A classical versus quantum mechanics study of the \hbox{OH}\,+\,\hbox{CO} \rightarrow\,\hbox{H}\,+\,\hbox{CO}_2 (J?=?0) reaction

When appropriately used, the multiconfigurational self-consistent field (MCSCF) approximation is useful in discerning correct electronic structure results. However, with the increasing size of chemical systems of interest, MCSCF rapidly becomes unfeasible due to the requirement of larger active spaces, which lead to computationally unmanageable numbers of configurations. This situation is especially true for complete active space self-consistent field (CASSCF). In particular, reducing this computational expense by using restricted active spaces in solving for gradients and nonadiabatic couplings (NACs) during dynamics runs would save computer time. However, the validity of such restricted spaces is not well-known even for recovering the majority of the nondynamical correlation and inevitably varies between chemical systems across a range of nuclear geometries. As such, we use the recently implemented coupled perturbed–occupation restricted multiple active space (CP-ORMAS) equations (West et al., unpublished) to verify the accuracy of this approximation for gradients and NACs vectors around two specific conical intersection geometries for the silaethylene and butadiene systems. Overall, no excitations between appropriate subspaces show qualitatively reasonable results while single excitations significantly improve ORMAS results relative to the CASSCF level in these particular systems. However, single excitation schemes do not always lead to the correct orbital subspaces, and as a result, seemingly smooth potential energy surfaces (PES) do not always result in smooth analytical gradients and NACs. In addition, while some of the single excitation ORMAS and CASSCF schemes have improper orbitals rotate into the active space, the schemes without excitations (even with more subspaces) do not exhibit this behavior.     

Efficient implementation of restricted active space configuration interaction with the hole and particle approximation

The restricted active space configuration interaction (RASCI) formalism with the hole and particle truncation of the wavefunction, that is, RASCI(h,p), holds very nice properties such as balanced treatment of ground and low‐lying excited states, spin‐completeness, large flexibility of the wavefunction, and moderate computational cost. In this article, I present a new implementation of the RASCI(h,p) method using a general algorithm based on the integral‐driven approach. The new implementation allows to choose any electronic configuration as the single reference in combination with an excitation operator with any number of ionization, electron attachment, or spin‐flip (SF) excitations. The applicability and good performance of the new computational code is tested in the ground state calculation of water molecule with increasingly large active spaces and up to the full‐CI limit, the calculation of all‐trans linear polyenes with variable number of SF excitations, and the low‐lying states of fluorine molecule with a double‐ionization potential operator. © 2012 Wiley Periodicals, Inc.     

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.     

Pure representability problem and new models of the electronic Fock space

New models of the Fock space sector corresponding to some fixed number of electrons are introduced. These models originate from the representability theory and their practical implementation may lead to essential reduction of dimensions of intermediate CI spaces. A certain zero‐order theory is proposed that gives wavefunctions approximately equivalent to ones obtained by accounting for all excitations from the Hartree–Fock reference state up to the qth order. Simple numerical examples are given to illustrate our approach. © 2001 Wiley Periodicals, Inc. Int J Quantum Chem, 2001     

The structure of linear SiCC: An ab initio SCF CI study including vibrational effects

Large-scale SCF CI calculations have been performed for the ground ¹Σ⁺ state of linear SiCC. The calculation includes up to quadruple excitations in the valence space plus all single and double excitations from the valence localized orbitals of the single HF configuration. Vibrational wavefunctions have been derived from the CI potential surface. Vibrational frequencies including anharmonicity corrections are calculated together with the zero-point vibrational correction to the rotational constant. The large dipole moment, 4.62 D, should make this molecule suitable for radioastronomic searches.     

Direct CI method in restricted configuration spaces

A configuration interaction (CI) method in restricted CI (RCI) space obtained by imposing inequality-type restrictions on the occupancies of groups of molecular orbitals (MOs) was studied. The direct CI approach in such space was analyzed, and some recommendations concerning practical implementation of the RCI method are given. The corresponding program has been written in FORTRAN 77 for an IBM 486 DX personal computer and has been used for electronic structure calculations on transition metal complexes using a valence MO basis with the INDO approximation. © 1996 by John Wiley & Sons, Inc.     

Efficient calculations of a large number of highly excited states for multiconfigurational wavefunctions

Electronically excited states play important roles in many chemical reactions and spectroscopic techniques. In quantum chemistry, a common technique to solve excited states is the multiroot Davidson algorithm, but it is not designed for processes like X-ray spectroscopy that involves hundreds of highly excited states. We show how the use of a restricted active space wavefunction together with a projection operator to remove low-lying electronic states offers an efficient way to reach single and double-core-hole states. Additionally, several improvements to the stability and efficiency of the configuration interaction (CI) algorithm for a large number of states are suggested. When applied to a series of transition metal complexes the new CI algorithm does not only resolve divergence issues but also leads to typical reduction in computational time by 70%, with the largest savings for small molecules and large active spaces. Together, the projection operator and the improved CI algorithm now make it possible to simulate a wide range of single- and two-photon spectroscopies. © 2019 Wiley Periodicals, Inc.     

A comparison of singlet and triplet states for one- and two-dimensional graphene nanoribbons using multireference theory

This study examines the radical nature and spin symmetry of the ground state of the quasi-linear acene and two-dimensional periacene series. For this purpose, high-level ab initio calculations have been performed using the multireference averaged quadratic coupled cluster theory and the COLUMBUS program package. A reference space consisting of restricted and complete active spaces is taken for the π-conjugated space, correlating 16 electrons with 16 orbitals with the most pronounced open-shell character for the acenes and a complete active-space reference approach with eight electrons in eight orbitals for the periacenes. This reference space is used to construct the total configuration space by means of single and double excitations. By comparison with more extended calculations, it is shown that a focus on the π space with a 6-31G basis set is sufficient to describe the major features of the electronic character of these compounds. The present findings suggest that the ground state is a singlet for the smaller members of these series, but that for the larger ones, singlet and triplet states are quasi-degenerate. Both the acenes and periacenes exhibit significant polyradical character beyond the traditional diradical.     

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

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

Reducing CAS-SDCI space. Using selected spaces in configuration interaction calculations in an efficient way

A new method is presented, which allows an important reduction of the size of some Configuration Interaction (CI) matrices. Starting from a Complete Active Space (CAS), the numerous configurations that have a small weight in the CAS wave function are eliminated. When excited configurations (e.g., singly and doubly excited) are added to the reference space, the resulting MR-SDCI space is reduced in the same proportion as compared with the full CAS-SDCI. A set of active orbitals is chosen, but some selection of the most relevant excitations is performed because not all the possible excitations act as SDCI generators. Thanks to a new addressing technique, the computational time is drastically reduced, because the new addressing of the selected active space is as efficient as the addressing of the CAS. The presentation of the method is followed by two test calculations on the N(2) and HCCH molecules. For the N(2) the FCI results are taken as a benchmark reference. The outer valence ionization potentials of HCCH are compared to the experimental values. Both examples allow to test the accuracy of the MR-SDCI compared to that of the corresponding CAS-SDCI, despite the noticeable reduction of the CI space. The algorithm is suitable for the dressing techniques that allow for the correction of the size-extensivity error. The corrected results are also shown and discussed.     

The generalized active space concept in multiconfigurational self-consistent field methods

A multiconfigurational self-consistent field method based on the concept of generalized active space (GAS) is presented. GAS wave functions are obtained by defining an arbitrary number of active spaces with arbitrary occupation constraints. By a suitable choice of the GAS spaces, numerous ineffective configurations present in a large complete active space (CAS) can be removed, while keeping the important ones in the CI space. As a consequence, the GAS self-consistent field approach retains the accuracy of the CAS self-consistent field (CASSCF) ansatz and, at the same time, can deal with larger active spaces, which would be unaffordable at the CASSCF level. Test calculations on the Gd atom, Gd(2) molecule, and oxoMn(salen) complex are presented. They show that GAS wave functions achieve the same accuracy as CAS wave functions on systems that would be prohibitive at the CAS level.     

Elastic scattering of low-energy electrons by N2 including the effect of target electronic correlation

A procedure to use configuration-interaction (CI) target wave-functions in the electron–molecule collision theory is applied to study the elastic e⁻–N₂ scattering in the (5–20) eV incident energy range. Correlated static and exchange contributions to the interaction potential are presented. Two different atomic basis sets are used. Differential cross sections (DCS) obtained by using Hartree–Fock or CI wave-functions are presented and compared. In the CI case, single and double, and single, double and triple excitations are considered. The effect of electron correlation is analyzed in all the cases. The continuum wave-functions were obtained via the Schwinger variational iterative method. The influence on the DCS of both the size of the atomic basis set and the inclusion of higher-order excitations in the CI calculation is discussed.     

Relative stability of the 3A2, 1A2, and 1A1 states of phenylnitrene: A difference-dedicated configuration interaction calculation

The relative stability of the ³A₂, ¹A₂, and ¹A₁ states of phenylnitrene is evaluated by means of ab initio calculations followed by difference-dedicated configuration interaction (DDCI). This approach is based on effective Hamiltonian theory at a low order of perturbation to select rationally the determinants which contribute to the energy difference. The CI space built on this criterion is then treated variationally. The method allows a considerable reduction of the CI space compared with a complete CAS*SDCI calculation (where CAS stands for complete active space). Depending on the concerned energy difference, different model spaces may be chosen, as illustrated in the ³A₂ → ¹A₂ and the ³A₂ → ¹A₁ transitions in phenylnitrene. Since the CI space may reach considerable dimensions, a direct CI algorithm for selected CI spaces, the SCIEL algorithm, has been used to perform the calculations. The results are in excellent agreement with previous calculations and with available experimental data. © 1996 by John Wiley & Sons, Inc.     

A relativistic 4-component general-order multi-reference coupled cluster method: initial implementation and application to HBr

We present the initial implementation of a determinant-based general-order coupled cluster method which fully accounts for relativistic effects within the four-component framework. The method opens the way for the treatment of multi-reference problems through a state-selective expansion of the model space. The evaluation of the coupled cluster vector function is carried out via relativistic configuration interaction expansions. The implementation is based on a large-scale configuration interaction technique, which may efficiently treat long determinant expansions of more than 10⁸ terms. We demonstrate the capabilities of the new method in calculations of complete potential energy curves of the HBr molecule. The inclusion of spin–orbit interaction and higher excitations than coupled cluster double excitations, either by multi-reference model spaces or the inclusion of full iterative triple excitations, lead to highly accurate results for spectral constants of HBr. An erratum to this article can be found at     

Ab initio calculations of the lowest electronic states in the CuNO system

The lowest singlet and triplet electronic levels of the A' and A" symmetry species of the neutral copper-nitrosyl (CuNO) system are calculated by ab initio methods at the multi-reference configuration interaction (MRCI) level of theory with single and double excitations, and at the coupled cluster level of theory with both perturbational (CCSD(T)) and full inclusion of triple excitations (CCSDT). Experimental data are difficult to obtain, hence the importance of carrying out calculations as accurate as possible to address the structure and dynamics of this system. This paper aims at validating a theoretical protocol to develop global potential energy surfaces for transition metal nitrosyl complexes. For the MRCI calculations, the comparison of level energies at linear structures and their values from C(2v) and C(s) symmetry restricted calculations has allowed to obtain clear settings regarding atomic basis sizes, active orbital spaces and roots obtained at the multi-configurational self-consistent field (MCSCF) level of theory. It is shown that a complete active space involving 18 valence electrons, 11 molecular orbitals and the prior determination of 12 roots in the MCSCF calculation is needed for overall qualitatively correct results from the MRCI calculations. Atomic basis sets of the valence triple-zeta type are sufficient. The present calculations yield a bound singlet A' ground state for CuNO. The CCSD(T) calculations give a quantitatively more reliable account of electronic correlation close to equilibrium, while the MRCI energies allow to ensure the qualitative assessment needed for global potential energy surfaces. Relativistic coupled cluster calculations using the Douglas-Kroll-Hess Hamiltonian yield a dissociation energy of CuNO into Cu and NO to be (59 ± 5) kJ mol(-1) ((4940 ± 400) hc?cm(-1)). Favorable comparison is made with some of previous theoretical results and a few known experimental data.     

Real space Hartree-Fock configuration interaction method for complex lateral quantum dot molecules

We present unrestricted Hartree-Fock method coupled with configuration interaction (CI) method (URHF-CI) suitable for the calculation of ground and excited states of large number of electrons localized by complex gate potentials in quasi-two-dimensional quantum dot molecules. The method employs real space finite difference method, incorporating strong magnetic field, for calculating single particle states. The Hartree-Fock method is employed for the calculation of direct and exchange interaction contributions to the ground state energy. The effects of correlations are included in energies and directly in the many-particle wave functions via CI method using a limited set of excitations above the Fermi level. The URHF-CI method and its performance are illustrated on the example of ten electrons confined in a two-dimensional quantum dot molecule.     

Selected excitation for CAS-SDCI calculations

A new selected-configuration interaction method is proposed, based on the use of local orbitals. A corresponding code has been written, which is devoted to CI calculations of rather large systems (about 50-100 carbon-like atoms). Taking advantage of the locality, and then of the fact that interactions vanish when the distance is large, the dimension of the CI space is largely reduced. The determinants that would be created by long range excitations are expected to have a small weight in the wave function and are therefore eliminated. This selected excitation CI space is particularly suited for large molecules. It is tested on large polyene chains and on a transition metal complex. For large enough systems, the CPU time saving is important and, what is more noticeable, calculations that were impossible to perform without selection are feasible in this approach.