A comparison of variational and non-variational internally contracted multiconfiguration-reference configuration interaction calculations

Summary The internally contracted multiconfiguration-reference configuration interaction (CMRCI) method and several non-variational variants of this method (averaged coupled pair approximation (ACPF), quasidegenerate variational perturbation theory (QD-VPT), linearized coupled pair many electron theory (LCPMET)) have been employed to compute potential energy functions and other properties for a number of diatomic molecules (F₂, O₂, N₂, CN, CO) using large basis sets and full valence CASSCF reference wavefunctions. In most cases the variational CMRCI wavefunctions yield more accurate spectroscopic constants than any of the employed non-variational methods. Several basis sets are compared for the N₂ molecule. It is found that atomic natural orbital (ANO) contractions led to significant errors in the computedr _e , _e , andD _e values.     

Hartree-fock calculations for excited rydberg states

A method is introduced which allows to compute self-consistent restricted Hartree-Fock wave functions for excited Rydberg configurations. The concepts of reorganization and electron correlation of Rydberg states are discussed. As an illustration Hartree-Fock calculations for the (ls)(nl) Rydberg series of He are presented.     

The quest for best suited references for configuration interaction singles calculations of core excited states

Near edge X‐ray absorption fine structure (NEXAFS) simulations based on the conventional configuration interaction singles (CIS) lead to excitation energies, which are systematically blue shifted. Using a (restricted) open shell core hole reference instead of the Hartree Fock (HF) ground state orbitals improves (Decleva et al., Chem. Phys., 1992, 168, 51) excitation energies and the shape of the spectra significantly. In this work, we systematically vary the underlying SCF approaches, that is, based on HF or density functional theory, to identify best suited reference orbitals using a series of small test molecules. We compare the energies of the K edges and NEXAFS spectra to experimental data. The main improvement compared to conventional CIS, that is, using HF ground state orbitals, is due to the electrostatic influence of the core hole. Different SCF approaches, density functionals, or the use of fractional occupations lead only to comparably small changes. Furthermore, to account for bigger systems, we adapt the core‐valence separation for our approach. We demonstrate that the good quality of the spectrum is not influenced by this approximation when used together with the non‐separated ground state wave function. Simultaneously, the computational demands are reduced remarkably. © 2016 Wiley Periodicals, Inc.     

Energies of excited states calculated with MNDO and AM1

Summary Singlet excitation energies of 18 organic molecules have been calculated using MNDO and AM1 semiempirical methods with limited configuration interaction. While both procedures systematically overstabilize energies of excited states, the ordering of states and the effects of substituents are reproduced, with AM1 being slightly better suited than MNDO. The best agreement with experiment was obtained for conjugated systems.

---

Energien für angeregte Zustände mittels MNDO- und AM1-Rechnungen

Zusammenfassung Es wurden die Singlet-Anregungsenergien von 18 organischen Molekülen mittels der semiempirischen MNDO- und AM1-Methode mit beschränkter Konfigurationswechselwirkung berechnet. Beide Methoden zeigen eine systematische Überstabilisierung von angeregten Zuständen, die Reihenfolge der Zustände und die Substituenteneffekte werden jedoch gut wiedergegeben, wobei sich AM1 als etwas zuverlässiger erwies. Die beste Übereinstimmung wurde für konjugierte Systeme gefunden.

     

An SCF technique for excited states

A method for deriving HF-SCF wave functions for excited states is presented here. All the active orbital transformations that are compatible with the orthogonality requirements are performed without unnecessary restrictions on the variational space and within a direct minimization approach. The method has been tested with an application on the first excited-singlet state of Be.     

Parallel internally contracted multireference configuration interaction

A parallel implementation of the internally contracted (IC) multireference configuration (MRCI) module of the MOLPRO quantum chemistry program is described. The global array (GA) toolkit has been used in order to map an existing disk-paging small-memory algorithm onto a massively parallel supercomputer, where disk storage is replaced by the combined memory of all processors. This model has enabled a rather complicated code to be ported to the parallel environment without the need for the wholesale redesign of algorithms and data structures. Examples show that the parallel ICMRCI program can deliver results in a fraction of the time needed for equivalent uncontracted MRCI computations. Further examples demonstrate that ICMRCI computations with up to 10⁷ variational parameters, and equivalent to uncontracted MRCI with 10⁹ configurations, are feasible. The largest calculation demonstrates a parallel efficiency of about 80% on 128 nodes of a Cray T3E-300. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1215–1228, 1998     

Molecular orbitals for excited states of atoms and molecules

A method is described for calculating SCF wavefunctions for excited electronic states of atoms and molecules. The orthogonality conditions with the ground state wavefunction and the underlying excited states wavefunctions are introduced in the SCF process in a simplified form.     

Test applications of a new SCF method for excited states

In order to test a recently proposed technique for deriving orthogonality-constrained HF wave functions for excited states, several applications to molecular systems, have been made and the results compared with those provided by other SCF techniques.     

A programmable spin-free method for configuration interaction

In this note a method is presented for quick implementation of configuration interaction (CI) calculations in molecules. A spin-free Hamiltonian for anN electron system in a spin stateS, expressed in terms of the generators for the unitary group algebra, is diagonalized over orbital configurations forming a basis for the irreducible representation [2^1/2N-S 1^2S ] of the permutation group S _N . It has been found that the basic algebraic expressions necessary for the CI calculation involve a limited category of permutations. These have been displayed explicitly. On leave from the Indian Institute of Technology, Bombay, India.     

Accuracy of energy extrapolation in multireference configuration interaction calculations

The accuracy of extrapolation procedures in conjunction with energy-based configuration selection in CI calculations is examined. The normally high accuracy of such extrapolation can deteriorate in multireference CI calculations when configuration functions of low weight are included in the root (reference) set. This is due to the inadequacy of second-order energy contribution estimates for the very large number of discarded low-contribution functions generated as single and double excitations from the minor members of the root set. The problem may be overcome by increasing the number of configurations included in the zero-order function used for the energy contribution estimation process. Illustrative results are presented for excited states of the H₂O molecule and the H₂O⁺ ion.     

Core and valence electrons in atoms and ions: configuration interaction calculations

Summary The partitioning of ground-state atoms or ions into inner spherical cores with radius _b and outer valence regions extending from _b to infinity is explored with the help of the expression for the valence-region energy (where T ^v and V ^v are, respectively, the kinetic and potential energies of the valence electrons N ^v found beyond the boundary surface defined by _b) using also the appropriate expression for E ^ion, the energy of the ion left behind after removal of the valence electrons. E ^v and E ^ion are meaningful only for discrete numbers, N ^c, of electrons assigned to the core, namely, when the exchange integrals, K ^cv, between N ^c and N ^v total (or at least closely approach) 0, i.e., for N ^c = 2 e or N ^c = 2 and 10 e for the first- or second-row elements, respectively.Part of the projected Ph.D. dissertation of N. D.     

Multi-configuration electron-hole potential method for excited states

The recently proposed electron-hole potential (EHP) method for excited states is extended to the multi-configurational case. The variation equation is solved using the quadratic convergence method. The EHP methods are shown to be approximations to the complete singly excited configuration interaction (CSECI) in the variational sense. Extended Brillouin theorems are proved for the EHP methods. The excitation energies and wave functions obtained by one and two configurational EHP methods agree well with those of the CSECI method. The EHP methods have clear advantage in the computer time requirement over the CI method and are especially suited for a calculation of approximate excited states of large molecules. The EHP methods are applicable to excited states which belong to the same irreducible representation as the ground state.     

Generalized brillouin theorem multiconfiguration method for excited states

The Generalized Brillouin Theorem Multiconfiguration Method (GBT-MC) of Grein and Chang is extended and applied to the calculation of excited states. Orthogonality constraints to lower states as well as second-order interaction effects of states lying close together have been taken into account. In this way quadratic convergence can be guaranteed. Difficulties with coupling coefficients and Lagrangian multipliers of SCF methods can be circumvented. Test calculations have been performed on valence electron excited states of C, H₂O, and CH₂O, and on core excited states of Li.     

Infrared vibrational band shapes in excited states

This article describes the behaviour of the shapes of the IR bands of coordination compounds on electronic excitation. Broadening on excitation is frequently, but not invariably, observed; any broadening is the result of a subtle interplay of the properties of the vibrational mode, the excited state and the solvent.     

Quantum Monte Carlo calculations for ground and excited states

A brief overview of the diffusion quantum Monte Carlo method is given. We illustrate the application to ground‐state calculations by a study of the relative stability of carbon clusters near the crossover to fullerene stability, thereby determining the smallest stable fullerene. The application to excited states is illustrated via a study of excitonic states in small hydrogenated silicon clusters. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

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.     

An ab initio multireference doubles excitation configuration interaction study of low-lying electronic states of Cd2 using Slater-type orbitals

Potential-energy curves for the ground state and lower excited states of the Cd₂ dimer have been calculated. They are obtained using a multireference doubles excitation configuration interaction procedure and employing Slater basis sets, previously optimized at the self-consistent-field level for excited states of the Cd atom. The spectroscopic constants and excitation energies for the bound states of Cd₂ have been compared with experimental as well as other theoretical results. The ground state of Cd₂ is essentially repulsive and presents a shallow van der Waals minimum. The computed adiabatic electronic transitions are in good agreement with the experimental ones. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Identification of deadwood in configuration spaces through general direct configuration interaction

 In order to identify ineffective and, hence, superfluous configurations in algorithmically generated configuration spaces, a direct configuration interaction (CI) method has been developed for determining completely general configurational expansions based on arbitrary determinantal configuration lists. While based on the determinantal ordering scheme of Knowles and Handy, our direct CI algorithm differs from previous ones by the use of the Slater–Condon expressions in direct conjunction with single and double replacements. A full, as well as a completely general selected, CI program has been implemented. With it, full configuration spaces of Ne, C₂, CO and H₂O with up to about 40 million determinants have been investigated. It has been found that, in all cases, fewer than 1% of the configurations in a natural-orbital-based configuration expansion reproduce the exact results within chemical accuracy. Received: 19 December 2000 / Accepted: 9 May 2001 / Published online: 11 October 2001