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In this paper, we examine decay and fragmentation of core-excited and core-ionized water molecules combining quantum chemical calculations and electron-energy-resolved electron-ion coincidence spectroscopy. The experimental technique allows us to connect electronic decay from core-excited states, electronic transitions between ionic states, and dissociation of the molecular ion. To this end, we calculate the minimum energy dissociation path of the core-excited molecule and the potential energy surfaces of the molecular ion. Our measurements highlight the role of ultra-fast nuclear motion in the 1a

In this paper, we examine decay and fragmentation of core-excited and core-ionized water molecules combining quantum chemical calculations and electron-energy-resolved electron–ion coincidence spectroscopy. The experimental technique allows us to connect electronic decay from core-excited states, electronic transitions between ionic states, and dissociation of the molecular ion. To this end, we calculate the minimum energy dissociation path of the core-excited molecule and the potential energy surfaces of the molecular ion. Our measurements highlight the role of ultra-fast nuclear motion in the 1a1−14a1" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">1a−114a11a1−14a1 core-excited molecule in the production of fragment ions. OH+ fragments dominate for spectator Auger decay. Complete atomization after sequential fragmentation is also evident through detection of slow H+ fragments. Additional measurements of the non-resonant Auger decay of the core-ionized molecule (1a1−1" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">1a−111a1−1) to the lower-energy dication states show that the formation of the OH+ + H+ ion pair dominates, whereas sequential fragmentation OH+ + H+ → O + H+ + H+ is observed for transitions to higher dication states, supporting previous theoretical investigations.

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions. ispartof: JOURNAL OF CHEMICAL PHYSICS vol:152 issue:21 ispartof: location:United States status: published

The Complete Active Space Second-Order Perturbation Theory (CASPT2) is well-established as a high-accuracy electronic structure method. It was originally implemented in the early 1990s to an efficient computer code in the molcas program suite, and this implementation has been extensively used as a standard tool. Here, we report a comparison of it against two independent computer-aided implementations of the CASPT2 method, revealing that the CASPT2 energies provided by the original code of molcas (version 8 or earlier) are inconsistent with the predictions of the lately developed computer-aided implementations. It is shown that this error is associated with the projections of the first-order equation onto the fully internally contracted multireference bases which are partially inconsistent between the left- and right-hand sides. The degree of the errors is assessed by performing illustrative CASPT2 calculations. The errors in total CASPT2 energies are demonstrated to be negligible relative to chemical accuracy in many cases, while there is a difficult case where they may substantially alter chemical description. The incorporation of the consistent projections into molcas has been carried out, which is available in the version 8 sp1. (Less)

In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with post calculation analysis and visualization, and new electronic and muonic basis sets.

In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics, and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism, and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets.

In this work, we present a parallel approach to complete and restricted active space second-order perturbation theory, (CASPT2/RASPT2). We also make an assessment of the performance characteristics of its particular implementation in the Molcas quantum chemistry programming package. Parallel scaling is limited by memory and I/O bandwidth instead of available cores. Significant time savings for calculations on large and complex systems can be achieved by increasing the number of processes on a single machine, as long as memory bandwidth allows, or by using multiple nodes with a fast, low-latency interconnect. We found that parallel efficiency drops below 50% when using 8-16 cores on the shared-memory architecture, or 16-32 nodes on the distributed-memory architecture, depending on the calculation. This limits the scalability of the implementation to a moderate amount of processes. Nonetheless, calculations that took more than 3 days on a serial machine could be performed in less than 5 h on an InfiniBand cluster, where the individual nodes were not even capable of running the calculation because of memory and I/O requirements. This ensures the continuing study of larger molecular systems by means of CASPT2/RASPT2 through the use of the aggregated computational resources offered by distributed computing systems.

The chromium dimer has long been a benchmark molecule to evaluate the performance of different computational methods ranging from density functional theory to wave function methods. Among the latter, multiconfigurational perturbation theory was shown to be able to reproduce the potential energy surface of the chromium dimer accurately. However, for modest active space sizes, it was later shown that different definitions of the zeroth-order Hamiltonian have a large impact on the results. In this work, we revisit the system for the third time with multiconfigurational perturbation theory, now in order to increase the active space of the reference wave function. This reduces the impact of the choice of zeroth-order Hamiltonian and improves the shape of the potential energy surface significantly. We conclude by comparing our results of the dissocation energy and vibrational spectrum to those obtained from several highly accurate multiconfigurational methods and experiment. For a meaningful comparison, we used the extrapolation to the complete basis set for all methods involved.

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization. QC 20210506

The well-known natural orbitals are defined as eigenfunctions of a one-particle reduced density operator, and can be obtained from a computed density matrix by diagonalization. Similarly, in this article we define the binatural orbitals, which are obtained for a pair of wave functions by a singular value decomposition of a reduced transition density matrix. The pair of states would usually be eigenstates of the electronic Hamiltonian, and the binatural orbitals then serve as a useful tool for the analysis of the transition between these states. More generally, application to any two state functions gives important information as to how the two states differ. Some examples are shown.

The electronic structure and low-lying electronic states of a Co(III)(diiminato)(NPh) complex have been studied using multiconfigurational wave function theory (CASSCF/CASPT2). The results have been compared to those obtained with density functional theory. The best agreement with ab initio results is obtained with a modified B3LYP functional containing a reduced amount (15%) of Hartree-Fock exchange. A relativistic basis set with 869 functions has been employed in the most extensive ab initio calculations, where a Cholesky decomposition technique was used to overcome problems arising from the large size of the two-electron integral matrix. It is shown that this approximation reproduces results obtained with the full integral set to a high accuracy, thus opening the possibility to use this approach to perform multiconfigurational wave-function-based quantum chemistry on much larger systems relative to what has been possible until now.

Bjorn Roos is one of the pioneers in the development and usage of multiconfigurational methods, in particular, the complete active space self-consistent field method and the perturbational complete active space perturbation theory through second order. To perform multiconfigurational calculations using these methods, a set of active orbitals must be selected, and the success of the methods depends on the choice of this set. This is not only sometimes easy but also sometimes difficult, especially for use of the more recent RASSCF and RASPT2 methods (which use a "restricted active space" rather than the complete one). Although an automated procedure for selecting the active orbitals would be a preferable solution, this does not seem feasible yet. An account of the problem is given, with examples and some approaches that usually work. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111: 3329-3338, 2011 (Less)

Laser evaporation of carbon-rich uranium/carbon alloys followed by atom reactions in a solid argon matrix and trapping at 8 K gives weak infrared absorptions for CUO at 852 and 804 cm(-1). A new band at 827 cm(-1) becomes a doublet with mixed carbon 12 and 13 isotopes and exhibits the 1.0381 isotopic frequency ratio, which is appropriate for the UC diatomic molecule, and another new band at 891 cm(-1) gives a three-band mixed isotopic spectrum with the 1.0366 isotopic frequency ratio, which is characteristic of the linear CUC molecule. CASPT2 calculations with dynamical correlation find the C[triple bond]U[triple bond]C ground state as linear 3Sigma(u)+ with 1.840 A bond length and molecular orbital occupancies for an effective bond order of 2.83. Similar calculations with spin-orbit coupling show that the U[triple bond]C diatomic molecule has a quintet (Lambda = 5, Omega = 3) ground state, a similar 1.855 A bond length, and a fully developed triple bond of 2.82 effective bond order.

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented inthis report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two-electron integrals and in the generation of so-called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self-consistent field, density functional theory, 2nd order perturbation theory, complete-active space self-consistent field multiconfigurational reference 2nd order perturbation theory, and coupled-cluster methods. The report further elaborates on the implementation of a restricted-active space self-consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas-Kroll-Hess transformation for one-component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so-called picture-change-free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies. (c) 2009 Wiley Periodicals, Inc. J Corn put Chem 31: 224-247, 2010

Laser-ablated group 6 metal atoms react with NF3 and PF3 to form the simple lowest energy N MF3 and P=MX3 products, and this investigation has been extended to AsF3. Mo and W atoms react with AsF3 upon excitation by laser ablation or UV irradiation to form stable trigonal As MF3 terminal arsenides. These molecules are identified by comparison of the closely related infrared spectra of the analogous phosphide species and with frequencies calculated by density functional theory and multiconfigurational second order perturbation theory (CASSCF/CASPT2). Computed CASSCF/CASPT2 triple bond lengths for the As MoF3 and As WF3 molecules are 2.240 angstrom and 2.250 angstrom, respectively. The natural bond orders calculated by CASSCF/CASPT2 decrease from 2.67 to 2.60 for P MoF3 to As MoF3 and from 2.74 to 2.70 for P WF3 to As WF3 as the arsenic valence orbitals are less effective than those of phosphorus in bonding to each metal atom and the larger metal orbital size becomes more compatible with the arsenic valence orbitals. The Cr atom reaction gives the arsinidene AsF=CrF2 product instead of the higher energy As CrF3 molecule as the Cr (VI) state is not supported by the softer pnictides. (Less)

An ab initio study of the role of electronic curve crossing of benzene S-1 state in the photo dissociation dynamics of the iodobenzene and effect of fluorination is presented. Two dissociative life times observed in iodobenzene is attributed to the coupled repulsive potential energy curves of the low-lying n-sigma*, pi-sigma*, pi-pi* states. The direct channel is attributed to the alkyl like transition and the indirect channel is attributed to the mixing of the alkyl like transitions with the low lying benzene pi-pi* transitions. Fluorination of iodobenzene results in a substantial increase in the direct channel product. To analyze the possible role of electronic curve crossing of these transitions, potential energy curves of low-lying n-sigma*, pi-sigma*, pi-pi* states were studied including spin-orbit and relativistic effects using the Restricted Active Space state interaction multistate complete active space perturbation theory (RASSI-MS-CASPT2) method. Crossing behavior of spin-free and spin-orbit potential energy curves was analyzed for the role of the benzene S-1 state. Our results indicate the curve crossing region to be around 2.00-2.35 angstrom for both C6H5I and C6F5I. Analysis of effect of fluorination on the energies of states corresponding to benzene pi-pi* and n-sigma* transitions suggests an increase in the energy of benzene pi-pi* states and a decrease in the energy of the states corresponding to n-sigma* transitions. Increased spin-orbit gap, increased separation of the benzene S-1(pi-pi*) state and n-sigma* states in the region of curve crossing, lesser mixing of the pi-pi* and n-sigma* states, an order of magnitude decrease in the transition strength to the benzene singlet transition all contributed to the observed Substantial increase in the quantum yield of the direct channel product on fluorination of aryl halides. (c) 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 1962-1974, 2009 (Less)

The computation of the electronic g tensor by two multireference methods is presented and applied to a selection of molecules including CN, BO, AlO, GaO, InO, ZnH, ZnF, O(2), H(2)O(+), O(3) (-), and H(2)CO(+) (group A) as well as TiF(3), CuCl(4) (2-), Cu(NH(3))(4) (2+), and a series of d(1)-MOX(4) (n-) compounds, with M=V, Cr, Mo, Tc, W, Re and X=F, Cl, Br (group B). Two approaches are considered, namely, one in which spin-orbit coupling and the Zeeman effect are included using second-order perturbation theory and another one in which the Zeeman effect is added through first-order degenerate perturbation theory within the ground-state Kramers doublet. The two methods have been implemented into the MOLCAS quantum chemistry software package. The results obtained for the molecules in group A are in good agreement with experiment and with previously reported calculated g values. The results for the molecules in group B vary. While the g values for the d(1) systems are superior to previous theoretical results, those obtained for the d(9) systems are too large compared to the experimental values.

Uranium atoms activate methane upon ultraviolet excitation to form the methyl uranium hydride CH3-UH, which undergoes alpha-H transfer to produce uranium methylidene dihydride, CH2UH2. This rearrangement most likely occurs on an excited-quintet potential-energy surface and is followed by relaxation in the argon matrix. These simple U + CH4 reaction products are identified through isotopic substitution ((CH4)-C-13, CD4, CH2D2) and density functional theory frequency and structure calculations for the strong U-H stretching modes. Relativistic multiconfiguration (CASSCF/CASPT2) calculations substantiate the agostic distorted C-1 ground-state structure for the triplet CH2UH2 molecule. We find that uranium atoms are less reactive in methane activation than thorium atoms. Our calculations show that the CH2UH2 complex is distorted more than CH2ThH2. A favorable interaction between the low energy open-shell U(5f) sigma orbital and the agostic hydrogen contributes to the distortion in the uranium methylidene complexes. (Less)

New basis sets of the atomic natural orbital (ANO) type have been developed for the actinide atoms Ac-Cm. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in a electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The lowest multiplet levels have been computed. These calculations include spin-orbit coupling using a variation-perturbation approach. The atomic polarizability of the spherically symmetric americium atom has been computed to be 116 au(3). (c) 2005 Elsevier B.V. All rights reserved.

The value of the two-particle density function at coalescence is frequently used as an additional variable for formulating approximate exchange-correlation or correlation functionals. Here, its applications as one of the key variables for the construction of new DFT (preferably multi-determinant) functionals is investigated. The basic formalism is presented and it is shown that this replacement avoids some difficulty to construct a Fock matrix in a ROKS (restricted open-shell Kohn–Sham) method and also to reduce the ‘double counting’ of correlation energy in CASDFT (complete active space density functional theory) calculations. Calculations of excitation energies for transition metals and dissociation curves for diatomic molecules are presented as an example.

An ab initio study of the role of electronic curve crossing in the photodissociation dynamics of the alkyl halides is presented. Recent experimental studies show that curve crossing plays a deterministic role in deciding the channel of dissociation. Coupled repulsive potential energy curves of the low-lying n-sigma(*) states are studied including spin-orbit and relativistic effects. Basis set including effect of core correlation is used. Ab initio vertical excitation spectra of CH(3)I and CF(3)I are in agreement with the experimental observation. The curve crossing region is around 2.371 A for CH(3)I and CF(3)I. The potential curves of the repulsive excited states have larger slope for CF(3)I, suggesting a higher velocity and decreased intersystem crossing probability on fluorination. We also report the potential curves and the region of curve crossing for CH(3)Br and CH(3)Cl.

A new shifted zeroth-order Hamiltonian is presented, which will be used in second-order multiconfigurational perturbation theory (CASPT2). The new approximation corrects for the systematic error of the original formulation, which led to an relative overestimate of the correlation energy for open shell system, resulting in too small dissociation and excitation energies. Errors in the D, values for 49 diatomic molecules have been reduced with more than 50%. Calculations on excited states of the N-2 and benzene molecules give a similar improvement. (C) 2004 Elsevier B.V. All rights reserved.

A density functional theory based on a complete active space self consistent field (CASSCF) reference function with exact exchange is discussed. It is first shown that such a theory may be formulated with a correlation potential dependent on the density function and on the active space used. Auxiliary functions, such as the on-top two-particle density, are used to define uniquely the potential for different active spaces. The paper also analyses the correlation functional for some atomic and molecular cases. Large ab initio calculations are performed to obtain accurate density functions. A correlation potential is then fitted such that the reference CASSCF function gives the same density. The correlation potential values are saved in a data base for future analysis.

New basis sets of the atomic natural orbital (ANO) type have been developed for the main group and rare gas atoms. The ANO's have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the dimer at its equilibrium geometry. Scalar relativistic effects are included through the use of a Douglas−Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and the ground-state potentials for the dimers. These calculations include spin−orbit coupling using the RASSCF State Interaction (RASSI-SO) method. The spin−orbit splitting for the lowest atomic term is reproduced with an accuracy of better than 0.05 eV, except for row 5, where it is 0.15 eV. Ionization energies and electron affinities have an accuracy bett...

The program system MOLCAS is a package for calculations of electronic and structural properties of molecular systems in gas, liquid, or solid phase. It contains a number of modern quantum chemical methods for studies of the electronic structure in ground and excited electronic states. A macromolecular environment can be modeled by a combination of quantum chemistry and molecular mechanics. It is further possible to describe a crystalline material using model potentials. Solvent effects can be treated using continuum models or by combining quantum chemical calculations with molecular dynamics or Monte-Carlo simulations. MOLCAS is especially adapted to treat systems with a complex electronic structure, where the simplest quantum chemical models do not work. These features together with the inclusion of relativistic effects makes it possible to treat with good accuracy systems including atoms from the entire periodic system. MOLCAS has effective methods for geometry optimization of equilibria, transition states, conical intersections, etc. This facilitates studies of excited state energy surfaces, spectroscopy, and photochemical processes.

The results of a theoretical study of the ground state, 1(1)A(g), and of the lowest B-1(u) states of trans-stilbene are presented. The vertical and adiabatic excitation energies of the lowest B-1(u) states have been computed using multiconfigurational SCF theory, followed by second-order perturbation. theory. It is shown that the two lowest excited states are separated by a small energy gap in the Franck-Condon region. They are the 1(1)B(u), characterized by the HOMO-->LUMO single excitation substantially localized on the ethylenic moiety, and the 2(1)B(u), formed by a combination,of one electron excitations localized mainly on the benzene rings. The most intense transition is found to be the lowest in energy when the interaction between different states is included at the level of second-order perturbation theory. The vibronic structure of emission and absorption spectra of the two lowest B-1(u) states have been determined within the Franck-Condon approximation. The spectrum calculated for the 1(1)B(u) state agrees with the experimental spectrum, while the low intensity band computed for the 2(1)B(u) state has no experimental counterpart. It is concluded that this band is buried in the strong 1(1)B(u) absorption and therefore not observed. (Less)

A new theoretical approach to two-photon transition intensities at the multiconfigurational self-consistent field (MCSCF) level of theory, is described in detail. The fundamental property of an MCSCF wave function, that it is possible to define the response equations for an excited state, is a prerequisite. The method requires solely first-order multiconfigurational response calculations, because the equations involve the response of both the initial and final state. However, the method is approximate as the coupling between the +ω and −ω parts of the linear response is disregarded. The complete active space state interaction (CASSI) method is applied in the evaluation of the involved matrix elements. To illustrate the performance and the requirements of this method, it was used to determine TP transitions in trans-1,3-butadiene and trans-stilbene.

The two-photon spectrum of the 2 1 A g ı1 1 A g transition in trans -stilbene has been calculated at the complete active space self-consistent field (CASSCF) level of theory. Energies were obtained at the complete active space second-order perturbation (CASPT2) level of theory, while the geometries of both the initial and final states were optimized at the CASSCF level. The energy and the geometry optimizations were performed using an active space of 14 electrons in 14 active πorbitals. The vibrational frequencies of both states and the two-photon transition (TPT) cross-section were calculated with a smaller active space where the two lowest πorbitals were kept inactive. A newly implemented algorithm, in the quantum chemical package Molcas was used to determine the two-photon transition intensity. This method requires only the linear response of the CASSCF wavefunction. Furthermore, the vibronic structure of this TPT was studied. The Franck-Condon factors were obtained by calculating the overlap between the vibrational states involved, which were determined from the force fields of both the initial and final states, at the CASSCF level of theory. The results are in agreement with experiment.

A method to compute spin-orbit coupling between electronic states is presented. An effective one-electron spin-orbit Hamiltonian is used, based on atomic mean field integrals, The basic electronic states are obtained using the restricted active space (RAS) SCF method. The Hamiltonian matrix is obtained by an extension of the restricted active space state interaction (RASSI) method. Several hundred states can be included. Tests for atoms and molecules from the entire periodic system show accurate results. Computed spin-orbit effects on relative energies are normally accurate within a few percent. The method has been included in the MOLCAS-5.0 quantum chemistry software. (C) 2002 Elsevier Science B.V. All rights reserved.

The structure and vibrational frequencies of the UO[2] molecule have been determined using multiconfigurational wave functions (CASSCF/CASPT2), together with a newly developed method to treat spin−orbit coupling. The molecule has been found to have a (5f[phi])(7s), [3]Φ[u], Ω = 2 ground state with a U−O bond distance of 1.77 Å. The computed antisymmetric stretching σu frequency is 923 cm[-1] with a 16/18 isotope ratio of 1.0525 which compares with the experimental values of 915 cm[-1] and 1.0526, respectively. Calculations of the first adiabatic ionization energy gave the value 6.17 eV, which is 0.7 eV larger than the currently accepted experimental result. Reasons for this difference are suggested.

The present contribution analyses the trans–cis photoisomerization mechanism of ethene and styrene on the singlet manifold. Within the framework of multiconfigurational second-order perturbation theory (CASPT2), the extended multistate approach (MS-CASPT2) is found to be flexible enough to describe energy hypersurfaces adiabatically. For ethene, torsion about the CC bond towards a perpendicular structure leads to a situation where the energy difference between the ground and the lowest excited state is still too large (2.5 eV) for efficient radiationless decay. However, the energy gap decreases to 0.4 eV when one of the methylene moieties is, in addition, pyramidalized from the twisted structure. A similar behaviour is obtained for styrene upon torsion-pyramidalization of the methylene subunit, with a computed energy gap of 0.2 eV. The intersection of the ground and excited states potential energy surfaces occurs by a slight additional pyramidalization from the optimal excited state structure. The actual barrier height on the S1 surface from the local planar minimum structure is estimated to be less than 0.8 eV.

The repulsive ground electronic state X2Σ+ of HeH is strongly coupled to the Rydberg states at small interatomic distances. Such large couplings also occur between some of the Rydberg states. HeH+ ions that capture an electron in a Rydberg state end up in separated He and H atoms by indirect predissociation. This paper presents a study of potential functions and pertinent matrix elements involving the lowest electronic states: the 2Σ+ states, X, A, C, and D, and the 2Π states B and E. Individual transition rates as well as total radiative and non-radiative lifetimes have been computed for the lowest vibrational and rotational levels.

An extension of the multiconfigurational second-order perturbation approach CASPT2 is suggested, where several electronic states are coupled at second order via an effective-Hamiltonian approach. The method has been implemented into the MOLCAS-4 program system, where it will replace the single-state CASPT2 program. The accuracy of the method is illustrated through calculations of the ionic-neutral avoided crossing in the potential curves for LiF and of the valence-Rydberg mixing in the V-state of the ethylene molecule.

We present a simple formula for the overlap integrals of two sets of multi-dimensional harmonic oscillators. The oscillators have in general different equilibrium points, force constants, and natural vibration modes. The formula expresses the overlap matrix in the one-dimensional case, 〈m′|n′′〉, as a so-called LU decomposition, 〈m′|n′′〉=〈0′|0′′〉 ∑ L mt U tn , where the summation index has a range 0≤t≤min(m,n), i.e., it is the matrix product of a lower-triangular matrix L with an upper-triangular U. These matrices are obtained from simple recursion formulae. This form is essentially retained in the multi-dimensional case. General matrix elements are obtained by exact and finite expressions, relating them to matrix elements over a single set of harmonic oscillator wave functions. We present test calculations with error estimates, also comparing with literature examples.

In multiconfigurational perturbation theory, so-called intruders may cause singularities in the potential energy functions, at geometries where an energy denominator becomes zero. When the singularities are weak, they may be successfully removed by level shift techniques. When applied to excited states, a small shift merely moves the singularity. A large shift may cause new divergencies, and too large shifts are unacceptable since the potential function is affected in regions further away from the singularities. This Letter presents an alternative which may be regarded as an imaginary shift. The singularities are not moved, but disappear completely. They are replaced by a small distortion of the potential function. Applications to the N 2 ground state, its A 3 / gE u + state, and the Cr 2 ground state show that the distortion caused by this procedure is small.

When a molecular equilibrium geometry is determined by minimizing the energy by a quasi-Newton-Raphson method, the number of iterations required depends critically on the choice of an approximate molecular Hessian matrix. We find that a simple 15-parameter function of the nuclear positions gives a good choice for any molecule with atoms from the first three rows of the periodic table. This Hessian is used for ab initio geometry optimizations with the quasi-Newton-Raphson method, with or without update. The equilibrium geometries of 30 molecules, with a variety of sizes and symmetries, is obtained with the new scheme, which is shown to converge significantly faster than other methods.

A theoretical study has been performed on the five lowest excited states of the ozone molecule using multiconfigurational second-order perturbation theory (CASPT2). The predicted order of states is: 3A2 (T0 = 1.15 eV), 3B2 (T0 = 1.33 eV, 3B1 (T0 = 1.33 eV), 1A2 (T0 = 1.44 eV) and 1B1 (T0 = 1.88 eV). Corresponding experimental data are: 1.18, 1.30, 1.45, 1.58, and 2.05 eV, respectively. Equilibrium geometries, harmonic frequencies of symmetric vibrations, and vertical excitation energies are also reported. The dissociation limit De for the ground state of ozone is found to be 1.08 eV, in agreement with the experimental value (1.13 eV). The calculations make use of a modified Fock operator in the CASPT2 theory. Relative energies of states with a different number of open shells are substantially improved. The modified CASPT2 method was checked by calculating spectroscopic constants of the oxygen molecule.

Bjorn Roos is one of the pioneers in the development and usage of multiconfigurational methods, in particular, the complete active space self-consistent field method and the perturbational complete active space perturbation theory through second order. To perform multiconfigurational calculations using these methods, a set of active orbitals must be selected, and the success of the methods depends on the choice of this set. This is not only sometimes easy but also sometimes difficult, especially for use of the more recent RASSCF and RASPT2 methods (which use a "restricted active space" rather than the complete one). Although an automated procedure for selecting the active orbitals would be a preferable solution, this does not seem feasible yet. An account of the problem is given, with examples and some approaches that usually work. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111: 3329-3338, 2011 (Less)

The tunneling rate for the transfer of an electron from an Fe2+ to an Fe3+ ion is determined by a Hamiltonian matrix element, which has been calculated for interionic distances in the range 5.10–7.22 A. The ions were either alone, or surrounded by water molecules. The calculations were made by computing the electronic wave function of the system by the complete active space self‐consistent field (CASSCF) method, and then evaluating the relevant matrix element for this wave function interacting with a symmetry image of itself, representing the final state. Basis set dependence, and in particular the effect of bond functions, was investigated, as well as the effect of removing some water molecules or replacing them with point charges. The results seem to indicate that earlier calculated values, which are frequently used, of the tunneling rate may be too large by as much as a factor of 10. If so, then the agreement between earlier calculated electron transfer rates and experimental data may be explained by c...

A method is presented, whereby dynamic σ-π polarization, i.e. the correlation effect expressed by simultaneous (σ-σ*, π-π*) excitations, can be approximately included in a multi-reference configuration interaction (MRCI) or multi-configurational self-consistent field (MC-SCF) calculation, without need to explicitly correlate the sigma orbitals. The method, which we call the capacitance matrix method, is based on the use of conventional one-electron integrals, from which a σ polarization potential (SPP) contribution is computed and added to the one- and two-electron Hamiltonian. In the present form, the method requires one parameter for each type of atom, and one for each type of bond. These parameters were adjusted to reproduce the dynamic σ-π polarization energy, computed by restricted multi-reference CI calculations, of a number of states of different hydrocarbons, and the agreement was within a few percent. Using the same parameters in CAS (Complete Active Space) SCF calculations of various states of benzene gives excitation energies, when SPP is included, which is comparable to those obtained by much more elaborate MRCI calculations.

The inversion potential of the X 1 A 1 electronic ground state of the methyl anion CH 3 − is investigated at the SCF/single-reference configuration interaction ( SCF SR-CI ) and at the completeactive-space SCF/multireference CI ( CASSCF MR-CI ) levels of theory employing large Gaussian basis sets augmented by diffuse functions to represent the weakly bound carbon lone-pair electrons. These calculations, together with the corresponding out-of-plane bending potential of the CH 3 radical, demonstrate that the Born-Oppenheimer separation of the electronic and nuclear motions becomes invalid when moving along the inversion potential of CH 3 − ion by conventional methods, a quasi-diabatic representation of the full-dimensional potential energy hypersurface is evaluated applying standard SCF SR-CI calculations. From the resulting anharmonic potential function the vibration-rotation energies of the CH 3 − and CD 3 − isotopic variants are calculated using an improved version of the nonrigid inverter Hamiltonian approximation. Combining the present results with the previously determined vibrational potential function for the methyl radical CH 3 , the different stabilities of the CH 3 − and CD 3 − isotopes against autodetachment are discussed in terms of effective potentials for the inversion motion and the adiabatic electron affinity of CH 3 is determined as EA = 0.09 eV close to the experimental value of 0.08 ± 0.03 eV. The photoelectron spectrum of CH 3 − is calculated within the Franck-Condon approximation in good agreement with the experimental spectrum. Present predictions of the lower inversion-vibration energy levels and the corresponding rotation constants of the CH 3 − ion are expected to be reliable.

Restricted Active Space (RAS) SCF calculations have been performed of the potential curves for theX3Σ− andA3Π states of the OH+ ion and on the lifetime of thev=0−2 vibrational levels of theA state. The convergence of the transition moment integral as a function of the size of the active orbital space was used to select the active orbitals. The calculated value of thev=0 lifetime is 2.4 µs. An estimate of the errors remaining in the calculation leads to a final theoretical value of 2.7±0.1 µs. Computed bond distances and bond energies are 1.031 (1.029) A and 5.05 (5.01) eV, respectively, for theX state, and 1.137 (1.135) A and 1.57 eV, respectively, for theA state (experimental values within parenthesis).

New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are included as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.

To a quantum chemist with no particular background in astrophysics or astronomy, a brief glance at journals and textbooks in these fields shows at least three areas where computational quantum chemistry has had a valuable impact: Interstellar cloud chemistry; stellar atmosphere modelling; and chemistry in extreme conditions, such as at the surface of a neutron star. The first two uses are particularly suitable, since standard methods are directly applicable. For such problems, good calculations of potential energy as well as expectation values and matrix elements of dipole and other operators appears to be in demand. Many electronic states may be involved, at least a broad range of problems involve fairly small molecules, often radicals, and conformation regions far from equilibrium. Such problems are addressed by three methods originated in our laboratory, and known by the acronyms RASSCF (Restricted Active Space Self-Consistent Field, Malmqvist et al. 1990), RASSI (RAS State Interaction) and CASPT2 (Complete Active Space Perturbation Theory to Second Order-Complete Active Space Perturbation Theory to Second Order, Andersson et al. 1990; Andersson et al. 1992).

Multiconfigurational quantum chemical methods (CASSCF/CASPT2) have been used to study the chemical bond in the actinide diatoms Ac2, Th2, Pa2, and U2. Scalar relativistic effects and spin-orbit coupling have been included in the calculations. In the Ac2 and Th2 diatoms the atomic 6d, 7s, and 7p orbitals are the significant contributors to the bond, while for the two heavier diatoms, the 5f orbitals become increasingly important. Ac2 is characterized by a double bond with a 3Sigmag-(0g+) ground state, a bond distance of 3.64. A, and a bond energy of 1.19 eV. Th2 has quadruple bond character with a 3Dg(1g) ground state. The bond distance is 2.76 A and the bond energy (D0) 3.28 eV. Pa2 is characterized by a quintuple bond with a 3Sigmag-(0g+) ground state. The bond distance is 2.37 A and the bond energy 4.00 eV. The uranium diatom has also a quintuple bond with a 7Og (8g) ground state, a bond distance of 2.43 A, and a bond energy of 1.15 eV. It is concluded that the strongest bound actinide diatom is Pa2, characterized by a well-developed quintuple bond.