Free-electron model for electronic spectra of benzene

Using a three dimensional free-electron model for the π-electron system the energies of the various singly and doubly excited configurations of benzene have been calculated. It has been found that the energies of the various singly excited configurations are in good agreement with the values obtained by Craig; whereas the energies of the doubly excited configurations are higher than those obtained by Craig. Therefore the configurational mixing for the doubly excited configurations is not necessary in this kind of model.     

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.     

Excited states of the benzyl radical

The CI method is used in the -electron approximation with orbitals for closed and open shells to calculate the properties of excited doublet states with allowance for all singly excited configurations and some doubly excited ones, and also for the first quartet and sextet states, which are calculated in the one-configuration approximation via the open-shell theory. The energies and transition moments agree satisfactorily with the available experimental evidence. A classification and assignment is given for the excited terms. Truncation of the complete set of singly excited configurations greatly distorts the calculated spectrum. Inclusion of doubly excited configurations in the CI also produces a substantial change in the spectrum; in some cases it alters the order of adjacent terms. Conversion in CI from basis closed-shell orbitals to open-shell ones produces a considerable lowering of all terms in the spectrum. As in the case of triplet terms for molecules, weakening of electron interaction brings the lowest excited term of the radical closer to the ground-state term. The electron-density and spin-density distributions are calculated for the excited states.     

Full configuration interaction for the benzyl radical

The electronic structure of the benzyl radical in its ground state has been computed using a model Hamiltonian due to Pariser–Parr with full configuration interaction as well as with different truncated configurational sets built on SCF open-shell orbitals. The correlation energy corresponding to this model was found to be equal to –0.929722 eV. With the singly excited configurations only 18% of this energy is taken into account. By extending the basis to include the doubly excited configurations one can account for 94% of the correlation energy. An analysis of the accuracy of the proton hyperfine splitting calculation caused by inaccurate computation of the wave function is given. If only singly and even doubly excited configurations are taken into account one cannot hope to obtain splittings with an accuracy of more than 0.5 g. Inclusion of triply excited configurations lowers this error by one order. In addition, the use of the simple McConnell relation may lead to an error in splitting calculations of no less than 1.5 g.     

Role of the low-lying two-electron excited Ag states of C60 in contributing to its hyperpolarizability γ

The role of the low-lying two-electron excited ¹A_g states of C₆₀ in contributing to its hyperpolarizability γ is investigated by singly and doubly excited CI calculations in the semi-empirical CNDO/S approximation. It is found that inclusion of the doubly excited configurations is essential in evaluating γ. The calculated values of γ_zzzz(−3ω; ω, ω, ω) at wavelengths of ∞, 1.9, 1.83 μm sufficiently far from the first resonance are in reasonable agreement with experiment.     

A study of the convergence in iterative natural orbital procedures

A series of five different Iterative Natural Orbital (INO ) procedures are tested for the ground state of water and are compared on the basis of their respective convergence properties. The choice of configuration space employed in these methods is shown to be a key factor in determining the results of such calculations. If the CI space is generated by taking all single excitations with respect to a series of dominant or reference configurations, it is concluded that the practice of varying such generating species at each iteration is highly desirable. In general the choice of the configuration space is found to be much more important than the attainment of strict NO convergence, whereby experience indicates that inclusion of all singly and doubly excited configurations (or at least a select subset thereof) relative to a series of dominant configurations provides the most efficient means of approximating the true NOS of a given system within the general INO framework.     

Excited states of porphyrin macrocycles

S1 --> S(n) spectra of porphyrin, diprotonated porphyrin, and tetraoxaporphyrin dication have been measured in the energy range 2-3 eV above S1 at room temperature in solution by means of transient absorption spectroscopy exciting with femtosecond pulses. Highly excited pi pi* states not active in the conventional S0 --> S(n) spectrum have been observed. The experimental data are discussed on the basis of the time dependent density functional theory taking advantage of large scale calculations of configuration interaction between singly excited configurations (DF/SCI). The DF/SCI calculation on porphyrin has allowed to assign g states active in the S1 --> S(n) spectrum. Applying the same calculation method to tetraoxaporphyrin dication the S0 --> S(n) spectrum is reproduced relatively to the Q and B (Soret) bands as well as to the weaker E(u) bands at higher energy. According to our calculation the S1 --> S(n) transient spectrum is related to states of g symmetry mainly arising from excitations between doubly degenerate pi and pi* orbitals such as 2e(g) --> 4e(g). In the case of diprotonated porphyrin it is shown that the complex of the macrocycle with two trifluoroacetate anions plays a significant role for absorption. Charge transfer excitations from the anions to the macrocycle contribute to absorption above the Soret band, justifying the intensity enhancement of the S0 --> S(n) spectrum with respect to the other two macrocyclic systems.     

AM1/CI, CNDO/S and ZINDO/S computations of absorption bands and their intensities in the UV spectra of some 4(3H)-quinazolinones

A detailed analysis of both frontier MOs and electronic transitions in UV spectra of 16 4-quinazolinone derivatives has been carried out in MO terms, by semiempirical methods AM1/CI, CNDO/S and ZINDO/S. On the basis of experimental and theoretical investigations by the ZINDO/S and CNDO/S methods the long-wavelength bands of 4(3H)-quinazolinone and its derivatives have been assigned to n-->pi(*) transition of the CO fragment and to the transition caused by intramolecular charge transfer from Ph and NCN fragments to CO group. It was shown that theoretically obtained electronic transitions applying method AM1/CI are not in agreement with experimental data observed for the 4(3H)-quinazolinone and 2,4(1H,3H)-quinazolinedione. Good correlation of theoretical and experimental data has been obtained by the method ZINDO/S for the wavelengths and the molar extinction coefficients of the compounds studied. Satisfactory correlation of theoretical and experimental data has also been obtained by the method CNDO/S with singly and doubly excited configurations, for the wavelengths only. Such correlations on experimental and theoretical wavelength and molar absorption coefficients of 4-quinazolinone derivatives are carried out for the first time.     

Electronic structure of the ground state of the benzyl radical

Results from the -electron approximation are given for the total energy, spin-density distribution, and electron density, which have been derived by configuration interaction via self-consistent orbitals for closed and open shells and with allowance for all singly excited configurations and some doubly excited ones. Some singly excited configurations do not mix with the ground-state configuration in the first order of perturbation theory but make a contribution to the latter greater than do some of the configurations that do mix. Incorporation of all singly excited configurations results in a lower ground-state energy if orbitals for a closed shell are used instead of those for an open one. Calculations via closed-shell orbitals lead to an inhomogeneous electron-density distribution, which is gradually smoothed out as the set of configurations is expanded. The spin-density distribution is very much dependent on the number of configurations used and on the orbitals employed in them.     

An AB initio SCF MO CI study of the n → π* transition of methylenimine

The electron correlation energies of both the ground and n → π* excited states of methylenimine (CH₂NH) are investigated by means of ab initio SCF MO CI calculations. Then n → π* singlet and triplet state energies of methylenimine are obtained through 3461-dimensional CI including the singly, doubly and triply excited configurations. the excitation energy from the ground state to the ¹(n → π*) state nearly coincides with that obtained in the framework of the singly excited configuration interaction (SECI) procedure. This result suggests that there is good cancellation of the correlation energy between the ground and the excited singlet sates, proving the usefulness of the SECI method for the excitation energies.     

The configuration interaction method,and the triplet-singlet splitting in CH2

A configuration-interaction (CI) method in which the interaction matrix is never constructed has been investigated, following the original suggestion of Roos. Two methods have been used (1) for singlet states, which can be represented by a one determinant configuration of doubly occupied orbitals, CI with all singly and doubly excited configurations, (2) for states for which the restricted self-consistent field approximation is a single determinant, CI with all singly and doubly excited determinants. In case (2), the wavefunction may not be exactly an eigenfunction of S ². The methods were investigated using a double-zeta plus polarisation basis for CH₂. Both methods must give the same result for the lowest singlet ground state. Keeping the bond length fixed at 2.10 and 2.04 bohr respectively the bond angle for the singlet and triplet were found to be 100.8 ° and 132.0 °, with energies ?39.0312 a.u. and ?39.0563 a.u. respectively. These are the lowest variational energies obtained for these systems; the singlet-triplet splitting is thus predicted to be 15.4 kcal/mol.     

Expanded electronic states of the fluorine molecule

Potential curves of electronically excited states of F₂ with an expanded outer orbital have been calculated using a modified frozen core technique: The ionic core has been described with a two-determinant wave function and for the excited states a mixing of configurations with different cores has been employed. An investigation of the valence shell states of F₂ is presented and potential curves for a singly excited as well as a doubly excited V-state of ¹Σ_u⁺ symmetry have been calculated. Further a low lying two-configuration state resulting from simultaneous excitation to a valence and a Rydberg orbital is predicted.     

Select-divide-and-conquer method for large-scale configuration interaction

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,S(R). S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds tao 0 identical with{Tao 0(egy),Tao 0(etc.)}; the CI coefficients in S0 remain always free to vary. S1 accommodates Ks with attributes above tao 1 < or = tao 0. An eigenproblem of dimension d0 + d1 for S0 + S1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j > or = 2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {tao j;j = 0,1,2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S0 + S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One mu hartree accuracy is achieved for an eigenproblem of order 24 x 10(6), involving 1.2 x 10(12) nonzero matrix elements, and 8.4 x 10(9) Slater determinants.     

Ab initio SCF-CI studies of the intermolecular interaction between two hydrogen molecules near the Van der Waals minimum

SCF-CI calculations have been used to study the intermolecular energy between two hydrogen molecules in four different geometrical configurations. The CI matrix was diagonalized using perturbation techniques. The importance of the perturbation expansion order upon the intermolecular energy could therefore be studied. The wave function includes all singly and doubly excited configurations. The natural orbitals have been determined and their relative importance on the intermolecular energy is considered.     

SCF MO CI perturbation calculations of inner shell and valence shell vertical ionization potentials

A CI method for calculating inner and valence shell vertical ionization potentials is presented. It is based on ab initio SCF MO calculations for the neutral closedshell ground state followed by CI perturbation calculations for the ground and ion states including all spin and symmetry adapted singly and doubly excited configurations with respect to the main configurations of the state of interest. The state energy is computed by performing a CI calculation for a set of selected configurations, and then adding the contributions of the remaining configurations as estimated by second order Brillouin-Wigner perturbation theory. The use of the same set of MO's for all states together with the CI perturbation method makes the method rather rapid. The numerical results are, in spite of the limited Gaussian basis sets used, in good agreement with experiment.     

Calculation of valence electron vertical ionization potentials using a limited Cl approach

A method is outlined for the calculation of valence electron vertical ionization potentials based on CNDO/2 and CNDO/S SCF molecular ground states improved by including a limited number of doubly excited configurations and ionic states obtained from a single Cl calculation considering a limited set of singly and doubly excited configurations based on the closed shell ground state MO's of the parent molecule. From numerical results on carbon dioxide, sulphur dioxide, ethylene, and trans-butadiene it is shown that the Cl procedure leads to the right sequence of ionic states and their reasonable relative location in contrast to respective Koopmans' ionic states predictions.     

Why do the heavy-atom analogues of acetylene E2H2 (E = Si-Pb) exhibit unusual structures?

DFT calculations at BP86/QZ4P have been carried out for different structures of E(2)H(2) (E = C, Si, Ge, Sn, Pb) with the goal to explain the unusual equilibrium geometries of the heavier group 14 homologues where E = Si-Pb. The global energy minima of the latter molecules have a nonplanar doubly bridged structure A followed by the singly bridged planar form B, the vinylidene-type structure C, and the trans-bent isomer D1. The energetically high-lying trans-bent structure D2 possessing an electron sextet at E and the linear form HEEH, which are not minima on the PES, have also been studied. The unusual structures of E(2)H(2) (E = Si-Pb) are explained with the interactions between the EH moieties in the (X(2)Pi) electronic ground state which differ from C(2)H(2), which is bound through interactions between CH in the a(4)Sigma(-) excited state. Bonding between two (X(2)Pi) fragments of the heavier EH hydrides is favored over the bonding in the a(4)Sigma(-) excited state because the X(2)Pi --> a(4)Sigma(-) excitation energy of EH (E = Si-Pb) is significantly higher than for CH. The doubly bridged structure A of E(2)H(2) has three bonding orbital contributions: one sigma bond and two E-H donor-acceptor bonds. The singly bridged isomer B also has three bonding orbital contributions: one pi bond, one E-H donor-acceptor bond, and one lone-pair donor-acceptor bond. The trans-bent form D1 has one pi bond and two lone-pair donor-acceptor bonds, while D2 has only one sigma bond. The strength of the stabilizing orbital contributions has been estimated with an energy decomposition analysis, which also gives the bonding contributions of the quasi-classical electrostatic interactions.     

The redox series [M(bpy)2(q)]n+, M = Ru or Os, Q = 3,5-di-tert-butyl-n-phenyl-1,2-benzoquinonemonoimine. Isolation and a complete X and W band EPR study of the semiquinone states (n = 1)

The complexes [M(bpy)(2)(Q)](PF(6)) (bpy = 2,2'-bipyridyl; M = Ru, Os; Q = 3,5-di-tert-butyl-N-phenyl-1,2-benzoquinonemonoimine) were isolated and studied by X and W band EPR in a dichloromethane solution at ambient temperatures and at 4 K. For M = Ru, the (14)N hyperfine splitting confirms the Ru(II)/semiquinone formulation, although at a > 1 mT, the (99,101)Ru satellite coupling is unusually high. W band EPR allowed us to determine the relatively small g anisotropy Delta g = g(1) - g(3) = 0.0665 for the ruthenium complex. The osmium analogue exhibits a much higher difference Delta g = 0.370, which is attributed not only to the larger spin-orbit coupling constant of Os versus that of Ru but also to a higher extent of metal contribution to the singly occupied molecular orbital. The difference Delta E between the oxidation and reduction potentials of the radical complexes is larger for the ruthenium compound (Delta E = 0.87 V) than for the osmium analogue (Delta E = 0.72), confirming the difference in metal/ligand interaction. The electrochemically generated states [M(bpy)(2)(Q)](n+), n = 0, 1, 2, and 3, were also characterized using UV-vis-near-infrared spectroelectrochemistry.     

Self consistent field perturbation theory for Frenkel and charge transfer states of hydrogen bonded crystals

Comparison is presented of energies, oscillator strengths, and polarization directions calculated using the dipole length and dipole velocity formulas for the lowest 4–7ππ ^* transitions in eight 6π-electron molecules of C _s symmetry using various amounts of CI, from singly excited configurations only (SCI) to complete CI (CCI), and also using the time-dependent Hartree-Fock (TDHF) method. The standard simple PPP approximation was used. For the strongest transitions, SCI and especially TDHF give results in fairly good agreement with CCI. For weaker transitions both SCI and TDHF give similar results, quite different from the CCI solutions. Rational methods for selecting a small number of configurations needed to reproduce correct order of excited states (SECI-1) or a somewhat larger number reproducing correct order, energies, oscillator strengths and polarization directions of transitions (SECI-2) are presented. Both, and particularly the latter, give similar results from both dipole length or dipole velocity formulas when Linderberg's relation is used for matrix elements of the linear momentum operator and in this respect resemble the TDHF and CCI methods for which both formulas necessarily give identical results.     

Inclusion of selected higher excitations involving active orbitals in the state-specific multireference coupled-cluster theory

The parent state-specific multireference coupled-cluster (SS-MRCC) theory proposed by Mukherjee et al. [J. Chem. Phys. 110, 6171 (1999)], though rigorously size-extensive and also size-consistent with localized orbitals, has some deficiencies in the minimal truncation scheme, viz. at the singles and doubles (SD) level (SS-MRCCSD). SS-MRCCSD does not involve the direct coupling of all the model functions with a given virtual function belonging to the uncontracted multiconfiguration CISD space. It also does not involve, even in the linear power of a cluster operator T(μ), the direct coupling of the virtual functions χ(l(μ)), which are up to doubly excited with respect to a model function φ(μ) to the other virtual functions of the MRCISD space which can be generated by triple and quadruple excitations from φ(μ). We argue that inclusion of a selection of triples and quadruples involving at most two inactive orbital excitations from every φ(μ) would ameliorate the shortcoming of the incomplete coupling of the triply and quadruply excited virtual functions which can couple with the singly and doubly excited ones. This extended ansatz for our SS-MRCC theory, to be called SS-MRCCSDtq by us, would still miss the direct coupling of the manifold of the model functions {φ(λ),λ ≠ μ} to singly and doubly excited virtual functions. However, this effect is expected to be less significant than the lack of the more complete virtual space couplings, these functions being many more numerous, suggesting the new methods to be significantly improved schemes. Excellent results on the potential energy surfaces of small molecules involving single, double, and triple bond dissociation bear out our expectations fully.