Multiconfiguration Pair-Density Functional Theory for Transition Metal Silicide Bond Dissociation Energies,Bond Lengths,and State Orderings

Transition metal silicides are promising materials for improved electronic devices, and this motivates achieving a better understanding of transition metal bonds to silicon. Here we model the ground and excited state bond dissociations of VSi, NbSi, and TaSi using a complete active space (CAS) wave function and a separated-pair (SP) wave function combined with two post-self-consistent field techniques: complete active space with perturbation theory at second order and multiconfiguration pair-density functional theory. The SP approximation is a multiconfiguration self-consistent field method with a selection of configurations based on generalized valence bond theory without the perfect pairing approximation. For both CAS and SP, the active-space composition corresponds to the nominal correlated-participating-orbital scheme. The ground state and low-lying excited states are explored to predict the state ordering for each molecule, and potential energy curves are calculated for the ground state to compare to experiment. The experimental bond dissociation energies of the three diatomic molecules are predicted with eight on-top pair-density functionals with a typical error of 0.2 eV for a CAS wave function and a typical error of 0.3 eV for the SP approximation. We also provide a survey of the accuracy achieved by the SP and extended separated-pair approximations for a broader set of 25 transition metal–ligand bond dissociation energies.     

Application of SCF perturbation theory to molecular calculations

A method for solving Roothaan's molecular orbital equations by means of SCF perturbation theory is presented. An estimate of the accuracy of the third order expansion is made for the CNDO/2 approximation from a comparison of the results from direct calculations. It is found that the third order theory is sufficiently accurate for quantitative studies.     

多组态二级微扰理论计算CH3O2激发光谱以及CH3O2→CH3＋O2解离反应

在C_s对称性和aug-cc-pVTZ基组水平下, 采用全活化空间自洽场方法(CASSCF)研究了CH₃O₂自由基基态及其阴阳离子的12个低激发态. 为了进一步考虑动态电子相关效应, 采用二级多组态微扰理论(CASPT2)获得更加精确的能量值. 所有计算得到的电子态都是价电子态, 而且所得绝热激发能和电子亲和势与实验值非常接近.在CASPT2//CASSCF理论水平下计算了CH₃O₂从²A"和²A'电子态的CH₃O₂→CH₃＋O₂的解离反应的势能曲线(PECs). 优化得到的裂解产物的几何结构和能量与分别优化CH₃和O₂得到的结果进行比较, 从而确定裂解产物的电子态. 结果表明, 从²A"和²A'电子态的解离反应分别对应产物CH₃(²A")＋O₂(³A")和CH₃(²A")＋O₂(¹A").     

Optimizing efficiency of perturbative Monte Carlo method

We introduce error weighting functions into the perturbative Monte Carlo method for use with a hybrid ab initio quantum mechanics/molecular mechanics (QM/MM) potential. The perturbative Monte Carlo approach introduced earlier provides a means to reduce the number of full SCF calculations in simulations using a QM/MM potential by evoking perturbation theory to calculate energy changes due to displacements of an MM molecule. The use of weighting functions, introduced here, allows an optimal number of MM molecule displacements to occur between the performance of the full self-consistent field calculations. This will allow the ab initio QM/MM approach to be applied to systems that require more accurate treatment of the QM and/or MM regions. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1632–1638, 1998     

The modified Hartree–Fock self-consistent field equation

A one-electron correlation operator is introduced into the Hartree–Fock self-consistent field equation. The correlation operator is derived from the second-order perturbation theory. Energies of atomic and molecular systems calculated from this modified Hartree–Fock equation are equal to that from second-order perturbation of Hartree–Fock equation. The modified equation can also be solved self-consistently by the LCAO approximation. We also presented the modified expressions for other operators.     

C6H5N光谱性质的多组态二级微扰理论研究

采用全活化空间自洽场方法(CASSCF)在C2v对称性和6-31g(d,p) 基组水平下, 研究了C6H5N自由基及其阴阳离子的基态和低激发态性质. 为了进一步考察动态电子相关效应, 采用多组态二级微扰理论(CASPT2)获得更加精确的能量值. 计算得到13A2→13A1和13A2→13B2在4303.1和4212.2 kJ/mol处的激发可分别归因于π(b1)→ny和π(a2)→ny的跃迁, 而13A2→13B1和13A2→11B1在2634.9和2700.4 kJ/mol处的激发具有nx→π*(a2)和π(a2)→nx的混合跃迁特征, 理论波长与紫外吸收光谱得到的实验数据一致. 计算得到的电离能与实验值也非常接近.     

Quasi-degenerate perturbation theory with general multiconfiguration self-consistent field reference functions

The quasi-degenerate perturbation theory (QDPT) with complete active space (CAS) self-consistent field (SCF) reference functions is extended to the general multiconfiguration (MC) SCF references functions case. A computational scheme that utilizes both diagrammatic and sum-over-states approaches is presented. The second-order effective Hamiltonian is computed for the external intermediate configurations (including virtual or/and core orbitals) by the diagrammatic approach and for internal intermediate configurations (including only active orbitals) by the configuration interaction matrix-based sum-over-states approach. The method is tested on the calculations of excitation energies of H(2)O, potential energy curves of LiF, and valence excitation energies of H(2)CO. The results show that the present method yields very close results to the corresponding CAS-SCF reference QDPT results and the available experimental values. The deviations from CAS-SCF reference QDPT values are less than 0.1 eV on the average for the excitation energies of H(2)O and less than 1 kcal/mol for the potential energy curves of LiF. In the calculation of the valence excited energies of H(2)CO, the maximum deviation from available experimental values is 0.28 eV.     

Analytic techniques for the coupled multiconfiguration SCF perturbation theory

The perturbation theory based on the paired excitation multiconfiguration self-consistent field approach of Clementi and Veillard is considered. The coupled first-order perturbed orbital equations are analysed and an appropriate computational scheme for their solution is discussed. The proposed computational scheme is analogous to the technique employed for the solution of the coupled Hartree–Fock equations in the one-configuration approximation. However, because of the presence ofnondiagonal Lagrangian multipliers and the use of different one-electron operators for different orbitals, the present scheme raises some new computational problems. In this context a new technique for the solution of the unperturbed multiconfiguration self-consistent field equations is proposed. A simple illustration of the superiority of the multiconfiguration perturbation approach with respect to the ordinary coupled Hartree–Fock scheme is given. Also the validity of the variation formulation of the presented scheme and its relation to the finite-field approach are discussed.     

Nonvariational time-dependent multiconfiguration self-consistent field equations for electronic dynamics in laser-driven molecules

A time-dependent multiconfiguration self-consistent field (TDMCSCF) scheme is developed to describe the time-resolved electron dynamics of a laser-driven many-electron atomic or molecular system, starting directly from the time-dependent Schrodinger equation for the system. This nonvariational formulation aims at the full exploitations of concepts, tools, and facilities of existing, well-developed quantum chemical MCSCF codes. The theory uses, in particular, a unitary representation of time-dependent configuration mixings and orbital transformations. Within a short-time, or adiabatic approximation, the TDMCSCF scheme amounts to a second-order split-operator algorithm involving generically the two noncommuting one-electron and two-electron parts of the time-dependent electronic Hamiltonian. We implement the scheme to calculate the laser-induced dynamics of the two-electron H2 molecule described within a minimal basis, and show how electron correlation is affected by the interaction of the molecule with a strong laser field.     

Quantum field theoretical methods in chemically bonded systems II

Summary Many-body perturbation theory is derived for chemical bonds. Paired quasiparticles represent the bonds. Products of the paired quasiparticles define a model Bardeen-Cooper-Schrieffer function. The pairing force is added as a model interaction to the self-consistent problem. The starting model is based on valency and adiabatic symmetry correlation. Symmetries are enforced by the model Hamiltonian. Perturbative corrections are expressed as ordinary Feynman diagrams. The number of diagrams needed is the same as for particle-hole theory.This work was supported in part by the U.S. Department of the Navy, Space and Naval Warfare Systems Command under Contract N00039-89-C-0001, and in part by NATO Research Grant 1861. It was presented, in part, at the A.C. Wahl Memorial Session, Molecular Spectroscopy Symposium, Columbus, Ohio, 1984; and Midwest Theoretical Chemistry Conference, Milwaukee, Wisconsin, 1985.     

Nonempirical Description of the Atmospherically Important Anionic Species. II. Hydrated Ozone Anions

Ozone–water clusters are nonempirically modeled in the complete active space self-consistent field approximation (CASSCF) with the energetic estimates obtained at the multiconfiguration quasidegenerate perturbation theory level (MCQDPT) with 6–31++G** basis set. Coordination of a neutral ozone molecule to small water clusters is either surface or interior, with the binding energy of the order of a weak hydrogen bond. Upon localization of an excess electron, the hydration of ozone becomes strong. The adiabatic affinities of water–ozone clusters and the energies of electron detachment from their anions, depending on the number of water molecules, estimate the electron hydration and vertical electron detachment thresholds of water or ice that superficially coordinates minor amounts of ozone.     

Calculating molecular vibrational spectra beyond the harmonic approximation

We present a new approach for calculating anharmonic corrections to vibrational frequency calculations. The vibrational wavefunction is modelled using translated Hermite functions thus allowing anharmonic effects to be incorporated directly into the wavefunction whilst still retaining the simplicity of the Hermite basis. We combine this new method with an optimised finite-difference grid for computing the necessary third and fourth nuclear derivatives of the energy. We compare our combined approach to existing anharmonic models—vibrational self-consistent field theory (VSCF), vibrational perturbation theory (VPT), and vibrational configuration interaction theory (VCI)—and find that it is more cost effective than these alternatives. This makes our method well-suited to computing anharmonic corrections for frequencies in medium-sized molecules. Contribution of the Mark S. Gordon 65th Birthday Festschrift Issue.     

The quasiparticle concept in vibrational–electronic problems in molecules. I. Partitioning of the vibrational–electronic Hamiltonian

The partitioning of the vibrational–electronic Hamiltonian is presented. This partitioning is based on a new quasiparticle transformation that is constructed in such a way that the adiabatic approximation is included into the unperturbed Hamiltonian; nonadiabacity, anharmonicity, and electron correlation are treated as perturbations. We also present the second quantization treatment for bosons. The many body perturbation theory expansion for the vibrational–electronic Hamiltonian is suggested. A comparison of this approach is made with gradient techniques.     

The perturbation theory model of a spherical oscillator in electric field and the vibrational stark effect in polyatomic molecular species

The effect of external electrostatic fields on the spherical oscillator energy states was studied using stationary perturbation theory. Besides the spherical oscillator with ideal symmetry, also a variety of the deformed systems were considered in which the deformations may be induced by the external fields, but also by the short-range crystal lattice forces. The perturbation theory analysis was carried out using the field-dependent basis functions. Predicted spectral appearances and band splittings due to the deformations and external field influences were shown to be helpful in interpreting the experimental spectra of molecular oscillator possessing subsets of mutually orthogonal triply degenerate normal modes (such as, e.g. tetrahedral species). To verify the results of the perturbation theory treatments, as well as to provide a further illustration of the usefulness of the employed technique, a numerical HF/aug-cc-pVTZ study of the vibrational states of methane molecule in external electrostatic field was performed.     

GPU acceleration of many-body perturbation theory methods in MOLGW with OpenACC

Quasiparticle self-consistent many-body perturbation theory (MBPT) methods that update both eigenvalues and eigenvectors can calculate the excited-state properties of molecular systems without depending on the choice of starting points. However, those methods are computationally intensive even on modern multi-core central processing units (CPUs) and thus typically limited to small systems. Many-core accelerators such as graphics processing units (GPUs) may be able to boost the performance of those methods without losing accuracy, making starting-point-independent MBPT methods applicable to large systems. Here, we GPU accelerate MOLGW, a Gaussian-based MBPT code for molecules, with open accelerators (OpenACC) and achieve speedups of up to $$ over 32 open multi-processing (OpenMP) CPU threads.     

基于完全活性空间自洽场的杂化多组态密度泛函方法λ-DFCAS

提出了一种杂化多组态密度泛函新方法——λ-DFCAS. 在λ-DFCAS方法中, 电子相关能被分为静态和动态相关能. 静态相关能由多组态波函数方法完全活性空间自洽场(CASSCF)得到, 而动态相关能由密度泛函理论方法描述. 两种相关能的杂化比例由一个可调节的参数λ控制. 参数λ的取值取决于分子体系的多组态特性, 在0~1之间变化, 从而使得λ-DFCAS可以应用于各种强相关分子体系. 该方法能够以与CASSCF相当的计算代价获得接近完全活性空间二阶微扰(CASPT2)的计算精度, 并具备了大小一致性.     

Intrinsic field theory of chemical reactions

An intrinsic principle of least action is presented for the intrinsic dynamism of chemical reactions. Then, as the stationary trajectory, a meta-IRC (intrinsic reaction coordinate) draws a geodesic curve in a rigged Riemannian space. This establishes a geodesic law for the intrinsic dynamism. Moreover, a diagrammatic perturbation theory is formulated for the intrinsic dynamism, and a dynamical interaction between a chemically reacting system and a background system is investigated. Then, the structural stability of the system is discussed using a new concept of the dynamical potential field. An example is given in order to elucidate the present theory.Dedicated to Prof. Hermann Hartmann on the occasion of his 65th birthday.     

H2CCC光谱性质的从头算研究

采用全活化空间自洽场方法(CASSCF)在C2v对称性和ANO-S基组水平下, 研究了H2CCC自由基及其阴阳离子的基态和低激发态性质. 为了进一步考虑动态电子相关效应, 采用多组态二级微扰理论(CASPT2)获得了更加精确的能量值. 计算得到X1A1 → 1A2, X1A1 → 1B1和X1A1 → 21A1在159.0, 216.5和476.4 kJ/mol处的激发可分别归因于π(b2)→π*(b1), n(a1)→π*(b1)和π(b1)→π*(b1)的跃迁, 理论波长与紫外吸收光谱得到的实验数据一致. 计算得到的电子亲和势与实验值也非常接近.     

Ladder operators in commutator perturbation method

The present work is a version of Van Vleck–Primas perturbation method in terms of generalized ladder operators. Using the superoperator approach, a fully general, self-consistent and a totally free scheme from representation is developed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 79–90, 1998     

Multiconfigurational Green's function approach with quasidegenerate perturbation theory

The new approach to approximation of polarization propagator (PP) for electronic states of atoms and molecules with reference state wave function (RSWF) constructed on the base of a multidimensional model space is presented. This approach exploiting the apparatus of the quasidegenerate perturbation theory (QDPT) is realized in the zeroth QDPT order and through the first one. The original complete system of excitation operators introduced in the approach is consistent with the RSWF by the perturbation order. This factor in conjunction with the flexibility of the RSWF creates the capabilities of balanced accounting of correlation and quasidegeneracy effects at different locations of nuclei in a molecule and for all the states concerned. In this way, the transition characteristics in electronic shells of molecules in a wide area of nuclear geometry parameters may be appropriately evaluated. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002