, potential step chronoamperometry and impedance spectroscopy. Freezing of the electrolyte affects both the shape and position of the cyclic voltammogram on the potential scale. Also the shapes of the current-time relationship and the impedance spectra change at temperatures below the melting point. It has been proposed that this behaviour is caused by slow transport of the reactant and the heterogeneous nature of the electrolyte. The activation energies of reactant transport are about four times larger in frozen electrolytes than those in liquid. It has been concluded that reactant transport is restricted to the intergrain space of the electrolyte. Received: 16 December 1997 / Accepted: 10 February 1998     

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     

Local-orbital-based correlated ab initio band structure calculations in insulating solids: LiF

 A local-orbital-based ab initio approach to calculate correlation effects on quasi-particle energies in insulating solids is presented. The use of localized Wannier-type Hartree–Fock orbitals allows correlation effects to be efficiently assessed. First a Green's function approach based on exact diagonalization is introduced and this is combined with an incremental scheme, while subsequently different levels of perturbative approximations are derived from the general procedure. With these methods the band structure of LiF is calculated and good agreement with experiment is found. By comparing the different approximations proposed, including the exact diagonalization procedure, their relative quality is established. Received: 25 June 2001 / Accepted: 31 August 2001 / Published online: 19 December 2001     

Dressed Second-order Epstein–Nesbet Perturbation Theory and Consequences of Orbital Delocalization for the BSSE Correction in Dimer Systems (in Honor of J.-P. Malrieu)

The dressed diagonal approximation to the self-consistent – size consistent CI, corrected for off-diagonal Fock matrix elements in localized orbitals is developed and applied to the ammoniac dimer system. A quite correct correlation energy can be obtained for this system, with a significantly reduced dependence of the results on the choice of the localization procedure. When calculating an interaction energy, the choice of the monomer orbitals and the application of the Boys–Bernardi counterpoise procedure shows in this case an unusual behavior: the correlation energy does not increase with the size of the atomic basis sets. Nevertheless a reasonable potential curve can be obtained.     

Second-order energy components in basis-set-superposition-error-free intermolecular perturbation theory

 Recently a basis-set-superposition-error-free second-order perturbation theory was introduced based on the “chemical Hamiltonian approach” providing the full antisymmetry of all wave functions by using second quantization. Subsequently, the “Heitler–London” interaction energy corresponding to the sum of the zero- and first-order perturbational energy terms was decomposed into different physically meaningful components, like electrostatics, exchange and overlap effects. The first-order wave function obtained in the framework of this perturbation theory also consists of terms having clear physical significance: intramolecular correlation, polarization, charge transfer, dispersion and combined polarization–charge transfer excitations. The second-order energy, however, does not represent a simple sum of the respective contributions, owing to the intermolecular overlap. Here we propose an approximate energy decomposition scheme by defining some “partial Hylleraas functionals” corresponding to the different physically meaningful terms of the first-order wave functions. The sample calculations show that at large and intermediate intermolecular distances the total second-order intermolecular interaction energy contribution is practically equal to the sum of these “physical” terms, while at shorter distances the overlap-caused interferences become of increasing importance. Received: 18 June 2001 / Accepted: 28 August 2001 / Published online: 16 November 2001     

Towards an order-N DFT method

One of the most important steps in a Kohn-Sham (KS) type density functional theory calculation is the construction of the matrix of the KS operator (the “Fock” matrix). It is desirable to develop an algorithm for this step that scales linearly with system size. We discuss attempts to achieve linear scaling for the calculation of the matrix elements of the exchange-correlation and Coulomb potentials within a particular implementation (the Amsterdam density functional, ADF, code) of the KS method. In the ADF scheme the matrix elements are completely determined by 3D numerical integration, the value of the potentials in each grid point being determined with the help of an auxiliary function representation of the electronic density. Nearly linear scaling for building the total Fock matrix is demonstrated for systems of intermediate size (in the order of 1000 atoms). For larger systems further development is desirable for the treatment of the Coulomb potential. Received: 30 March 1998 / Accepted: 6 July 1998 / Published online: 15 September 1998     

Different forms of perturbation theory for the calculation of the correlation energy

Different forms of perturbation theory for the calculation of correlation energy in both closed-and open-shell systems are discussed. For closed-shell systems, Epstein–Nesbet perturbation theory is compared with Møller–Plesset (MP ) perturbation theory based on canonical Hartree–Fock orbitals and with MP theory based on internally consistent SCF orbitals. The traditional MP theory gives superior results despite its use of an inferior zeroth-order Hamiltonian. This behavior is rationalized in terms of the larger denominators present in the traditional MP theory. These conclusions are used to support the restricted open-shell perturbation methods proposed recently by Murray and Davidson, and these new methods are compared with spin-restricted Epstein–Nesbet theory and the unrestricted MP (UMP ) approach. © 1992 John Wiley & Sons, Inc.     

A Fourier transform infrared study of the phase transition in aqueous solutions of Ethylene oxide–propylene oxide triblock copolymer

The phase transition between unimer and micellar phases of poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) (PEO–PPO–PEO) triblock copolymer Pluronic P105 in aqueous solution has been investigated as a function of temperature using Fourier transform infrared spectroscopy. The transition of 8 wt% Pluronic P105 in aqueous solution was found to occur at 25 °C. As temperature increases, PO blocks appear to be stretched conformers with strong interchain interaction, and the formation of a hydrophobic core in the micellar phase. The EO chains are found to change to a more disordered structure with low-chain packing density from the unimer phase to the micellar phase. Both the EO and PO blocks exhibit dehydration during the phase transition. Received: 17 September 1998 Accepted in revised form: 10 December 1998     

The role of initiation in the synthesis of silica/poly(methyl methacrylate) nanocomposite latex particles through emulsion polymerization

Silica/poly(methyl methacrylate) nanocomposite latex particles have been synthesized by emulsion polymerization of methyl methacrylate using a nonionic surfactant: nonylphenol poly(oxyethylene) and three different initiators, namely: 2,2′-azobis(2-amidinopropane) dihydrochloride (AIBA), potassium persulfate (KPS) and azobis(isobutyronitrile) (AIBN), being cationic, anionic and nonionic, respectively. A silica sol with an average diameter of 68 nm was used as the seed. The polymerization reaction was conducted under alkaline conditions in order to evaluate the role of the surface charge of the hydrophilic silica on the coating reaction. AIBA was found to be adsorbed on the silica surface owing to electrostatic interactions of the amidine function of the cationic initiator with the silanolate groups of the oxide surface, while the anionic and the nonionic initiators did not adsorb on silica under the same conditions. Nonetheless, whatever the nature of the initiator, polymerization took place on the silica particles as evidenced by transmission electron microscopy. The extent of interaction between the inorganic surface and the polymer particles was quantified by means of ultracentrifugation and a material balance. As much as 65% by weight of the total polymer formed was found to be present at the silica surface using AIBA, while only 40% for KPS and 25% for AIBN was found to cover the silica particles under alkaline conditions. We demonstrate that by using a cationic initiator and by controlling the pH of the suspension it is possible to significantly decrease the amount of free polymer. Coating of the silica particles took place through a kind of in situ heterocoagulation mechanism. Received: 8 December 2000 Accepted: 22 February 2001     

Time-dependent perturbation theory in transannular π-systems

The lifetimes of a local π perturbation (hole state, vacancy) have been investigated by means of time-dependent perturbation theory for six polycyclic transannular diene systems. Equilibration times in the range 3.5 × 10^?16?7.6 × 10^?16 s are predicted. With one exception, the interaction between the π fragments is predominantly of through-space type, the evolving states being coupled by CH σ orbitals for the remaining diene. The theoretical framework of this study involves a unitary transformation of the canonical molecular orbitals using a diagonal Fock operator to a time-dependent one-electron set with a Fockian similar to the transport-type Hubbard—Hamiltonian.     

Valence p functions for alkali and alkaline-earth atoms

Contracted Gaussian-type function (CGTF) basis sets are reported for valence p orbitals of the six alkali and alkaline-earth atoms Li, Be, Na, Mg, K, and Ca for molecular applications. These sets are constructed by Roothaan–Hartree–Fock calculations for the ns → np excited states of atoms, in which both linear and nonlinear parameters of CGTFs are variationally optimized. The present CGTF sets reproduce well the numerical Hartree–Fock ns → np excitation energies: the largest error is 0.0009 hartrees for Li. New CGTFs are tested with diatomic Li₂, Na₂, K₂, and MH molecules, where M = Li, Be, Na, Mg, K, and Ca, by self-consistent-field (SCF) and multiconfiguration SCF calculations. The resultant spectroscopic constants compare well with those of more elaborate calculations and are sufficiently close to experimental values, supporting the efficiency of the present set for the valence p orbitals. Received: 9 July 1998 / Accepted: 17 September 1998 / Published online: 1 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     

Ab initio calculations with effective core potentials on trivalent lanthanide–terpyridine complexes

 The electronic structures of complexes of terpyridine (tpy) with trivalent lanthanides (Ln) were calculated using ab initio methods with effective core potentials at Hartree–Fock and post-Hartree–Fock levels of theory. The quasirelativistic large-core (with 4f electrons included in the core) pseudopotentials of the Stuttgart group were chosen for the Ln atoms. The variation of several properties of the Ln(tpy)³⁺ complexes was studied for the whole Ln series. It was shown that there was a monotonous variation for all properties (geometrical and energetic) along the Ln series, except for Mulliken charges on the metal atom. Calculations were performed on three complexes of known solid-state structure. The difference between experimental and calculated geometries is discussed; for all structures, it is found to be lower than 0.2 ?. In all cases, the relative order from one complex to another is conserved. Received: 13 September 1999 / Accepted: 3 February 2000 / Published online: 19 April 2000     

Near-degeneracy corrections for second-order perturbation theory: comparison of two approaches

 We compare two approximate perturbation schemes which were developed recently to deal with the (quasi)degeneracy problem in many-body perturbation theory. We conclude that although the two methods were introduced on quite different theoretical grounds, their performances are quite similar, and present an improvement over traditional perturbation theory. Both methods are cheap in computation time, but cannot compete in accuracy with more sophisticated schemes such as complete-active-space perturbation theory or dressed particle theories. Received: 1 August 2000 / Accepted: 2 August 2000 / Published online: 19 January 2001