Structures and spectra of Na(NH3) n=1,2

Geometric structures and the energies for the ground and several excited electronic states of a sodium atom bound with one or two ammonia molecules are presented. All self consistent field (SCF) calculations are performed with extended basis sets. Geometry optimization and one electron properties have been performed within the SCF approximation. Excited states have been calculated with the multi-configuration SCF (MCSCF) technique. This system may be viewed as a precursor to solvation in a macroscopic system. The excited state calculations provide important information for spectroscopic studies of these complexes.     

On the SCF calculation of excited states: Singlet states in the two-electron problem

The problem of determining SCF wave functions for excited electronic states is examined for singlet states of two-electron systems using a Lowdin natural orbital transformation of the full CI wave function. This analysis facilitates the comparison of various SCF methods with one another. The distribution of the full CI states among the natural orbital MCSCF states is obtained for the S states of helium using a modest Gaussian basis set. For SCF methods that are not equivalent to the full CI wave functions, it is shown that the Hartree-Fock plus all single excitation wave functions are equivalent to that of Hartree-Fock plus one single excitation. It is further shown that these wave functions are equivalent to the perfect pair or TCSCF wave functions in which the CI expansion coefficients are restricted to have opposite signs. The case of the natural orbital MCSCF wave function for two orbitals is examined in greater detail. It is shown that the first excited state must always be found on the lower natural orbital MCSCF CI root, thus precluding the use of the Hylleras-Undeim-MacDonald (HUM) theorem in locating this state. It is finally demonstrated that the solution obtained by applying the HUM theorem (minimizing the upper MCSCF CI root with respect to orbital mixing parameters) is an artifact of the MCSCF method and does not correspond to any of the full CI states.     

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.     

Determination of contracted atomic basis sets for the study of CN; application to the MCSCF calculations of its spectroscopic constants

Contracted atomic basis sets have been constructed from ANOs in order to describe the ground and excited states of C and N and their anions. Application is given with the MCSCF calculation of the vibration frequency of CN⁻ and of other spectroscopic constants. A procedure is proposed to do MCSCF calculations when some problems of convergence arise.     

The generalized active space concept for the relativistic treatment of electron correlation. III. Large-scale configuration interaction and multiconfiguration self-consistent-field four-component methods with application to UO2

We present an implementation for large-scale relativistic electronic structure calculations including spin-dependent contributions and electron correlation in a fully variational procedure. The modular implementation of the double group configuration interaction (CI) program into a multiconfiguration self-consistent-field (MCSCF) code allows for the treatment of large CI expansions in both the spinor optimization step and the post-MCSCF dynamic electron correlation step. As an illustration of the potential of the new code, we calculate the spectroscopic properties of the UO2 molecule where we study the ground state and a few excited states in vertical and adiabatic calculations.     

Potential curves for inner-shell states of CO calculated at multiconfigurational self-consistent field level

A general strategy to calculate potential curves at multiconfigurational self-consistent field (MCSCF) level for inner-shell states is reported in this paper. Convergence is commonly very tough for inner-shell states, especially at this level of calculation, due to the problem of variational collapse of the inner-shell wave function to the ground or to a low-lying excited state. The present method allows to avoid this drawback by a sequence of constrained optimization in the orbital mixing step. The specific states studied are that resulting from transitions X (1)Σ(+) → (C 1s(-1) π(?)) (1,3)Π of CO. Accurate values are achieved for transition energies and vibrational splittings. A comparison is made with other approach, i.e., inner-shell CI based on a MCSCF wave function optimized for ground or low-lying excited states. This last approach is shown to fail in describing the whole potential curve.     

Symmetry and equivalence restrictions in electronic structure calculations

A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalence restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.     

Open-shell SCF calculations with a model potential method

A model potential proposed by Huzinaga and his coworkers has been incorporated into the generalized coupling operator for open-shell SCF. With this modified operator, valence-only calculations have been performed on the ground and Rydberg excited states of the water molecule and compared with the ab initio SCF results previously reported.     

A pair-excitation MCSCF calculation based on CNDO/INDO approximation I

Second-order multiconfigurational self-consistent field (MCSCF ) calculation has been programmed on the basis of CNDO /INDO molecular orbital bases, in which the configuration space employed is restricted within pair-excitations. Test calculations have been carried out for 17 small molecules. All the MCSCF ground states of these molecules have been successfully converged to their respective optimal states by employing a simple weighting scheme. This procedure provides a great savings in computer time. The MCSCF calculation on azetidine required only 27 min on a HITAC M-680H. The MCSCF energies of HF, F₂, and BH show improved behaviors up to large atomic distances (～7au).     

Symmetry adaptation of configuration basis in MCSCF method

Summary A novel approach of space symmetry adaptation is developed for multiconfigurational (MC) functions in fully optimized reaction space and complete active space SCF calculations. The bonded tableau and two box symmetric tableau are basic representations (rep) of configuration functions; the group symmetric localized orbitals are used as one-electron orbitals. The method is proposed for generating a complete and orthonormal set of MC single excited functions. The redundant variable in MCSCF can be eliminated by symmetry adaptation.     

SCF and limited CI calculations for assignment of the Auger spectrum and of the satellites in the soft X-ray spectrum of H2O

SCF and limited CI calculations have been performed for a number of excited states of doubly ionized water. The calculations allowed an assignment of both the Auger spectrum and most of the satellites in the soft X-ray spectrum. The assignment for the two highest peaks in the Auger spectrum was ambiguous. SCF calculations of the K emission spectrum of H₂O were also performed. It was found that limited CI calculations were of importance for some states with two open shells in one symmetry. Such effects are caused by large off-diagonal lagrangian multiplies connecting the open shells in the reference configuration.     

Optimized effective potential method for individual low-lying excited states

This paper presents an optimized effective potential (OEP) approach based on density functional theory (DFT) for individual excited states that implements a simple method of taking the necessary orthogonality constraints into account. The amended Kohn-Sham (KS) equations for orbitals of excited states having the same symmetry as the ground one are proposed. Using a variational principle with some orthogonality constraints, the OEP equations determining a local exchange potential for excited states are derived. Specifically, local potentials are derived whose KS determinants minimize the total energies and are simultaneously orthogonal to the determinants for states of lower energies. The parametrized form of an effective DFT potential expressed as a direct mapping of the external potential is used to simplify the OEP integral equations. A performance of the presented method is examined by exchange-only calculations of excited state energies for simple atoms and molecules.     

Carbazole and trinitrofluorenone: an ab initio investigation of ionization potentials,electron affinities and excited states

Minimal basis set SCF calculations are reported for the ground states and positive and negative ions of carbazole and tirnitrofluorenone. For carbazole, wavefunctions for several low-lyng excited states have also been obtained. Methods for surmounting convergence difficulties for these large systems are discussed. Relaxation effects in the calculations of excitations energies are considered and found to be significant. Calculated energies are compared to experimental results.     

离子簇合物HeN_2~+的电子光谱的从头算研究

本文报道了离子簇合物HeN2＋的电子光谱的从头算结果。在MCSCF／6－31G（d，p）水平上，对其基态进行了几何优化，用该构型．在SDC1／6－31（d，p）水平上计算了基态的总能量。用SDCI方法计算得到HeN2＋从基态到选择激发态的垂直跃迁能、振子强度、跃迁频率、辐射寿命以及Einstain系数。该结果可以较好的验证maier的实验。     

Calculating energy levels of isomerizing tetra-atomic molecules. II. The vibrational states of acetylene and vinylidene

A general, full-dimensional computational method for the accurate calculation of rotationally and vibrationally excited states of tetra-atomic molecules is further developed. The resulting computer program may be run in serial and parallel modes and is particularly appropriate for molecules executing wide-amplitude motions and isomerizations. An application to the isomerizing acetylene/vinylidene system is presented. Large-scale calculations using a coordinate system based on orthogonal satellite vectors have been performed in six dimensions and vibrational term values and wave functions for acetylene and vinylidene states up to approximately 23 000 cm(-1) above the potential minimum have been determined. This has permitted the characterization of acetylene and vinylidene states at and above the isomerization barrier. These calculations employ more extensive vibrational basis sets and hence consider a much higher density of states than in any variational calculations reported hitherto for this system. Comparison of the calculated density of states with that determined empirically suggests that our calculations are the most realistic achieved for this system to date. Indeed more states have been converged than in any previous study of this system. Calculations on lower lying excited states of acetylene based on HC-CH diatom-diatom coordinates give nearly identical results to those based on orthogonal satellite vectors. Comparisons are also made with calculations based on HH-CC diatom-diatom coordinates.     

A SELF-CONSISTENT-FIELD STUDY OF THE EXCITED STATE π-ELECTRON CHARGES IN PHENOL

Abstract— –The semiempirical self-consistent-field (SCF) method was used to calculate the net π-electron charges for phenol in the first excited singlet and first excited triplet states. These calculations differ from the usual ground state calculations in that (i) recently available static excited state data were used wherever possible as the empirical basis for evaluating SCF parameters and (ii) the theory of density matrices was used to include the effects of all singly-excited configurations in the configuration interaction contributions to the excited state π-electron charge densities.     

Geometry relaxation effects in the 1 Bu and 2 Ag states of trans-1,3-butadiene

MCSCF and MRCI calculations on the first three singlet states of trans-1,3-butadiene are presented. Flexible basis sets were applied and full geometry optimization was carried out at the MCSCF level for planar and selected non-planar structures including twisting and pyramidalization of terminal CH₂-groups. Geometry relaxations in and excitation energies to 1 ¹B_u and 2 ¹A_g states are discussed in detail. For planar structures the covalent 2 ¹A_g state is lower in energy than the 1 ¹B_u state. If non-planar geometry relaxations are allowed, the lowest lying non-planar excited singlet state turns out to be ionic with one terminal CH₂ group rotated by 90°. Limitations of the current investigations due to restrictions in the MRCI treatment and because of incomplete scanning of excited state surfaces are pointed out.     

Linear response calculation of potential energy curves of BH

The multiconfiguration time-dependent Hartree–Fock (MC TDHF ) approximation is applied to study the excited states of the BH molecule. The potential energy curves and spectroscopic properties of the excited states are analyzed. The MC TDHF results are compared to similar MC SCF calculations for individual excited states. © 1994 John Wiley & Sons, Inc.     

On the computation of excited states with MCSCF methods

We discuss the theoretical and practical problems arising when trying to compute excited states of nonrelativistic electrons in a molecular system, by multiconfiguration (MCSCF) methods. These nonlinear models approximate the linear Schrödinger theory and are a generalization of the well-known Hartree–Fock approach. Due to the MCSCF nonlinearity, a theoretical definition of what should be a MCSCF excited state is not clear at all, contrarily to the ground state case. We compare various definitions used in Quantum Chemistry. We in particular stress that some defects may lead to important computational problems, already observed in Quantum Chemistry (root flipping). We then present a definition of MCSCF excited states based on a solid mathematical ground and compare it with the most used methods. This new definition leads to a completely new algorithm for computing the first excited state, which was proposed and tested in a collaboration with Cancès and Galicher. Numerical results are provided for the simple case of two-electron systems, as an illustration of the possible issues which can arise as consequences of the nonlinearity of the MCSCF method.