Complete multi-configuration self-consistent field theory

The two-configuration self-consistent field formalism previously presented in this Journal is extended and the CMC SCF LCAO MO (complete multi-configuration self-consistent field LCAO MO) technique is presented. The single Slater determinant for a 2n electron system is replaced by a combination of determinants built from two sets of MO's, one containingn orbitals; the second, ( —n) orbitals. All the possible double excitations from the (n) set to the ( —n) set are considered. The orbitals as well as the linear combination of determinants are simultaneously optimized making use of the self-consistent field technique.

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Zusammenfassung Es wird die Methode des self-consistent field für eine Gesamtheit mehrerer Konfigurationen in der LCAO-Näherung entwickelt. Ein 2n-Elektronensystem wird nicht mehr durch eine einzige Slaterdeterminante, sondern durch eine Kombination von Determinanten beschrieben, die aus zwei Sätzen von Molekülfunktionen mitn bzw. ( —n) Orbitalen aufgebaut werden. Alle möglichen zweifachen Anregungen vom (n) zum ( —n) Satz werden berücksichtigt. Mit Hilfe der SCF-Teehnik werden sowohl die Orbitale als auch die Kombination der Determinanten gleichzeitig optimiert.

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Résumé On expose la méthode du champ self-consistant pour un ensemble complet de plusieurs configurations, dans l'approximation LCAO-MO (CMC SCF LCAO MO). Le déterminant de Slater pour un système de 2n électrons est remplacé par une combinaison de déterminants construits a partir de deux ensembles d'orbitales moléculaires, l'un contenant (n) orbitales et l'autre (-n) orbitales. On considère toutes les doubles excitations possibles, de l'ensemble (n) à l'ensemble (-n). La technique du champ self-consistant permet d'optimiser simultanément les orbitales ainsi que les coefficients dans la combinaison linéaire de determinants. La méthode CMC SCF tient plainement compte de la corrélation associée à chaque paire d'électrons et fait intervenir toutes les interactions paire-paire. L'optimisation simultanée des orbitales des deux ensembles (n) et (-n) garantit une convergence rapide.

     

Accurate ab initio density fitting for multiconfigurational self-consistent field methods

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra-mu-acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals.     

Protonation enthalpies in fluorosulfonic acid using ab initio self-consistent reaction field theory

Electrostatic solvation free energies were computed for several small neutral bases and their conjugate acids using a continuum solvation model called the self-consistent isodensity polarizable continuum model (SCIPCM). The solvation energies were computed at the restricted Hartree–Fock (RHF) and second-order Møller–Plesset (MP2) levels of theory, as well as with the Becke3–Lee–Yang–Parr (B3LYP) density functional theory, using the standard 6–31G** Gaussian basis set. The RHF solvation energies are similar to those computed at the correlated MP2 and B3LYP theoretical levels. A model for computing protonation enthalpies for neutral bases in fluorosulfonic acid solvent leads to the equation ΔH(B)=−PA(B)+ΔE_t(BH⁺)−ΔE_t(B)+β, where PA(B) is the gas phase proton affinity for base B, ΔE_t(BH⁺) is the SCIPCM solvation energy for the conjugate acid, and ΔE_t(B) is the solvation energy for the base. A fit to experimental values of ΔH(B) for 10 neutral bases (H₂O, MeOH, Me₂O, H₂S, MeSH, Me₂S, NH₃, MeNH₂, Me₂NH, and PH₃) gives β=238.4±2.9 kcal/mol when ΔΔE_t is computed using the 0.0004 e⋅bohr⁻³ isodensity surface for defining the solute cavity at the RHF/6–31G** level. The model predicts that for carbon monoxide ΔH(CO)=10 kcal/mol. Thus, protonation of CO is endothermic, and the conjugate acid HCO⁺ (formyl cation) behaves as a strong acid in fluorosulfonic acid. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 250–257, 1998     

Time-reversible ab initio molecular dynamics

Time-reversible ab initio molecular dynamics based on a lossless multichannel decomposition for the integration of the electronic degrees of freedom [Phys. Rev. Lett. 97, 123001 (2006)] is explored. The authors present a lossless time-reversible density matrix molecular dynamics scheme. This approach often allows for stable Hartree-Fock simulations using only one single self-consistent field cycle per time step. They also present a generalization, introducing an additional "forcing" term, that in a special case includes a hybrid Lagrangian, i.e., Car-Parrinello-type, method, which can systematically be constrained to the Born-Oppenheimer potential energy surface by using an increasing number of self-consistency cycles in the nuclear force calculations. Furthermore, in analog to the reversible and symplectic leapfrog or velocity Verlet schemes, where not only the position but also the velocity is propagated, the authors propose a Verlet-type density velocity formalism for time-reversible Born-Oppenheimer molecular dynamics.     

Variable ζ calculation for self-consistent screening parameters in ab initio molecular theory

A resolution of Roothaan's HF–SCF–LCAO–MO equations is proposed in which atomic orbital exponents (ζ) are made dependent on the molecular charge distribution and included in the self-consistent scheme. Screening parameters so obtained are self-consistent with the molecular orbital coefficients and compare closely to optimum orbital exponents found by other methods. The technique is applied to the ground, lowest positive, and lowest negative ion states of the hydride series LiH, BH, and HF. Calculated potential curves are used to define purely theoretical values for the vertical and adiabatic ionization energies and electron affinities. Predictions are compared to experimental values where available.     

Energetics of Zn2+ binding to a series of biologically relevant ligands: A molecular mechanics investigation grounded on ab initio self-consistent field supermolecular computations

Detailed investigations are performed of the binding energetics of Zn²⁺ to a series of neutral and anionic ligands making up the sidechains of amino acid residues of proteins, as well as ligands which can be involved in Zn²⁺ binding during enzymatic activation: imidazole, formamide, methanethiol, methanethiolate, methoxy, and hydroxy. The computations are performed using the SIBFA molecular mechanics procedure (SMM), which expresses the interaction energy under the form of four separate contributions related to the corresponding ab initio supermolecular ones: electrostatic, short-range repulsion, polarization, and charge transfer. Recent refinements to this procedure are first exposed. To test the reliability of this procedure in large-scale simulations of inhibitor binding to metalloenzyme cavities, we undertake systematic comparisons of the SMM results with those of recent large basis set ab initio self-consistent field (SCF) supermolecule computations, in which a decomposition of the total ΔE into its four corresponding components is done (N. Gresh, W. Stevens, and M. Krauss, J. Comp. Chem., 16 , 843, 1995). For each complex, the evolution of each individual SMM energy component as a function of radial and in- and out-of-plane angular variations of the Zn²⁺ position reproduces with good accuracy the behavior of the corresponding SCF term. Computations performed subsequently on di- and oligoligated complexes of Zn²⁺ show that the SIBFA molecular mechanics (SMM) functionals, E_pol and E_ct, closely account for the nonadditive behaviors of the corresponding second-order energy contributions determined from the ab initio SCF calculations on these complexes and their nonlinear dependence on the number of ligands. Thus, the total intermolecular interaction energies computed with this procedure reproduce, with good accuracy, the corresponding SCF ones without the need for additional, extraneous terms in the intermolecular potential of polyligated complexes of divalent cations. © 1995 by John Wiley & Sons, Inc.     

原子簇量子化学从头算的自洽晶体场模型

本文提出一种收敛的点电荷和Hartree-Fock表面势构成的自洽晶体场Madelung势用于原子簇量子化学从头计算。前者的计算类似于核吸引积分的单电子积分, 后者可以通过点群对称性操作从原子簇内的积分矩阵元得到。点电荷的大小和原子簇内对应的原子电荷相等, 其数目以晶体场势收敛为标准确定。介绍加速计算的程序技巧。该模型用于高温超导体YBa2Cu3O7的全电子从头计算并得到一些新结果。     

A transferable ab initio based force field for aqueous ions

We present a new polarizable force field for aqueous ions (Li(+), Na(+), K(+), Rb(+), Cs(+), Mg(2 +), Ca(2 +), Sr(2 +), and Cl(-)) derived from condensed phase ab initio calculations. We use maximally localized Wannier functions together with a generalized force and dipole-matching procedure to determine the whole set of parameters. Experimental data are then used only for validation purposes and a good agreement is obtained for structural, dynamic, and thermodynamic properties. The same procedure applied to crystalline phases allows to parametrize the interaction between cations and the chloride anion. Finally, we illustrate the good transferability of the force field to other thermodynamic conditions by investigating concentrated solutions.     

Pathway analysis of super-exchange electronic couplings in electron transfer reactions using a multi-configuration self-consistent field method

We present a novel pathway analysis of super-exchange electronic couplings in electron transfer reactions using localized molecular orbitals from multi-configuration self-consistent field (MCSCF) calculations. In our analysis, the electronic coupling and the tunneling pathways can be calculated in terms of the configuration interaction (CI) Hamiltonian matrix obtained from the localized MCSCF wave function. Making use of the occupation restricted multiple active spaces (ORMAS) method can effectively produce the donor, acceptor, and intermediate configuration state functions (CSFs) and CIs among these CSFs. In order to express the electronic coupling as a sum of individual tunneling pathways contributions, we employed two perturbative methods: L?wdin projection-iteration method and higher-order super-exchange method. We applied them to anion couplings of butane-1,4-diyl and pentane-1,5-diyl. The results were (1) the electronic couplings calculated from the two perturbative methods were in reasonable agreement with those from a non-perturbative method (one-half value of the energy difference between the ground and first excited states), (2) the main tunneling pathways consisted of a small number of lower-order super-exchange pathways where bonding, anti-bonding, or extra-valence-shell orbitals were used once or twice, and (3) the interference among a huge number of higher-order super-exchange pathways significantly contributed to the overall electronic coupling, whereas each of them contributed only fractionally. Our method can adequately take into account both effects of non-dynamical electron correlation and orbital relaxation. Comparing with the analyses based on the Koopmans' theorem (ignoring both effects) and the ORMAS-CIs from frozen localized reference orbitals (ignoring the effect of orbital relaxation), we discuss these effects.     

Approximate ab initio energies by systematic molecular fragmentation

A scheme is introduced for generating a hierarchy of molecular fragmentations by which the total electronic energy can be approximated from the energies of the fragments. Higher levels in the hierarchy produce molecular fragments of larger size and approximate the total electronic energy more reliably. A correction to account for nonbonded interactions is also presented. The accuracy of the approach is tested for a number of examples, and shown to be essentially independent of the level of ab initio theory employed. The computational cost increases linearly with the size of the molecule.     

Insights into amine-based CO<Subscript>2</Subscript> capture: an ab initio self-consistent reaction field investigation

Ab initio many-body perturbation theory (MP2/6-311++G(,dp)), density functional theory (B3LYP/6-31++G(d,p)) and self-consistent reaction field (IEF-PCM UA HF/6-31G(d)) calculations have been used to study the CO₂ capture reagents NH₃, 2-hydroxyethylamine (MEA), diaminoethane (EN), 2-amino-1-propanol (2A1P), diethanolamine (DEA), N-methyl-2-hydroxyethylamine (N-methylMEA), 2-amino-2-methyl-1-propanol (AMP), trishydroxymethylaminomethane (tris), piperazine (PZ) and piperidine (PD). This study involved full conformational searches of the capture amines in their native and protonated forms, and their carbamic acid and carbamate derivatives. Using this data, we were able to compute Boltzmann-averaged thermodynamic values for the amines, carbamates and carbamic acid derivatives, as well as equilibrium constants for a series of ‘universal’ aqueous capture reactions. Important findings include (i) relative pK _a values for the carbamic acid derivatives are a useful measure of carbamate stability, due to a particular chemical resonance which is also manifest in short computed N–CO₂H bonds at both levels of theory, (ii) the computational results for sterically hindered amines such as AMP and tris are consistent with these species forming carbamates which readily hydrolyse and (iii) the amine-catalysed reaction between OH⁻ and CO₂ to generate bicarbonate correlates with amine pK _a. Thermodynamic data from the ab initio computations predicts that the heterocycles PD and PZ and the acyclic sorbent EN are good choices for a capture solvent. AMP and tris perform poorly in comparison.     

Quantum wavepacket ab initio molecular dynamics for extended systems

In this paper, we introduce a symmetry-adapted quantum nuclear propagation technique that utilizes distributed approximating functionals for quantum wavepacket dynamics in extended condensed-phase systems. The approach is developed with a goal for implementation in quantum-classical methods such as the recently developed quantum wavepacket ab intio molecular dynamics (QWAIMD) to facilitate the study of extended systems. The method has been numerically benchmarked for extended electronic systems as well as protonic conducting systems that benefit from quantum nuclear treatment. Vibrational properties are computed for the case of the protonic systems through use of a novel velocity-flux correlation function. The treatment is found to be numerically accurate and efficient.     

On the ab initio geometry optimization of molecular solutes

We present several variants of methods for the automatic search of optimum geometries of solutes via ab initio SCF procedures. The physical meaning of geometry optimization in solution is discussed. Advantages and disadvantages of the different variants are shown making use of calculations on the HF dimer with different basis sets, supplemented by information on the computational times. Suggestions for the most convenient strategies (which in part depend on the nature of the solute) are also done.     

An ab initio quantum mechanical charge field molecular dynamics simulation of a dilute aqueous HCl solution

An ab initio quantum mechanical charge field (QMCF) molecular dynamics simulation has been performed to study the structural and dynamical properties of a dilute aqueous HCl solution. The solute molecule HCl and its surrounding water molecules were treated at Hartree‐Fock level in conjunction with Dunning double‐ζ plus polarization function basis sets. The simulation predicts an average H? Cl bond distance of 1.28 Å, which is in good agreement with the experimental value. The H_HCl···O_w and Cl_HCl···H_w distances of 1.84 and 3.51 Å were found for the first hydration shell. At the hydrogen site of HCl, a single water molecule is the most preferred coordination, whereas an average coordination number of 12 water molecules of the full first shell was observed for the chloride site. The hydrogen bonding at the hydrogen site of HCl is weakened by proton transfer reactions and an associated lability of ligand binding. Two proton transfer processes were observed in the QMCF MD simulation, demonstrating acid dissociation of HCl. A weak structure‐making/breaking effect of HCl in water is recognized from the mean residence times of 2.1 and 0.8 ps for ligands in the neighborhood of Cl and H sites of HCl, respectively. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Linear-scaling implementation of molecular electronic self-consistent field theory

A linear-scaling implementation of Hartree-Fock and Kohn-Sham self-consistent field (SCF) theories is presented and illustrated with applications to molecules consisting of more than 1000 atoms. The diagonalization bottleneck of traditional SCF methods is avoided by carrying out a minimization of the Roothaan-Hall (RH) energy function and solving the Newton equations using the preconditioned conjugate-gradient (PCG) method. For rapid PCG convergence, the Lowdin orthogonal atomic orbital basis is used. The resulting linear-scaling trust-region Roothaan-Hall (LS-TRRH) method works by the introduction of a level-shift parameter in the RH Newton equations. A great advantage of the LS-TRRH method is that the optimal level shift can be determined at no extra cost, ensuring fast and robust convergence of both the SCF iterations and the level-shifted Newton equations. For density averaging, the authors use the trust-region density-subspace minimization (TRDSM) method, which, unlike the traditional direct inversion in the iterative subspace (DIIS) scheme, is firmly based on the principle of energy minimization. When combined with a linear-scaling evaluation of the Fock/Kohn-Sham matrix (including a boxed fitting of the electron density), LS-TRRH and TRDSM methods constitute the linear-scaling trust-region SCF (LS-TRSCF) method. The LS-TRSCF method compares favorably with the traditional SCF/DIIS scheme, converging smoothly and reliably in cases where the latter method fails. In one case where the LS-TRSCF method converges smoothly to a minimum, the SCF/DIIS method converges to a saddle point.     

Controlling the shape and flexibility of arylamides: a combined ab initio, ab initio molecular dynamics, and classical molecular dynamics study

Using quantum chemistry plus ab initio molecular dynamics and classical molecular dynamics methods, we address the relationship between molecular conformation and the biomedical function of arylamide polymers. Specifically, we have developed new torsional parameters for a class of these polymers and applied them in a study of the interaction between a representative arylamide and one of its biomedical targets, the anticoagulant drug heparin. Our main finding is that the torsional barrier of a C(aromatic)-C(carbonyl) bond increases significantly upon addition of an o-OCH2CH2NH3+ substituent on the benzene ring. Our molecular dynamics studies that are based on the original general AMBER force field (GAFF) and GAFF modified to include our newly developed torsional parameters show that the binding mechanism between the arylamide and heparin is very sensitive to the choice of torsional potentials. Ab initio molecular dynamics simulation of the arylamide independently confirms the degree of flexibility we obtain by classical molecular dynamics when newly developed torsional potentials are used.