Geometrical linear responses and directional energy derivatives for energetically degenerate MCSCF electronic functions

Summary For state-averaged multiconfigurational self consistent field (SA-MCSCF) wave functions, second-order geometrical response equations are derived that allow the determination of first-order configuration amplitude response for equally weighted, energetically degenerate states. The first-order response equations obtained in earlier work do not suffice to determine these particular responses parameters. To formulate such a derivation in a well defined manner, it is found that a specific linear combination of the degenerate states must be formed; this specific combination of states then defines how state energies and wave functions evolve as one passes through the surface intersection. The linear combination among the degenerate states is dependent upon the molecular distortion for which the responses are to be evaluated. Expressions for first- and second-order directional energy derivatives for these energetically degenerate wave functions are also derived. All the equations obtained are computationally tractable and expressed in terms of quantities that result from optimizing the SA-MCSCF wave functions and from solving the first- and part of the second-order geometrical response equations.     

Parallel algorithm for integral transformations and GUGA MCSCF

Summary An algorithm for the parallelization of the atomic to molecular integral transformation and the subsequent steps in a GUGA based MCSCF calculation is presented. Timing data shows that the transformation and diagonalization steps are well parallelized and that several of the other portions of the MCSCF code are moderately parallel. Remaining sequential bottlenecks are identified.     

Dynamic correlation for MCSCF wave functions: An effective potential method

A method is suggested which allows the inclusion of dynamic correlation into CASSCF calculations. An effective Coulomb hole potential is added to the Hamiltonian. The potential has a simple form, which allows its implementation into existing LCAO programs using Gaussian integral packages. The parameters appearing in the potential are determined by fitting to empirical valence correlation energies for first row atoms. Calculations of ionization energies and electron affinities show considerable improvement compared to the MCSCF values. Test calculations on three molecules give the following results, H₂ r _e=0.745 (0.741) Å, D _e=4.62 (4.75) eV; N₂ r _e=1.099 (1.098) Å, D _e= 10.42 (9.91) eV; O₂ r _e=1.198 (1.207) Å, D _e=4.73 (5.21) eV. Experimental values within parenthesis. On leave from: Institute of Organic Chemistry, Polish Academy of Sciences, PL-01-224 Warszawa 42, ul. Kasprzaka 44, Poland.     

On the choice of active space orbitals in MCSCF calculations

We describe a procedure which may be used to aid selection of the active space in multiconfigurational self-consistent field (MCSCF) calculations for general chemical systems. Starting from a restricted Hartree-Fock calculation, we define a hierarchy of interacting virtual orbitals for every occupied orbital. The most strongly interacting orbitals are then taken to constitute the active space in a configuration interaction (CI) calculation. The natural orbital occupation numbers obtained from the CI calculation are then used to choose the active space to be used in a subsequent MCSCF calculation. We illustrate our method on a number of systems (Li₂, B₂, C₂, carbonyl oxide and the transition state for oxidation of H₂S by dioxirane). In all these cases, ‘intuitive’ active spaces are inadequate, as are active spaces derived from the natural orbitals of unrestricted Hartree-Fock calculations.     

Numerical Hartree-Fock and MCSCF calculations on diatomic copper: calibration of basis sets

NHF and NMCSCF results for Cu₂ are compared with calculations employing basis set expansions. We find that nearly all previous SCF calculations using Gaussian basis sets have underestimated the bond length by about the same amount (0.03 Å) as that attributed to the unlinked cluster and relativistic corrections. The error is shown to be due to deficiencies in the 3d primitive set which yield sizable basis set superposition errors.     

Symmetry adaptation of configuration basis in MCSCF method

Summary A novel approach of space symmetry adaptation is developed for multiconfigurational (MC) functions in fully optimized reaction space and complete active space SCF calculations. The bonded tableau and two box symmetric tableau are basic representations (rep) of configuration functions; the group symmetric localized orbitals are used as one-electron orbitals. The method is proposed for generating a complete and orthonormal set of MC single excited functions. The redundant variable in MCSCF can be eliminated by symmetry adaptation.     

Argon plasma transport properties at reduced pressures

Argon plasma transport properties at low pressures (0.01 atm) are calculated using a modified Debve length suggested by T. Kihara et al. Electrons and heavy species are treated as two different gases, and the method of calculation is based on the simplified theory (or transport properties developed by R. S. Devoto. A generalized Saha equation is used to calculate the species composition, and experimental data by Y. Itikawa for momentum transfer cross sections are adapted for the evaluation of electron-atom collision cross sections.     

Approximate second order method for orbital optimization of SCF and MCSCF wavefunctions

A quasi-Newton method involving a diagonal guess orbital hessian with iterative updates has been proposed recently by Almlof for the optimization of closed shell self-consistent field (SCF) wavefunctions. The technique is extended in the present work to more general wavefunctions, ranging from open shell SCF through multiconfigurational SCF. A number of examples are presented to show that convergence for closed and open shell SCF rivals conventional direct inversion in the iterative subspace (DIIS). For multiconfigurational SCF wavefunctions, the method presented here requires more iterations than an exact second order program, but since each iteration is substantially faster, leads to a more efficient overall program. Received: 15 August 1996 / Accepted: 22 January 1997     

GVB–RP: A reliable MCSCF wave function for large systems

We have developed a version of generalized valence bond (GVB) that overcomes the major weakness of the perfect pairing approximation without requiring a full transformation of the integrals at each step of the self‐consistent orbital optimization. The method, called generalized valence bond–restricted pairing (GVB–RP), describes properly the dissociation of up to triple bonds and provides smooth potential energy surfaces for most chemical reactions. The wave functions obtained are a good starting point for more sophisticated computational techniques. The applicability of the method is illustrated with a few simple examples including multiple‐bond dissociations, transition states for symmetry allowed, symmetry forbidden, and radical reactions, as well as reactions at a transition‐metal center. The cost of the method compares well with other self‐consistent correlated techniques. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 1–22, 1999     

Macroscopic solvation of molecules in excited states: An MCSCF model including solvent polarization effects-I

An MCSCF model including the effects of solvent polarization is developed. The model is applied within the limitations of INDO approximations to look into the dominant effects of solvent polarization on the electronic structure in the excited states of a model system (e.g.nπ ^* states of H₂CO). Important features of macroscopic solvation-induced reorganization of electron density and some consequence thereof are noted.     

Reactions of 1S, 1D,and 3P carbon atoms with water. Oxygen abstraction and intermolecular formaldehyde generation mechanisms; An MCSCF study

Reactions of singlet and triplet carbon atoms with water are explored theoretically using CASSCF–MCQDPT2, CCSD, and DFT methodologies. The ¹S carbons are found to be unreactive. Depending on the carbon atom generation method and the reaction medium, gas‐phase C(³P) attacking water may generate CO and atomic hydrogen as the end products. Reaction paths of the C(¹D) + H₂O system are complicated due to the involvement of two reactive potential energy surfaces with branchings occurring along each. Modifications in product distributions for reactions taking place in condensed phases are elaborated. The decisive reaction conditions, under which the oxygen abstraction and intermolecular formaldehyde generation dominate, are suggested to clarify the discrepancy related with experimental CO observation. The findings are consistent with available experimental data on this system. Oxygen abstraction and intermolecular formaldehyde generation mechanisms suggested here are capable of serving as models for similar reactions of alcohols. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

MCSCF study of singlet oxygen addition to ethenol—a model of photooxidation reactions of unsaturated and aromatic compounds bearing hydroxy groups

The reaction path of singlet (¹Δ_g) oxygen addition to ethenol (vinyl alcohol)—a model of the reactions of singlet oxygen with aromatic and unsaturated compounds bearing the hydroxy groups—has been studied by means of MCSCF calculations, using various active spaces and basis sets. The effects of dynamic correlation (at the PT2 level) and basis set superposition error (BSSE) on relative energies were also investigated. It was found that including polarization functions is necessary to obtain geometries of the oxygen moiety consistent with the available experimental data. Two possible reaction products were considered: 1-hydroxy-1,2-dioxethane (peroxide) and 2-hydroperoxyethanal-1 (hydroperoxide); their energies are 24.1 and 36.6 kcal/mol (44.1 and 78.2 kcal/mol with the PT2 contribution and BSSE correction) below the dissociation limit, respectively (all energies reported here refer to the 6-31G** basis set and an active space composed of eight orbitals and ten electrons). A common stage of both reactions is the formation of a peralcoxyl intermediate with one of the oxygen atoms attached to the unsubstituted carbon atom; the energies of the respective transition state and that of the intermediate are 30.2 and 18.7 kcal/mol (15.9 and 10.3 kcal/mol with the PT2 contribution and BSSE correction) above the dissociation limit, respectively. The energy of this transition state is the dominant energy barrier to the reaction. The intermediate can then undergo conversion to the dioxethane product, to the perepoxide intermediate, or via a proton transfer, directly to the hydroperoxide, the last route being the most probable one. The perepoxide intermediate, after a proton transfer, also readily gives the hydroperoxide. It was also found that the unimolecular conversion from dioxethane to hydroperoxide via a proton transfer from the hydroxy group accompanied with ring cleavage requires an activation energy of at least 56 kcal/mol, making this reaction path highly improbable. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1668–1681, 1997     

MCSCF calculation of the frequency-dependent hyperpolarizability of the lithium atom

The second electric dipole hyperpolarizability of the lithium atom is calculated using a series of multiconfiguration SCF wave functions with an increasing number of active space orbitals. In agreement with other recent calculations, we find a very large correlation correction to the hyperpolarizability. We analyze the frequency dependence of the dc Kerr hyperpolarizability γ^K(o) = γ (− o o, 0, 0) and observe very significant dispersion effects. © 1996 John Wiley & Sons, Inc.     

On the uncorrelated reference for calculation of properties

Summary We consider various possibilities for the uncorrelated reference for the calculation of properties. According to the philosophy of Löwdin, to whom this volume is dedicated, the uncorrelated reference state for response properties ought to be taken as the unperturbed Hartree-Fock state for properties of all orders in the applied field. Frequently, however, it is operationally convenient to use the coupled Hartree-Fock like results as a standard of comparison for second- and higher-order properties, even though this is not consistent with Löwdin's choice for the uncorrelated reference state. In this method the reference state is the perturbed Hartree-Fock state. Numerical examples demonstrate a rather large difference between the two uncorrelated references. We consider the pros and cons of each choice.     

Ar原子电离能谱和Ar3p电子动量谱研究

电子动量谱学（ElectronMomentumSPectroscoP则是近．二十年来发展起来的一种新兴的探测原子、分子和固体结构的手段，它不仅能够获得轨道结合能的信息，而且能够能壳分辨地得到轨道电子的动量分布（即动量表象中的波函数模方）；同时它还是研究电子关联的最有效的实验手段．其     

The optimization of MCSCF functions by application of the generalized brillouin theorem: The LiH2 potential energy surface

The generalized Brillouin theorem is used to construct an optimization procedure for MCSCF functions by iterative contracted CI calculations. Special attention is paid to the MO transformation step in each iteration. In this method the MCSCF calculation may easily be augmented by a restricted CI calculation involving a configuration set which is uniquely determined by the trial function. An application to the calculation of the potential energy surface for linear LiH₂ in the reaction LiH + HLi + H₂ leads to the conclusion that this restricted CI is necessary, in order to obtain satisfactory results for the potential energy barrier in this reaction.     

A MCSCF method for ground and excited states based on full optimizations of successive Jacobi rotations

A new multiconfigurational self-consistent field (MCSCF) method based on successive optimizations of Jacobi rotation angles is presented. For given one- and two-particle density matrices and an initial set of corresponding integrals, a technique is developed for the determination of a Jacobi angle for the mixing of two orbitals, such that the exact energy, written as a function of the angle, is fully minimized. Determination of the energy-minimizing orbitals for given density matrices is accomplished by successive optimization and updating of Jacobi angles and integrals. The total MCSCF energy is minimized by alternating between CI and orbital optimization steps. Efficiency is realized by optimizing CI and orbital vectors quasi-simultaneously by not fully optimizing each in each improvement step. On the basis of the Jacobi-rotation based approach, a novel MCSCF procedure is formulated for excited states, which avoids certain shortcomings of traditional excited-state MCSCF methods. Applications to specific systems show the practicability of the developed methods.     

纳米尺度氩液体线物性的分子动力学模拟

运用分子动力学模拟方法,对纳米尺度氩液体线的物理性质进行了研究。文中模拟计算了纳米线的熔点温度以及气液平衡状态下液态区密度、气态区密度和液体线的半径,并分析了模拟盒子尺寸和模拟温度对液体线物性的影响。结果表明,由于在初始结构中增加了气体分子,当模拟温度不变时,随模拟盒子尺寸的增加,液态区密度增大,气态区密度减小。但模拟盒子尺寸较小时,液体线半径不随模拟盒子尺寸发生变化。模拟计算所得的液态区密度十分接近宏观尺度氩液体密度时,模拟盒子的尺寸较合适。当模拟盒子尺寸固定不变时,液态区密度和气态区密度随温度的变化趋势与文献中宏观尺度氩液体和气体密度的变化趋势相同。结论可以为进一步系统地分析纳米尺度液体线的稳定性提供一定的依据。     

氩离子激光固化环氧树脂制作三维微结构

利用激光束进行三维成像是通过逐层光引发聚合形成宏观尺度的三维实体 .最近出现的激光全息光刻技术是利用激光束的干涉产生三维全息图案 ,让感光树脂在全息图案中曝光 ,从而一次形成三维周期有序微结构 .通过调节激光干涉及波长可控制三维结构的形状及尺寸 .利用该技术获得亚微米尺度上周期性重复的三维微结构 ,可用于制作三维光子晶体 [1,2 ]等具有独特性能的聚合物材料 .本文用铁芳烃化合物与特种环氧树脂配制成阳离子型可见光固化树脂 ,在氩离子激光器产生的多束可见连续激光相干形成的空间干涉光场中曝光 ,成功地制备出亚微米量级的三…