Internally contracted multiconfiguration-reference configuration interaction calculations for excited states

Summary The calculation of electronically excited states with the internally contracted multiconfiguration-reference configuration interaction (CMRCI) method is discussed. A straightforward method, in which contracted functions for all states are included in the basis, is shown to be very accurate and stable even in cases of narrow avoided crossings. However, the expense strongly increases with the number of states. A new method is proposed, which employs different contracted basis sets for each state, and in which eigensolutions of the Hamiltonian are found using an approximate projection operator technique. The computational effort for this method scales only linearly with the number of states. The two methods are compared for various applications.Dedicated in honor of Prof. Klaus Ruedenberg     

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.     

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.     

Theoretical investigation of excited states of molecules. An application on the nitrogen molecule

Diverse existing lines for the calculation of excited states are exposed, with an emphasis on those methods that consider both types of correlation energy: the dynamic and the non-dynamic one. We analyze the possibility of to calculate the dynamic correlation energy using a correlation energy density functional applied to a multi-determinantal wavefunction, which would include the non-dynamic correlation energy, versus the use of mono-determinantal wavefunctions, which are not able to include the long-range correlation energy, and versus the use of variational or perturbative calculations from multi-determinantal wavefunctions, with their excessive computational cost. The results obtained with several methods are compared. Contribution to the Serafin Fraga Memorial Issue.     

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     

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.     

Comments about the representation of Rydberg and ionic excited states and their photochemistry

This paper discusses the conditions for representing Rydberg and ionic excited states of molecules. It especially shows the intrinsic difficulties of MO methods to treat the weak resonances between strongly polarized situations in highly polarizable symmetric systems; such situations occur in the long distance region for Rydberg excited states of homonuclear molecules, and for the 90 ° twisted singlet excited states of polyenes. The valence/Rydberg mixing is discussed, and some principles for the understanding of Rydberg photochemistry are proprosed, based on a few examples. The present knowledge of the photochemistry of zwitterionic excited states of polyenes is summarized.     

CEPA calculations on open-shell molecules. III. Potential curves for the six lowest excited states of He2 in the vicinity of their equilibrium distances

CEPA-PNO and PNO-CI calculations have been performed for the potential energy curves of the He ₂ ⁺ ground state and the six lowest excited states of He₂ in the range of 1.4 a₀ ≤R ≤ 3.5 a₀. The calculated equilibrium distances as well as the spectroscopic constants are in very good agreement with molecular constants as derived experimentally from the rotation-vibration spectrum of He₂ by Ginter, except for thec ³∑ _g ⁺ state. This latter discrepancy is probably due to an “obligatory” hump in thec ³∑ _g ⁺ state occurring at 3.5 a₀ which cannot be properly treated in our calculation. The relative energetic positions of the six lowest states and their ionization energies are reproduced by our calculations with an accuracy of 0–400 cm⁻¹. Extrapolation of our results to infinite basis sets leads to estimates of the dissociation energies of He₂ excited states which cannot be measured spectroscopically because of the humps in all these states.     

Contracted well-tempered Gaussian basis sets in SCF calculations on the ground and excited electronic states of neutral and ionized diatomic molecules containing first-row atoms

Summary Calculations were done on ground and excited states of C₂, C ₂ ⁺ , C ₂ ^– , N₂, N ₂ ⁺ , O₂, O ₂ ⁺ , O ₂ ^– , CO, CO⁺, CO²⁺, and CO^– using contracted well-tempered basis sets. The (14s 10p) basis sets were augmented with threed, one or twof, and oneg functions. Total energies, orbital energies, and spectroscopic constants were compared with the best available computational data.     

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.

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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.

     

Ab initio studies of ground and excited electronic states of MgAr,CdAr, and BeAr

Summary The ground state (X ¹⁺) and several excited state (A ³,c ³+,C ¹,D ¹⁺, andE ³⁺) potential energy surfaces for the diatomic molecules MgAr, CdAr, and BeAr have been computed using complete active space self-consistent field (CASSCF) wavefunctions and valence double- and triplezeta quality basis sets augmented with polarization and diffuse functions. Pump-and-probe laser experiments have examined the quenching, of excited singlet states of metal-rare gas complexes such as CdXe to produce triplets that dissociate to³ P _Jmetal atoms. This quenching, which is detected for CdXe but not for CdAr or MgAr, is thought to occur via a crossing or strong coupling of a repulsive triplet curve correlating to the underlying³ P state of the metal, with an attractive singlet curve that correlates to the higher¹ P state of the metal. The present work indicates that the attractiveC ¹ and repulsivec ³⁺ curves of MgAr and CdArdo not intersect in the energetically accessible region of theC ¹ surface, unlike the corresponding curves for the CdXe diatom. These data are consistent with the absence of³ P _J Cd atoms in the MgAr and CdAr experiments, respectively. However, an alternative quenching mechanism involving vibronic coupling between theC ¹ vibrational eigenstates and the continuum eigenstates of the underlying repulsive³⁺ surface may be operative; this possibility is examined qualitatively and predicted to be unlikely for MgAr (due to small spin-orbit coupling) and CdAr (due to unfavorable vibronic factors). BeAr, which has yet to be probed experimentally, is predicted to be bound by 770 and 900 cm^–1 in theD ¹⁺ state (which has metal 2s2p character) and theE ³⁺ state (which has Rydberg metal 2s3s character), respectively, and to display interesting potential curve intersections.Dedicated to Prof. Klaus Ruedenberg     

Non-empirical calculations on the rydberg states of ethylene

Different methods for representing the upper orbitals in Rydberg transitions are tested by means of a series of ab initio SCF and CI calculations for ethylene and various properties for such diffuse united-atom species are reported. Calculated transition energies indicates the maximum separation between individual components of the (π,3d) Rydberg species to be in the 0.1-0.2 range, with similarly small energy separations being obtained for the corresponding (π, 3p) states     

Change of molecular structure in the excited states: A (CNDO/2) hole-potential study on phosphine

Molecular structure of phosphine in a number of excited electronic states is studied using the method of hole-potential within the basic framework of CNDO/2 theory. Effects of including 3d-functions of phosphorus in the basis set on computed molecular geometries, transition energies and inversion barriers in the excited states have been investigated. An attempt is made to rationalise qualitatively the structural changes in the excitedstate in terms of Walsh-type correlation diagram constructed with the eigenvalues of the Fock operator in theV _N-1 potential model. A simple orbital model for predicting the nature of structural changes in the excited states is proposed.     

Time-dependent Hartree-Fock calculations for the excited ‘S’ states of lithium isoelectronic sequence

Time-dependent HF (RPA) calculations have been performed to estimate the transition energies and excited state wavefunctions of Li, Be⁺, B²⁺ and C³⁺ for the transitions 1s ²2s ² S 1s ² ns ² S (n = 3,4, ... 8). The excitation energies and excited state wavefunctions are extracted from the position of the poles of a linearised variational functional. The excitation energies are in excellent agreement with those obtained spectroscopically. The excited state wavefunctions are utilised to find the matrix elements of different operators and the cusp values.     

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.