Perspective on “An extended Hückel theory. I. Hydrocarbons”

 The size-consistent self-consistent matrix dressing method has been applied on an open-shell single-configuration reference state. Once the reference state is converged, several low-lying roots can be obtained for the dressed configuration interaction (CI) matrices of appropriate symmetry. The CI matrices were built with a complete-active-space singles and doubles CI method in order to deal properly with multiconfiguration excited states. The vertical ionization and ionization–excitation transitions are obtained from the difference to the closed shell ground-state energy of the neutral molecule. The method has been applied to NH⁺ ₃ and N⁺ ₂ using atomic natural orbital basis sets and state-average adapted molecular orbitals. Two ²A₁ states, very similar and showing great mixing of the (2a _l ⁻¹) and (3a _l ⁻²5a _l ¹) determinants, can be assigned to the broad asymmetric band at 27.6 ± 2 eV in the photoelectron spectrum of NH₃. The possible contribution of a ²Π _g (3σ _g ⁻²1π _g ¹) state to the A shake-up peak of N₂ at 24.6 eV is also discussed. Other states, doublets and quadruplets, are reported for both systems up to 30 eV for NH₃ and 37 eV for N₂. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

AB initio SCF study of the electronic structure and spectrum of CuF2

MC SCF and contracted CI calculations have been performed for the three ligand-field states of CuF₂ and also for two charge-transfer states. With the most extensive basis set the calculated d-d transition energies, including a Davidson correctior for cluster effects, are 4150 cm^?1 (²11g) and 10560 cm^?1 (²Δg). These calculations were made with 98 basis functions, including of orbitals on Cu and d orbitals on F. To check the charge distribution in the molecule, calculations of the ESR g factors were also made at the SCF and CI levels of approximation. Resulting CI values are g_| = 1.93 (1.91) and g₁ = 2.76 (2.60). with corresponding experimental numbers in parentheses.     

Collisional Line Assignments and Hyperfine Structure Interpretation in Cs2 23△1g State

Accurately known energy level structure of the Cs₂ A¹∑⁺_u -b³Πu complex of states from a recent global de-perturbation of these states has enabled additional assignments of 140 per-turbation facilitated infrared-infrared double resonance (PFIIDR) transitions to the 2³△_1g state from collisionally populated intermediate A¹∑⁺_u levels. Together with the 221 previ-ously observed 2³△_1g←A¹∑⁺_u← X¹∑⁺_g double resonance lines [J. Chem. Phys. 128, 204313 (2008)], molecular constants and the Rydberg-Klein-Rees potential energy curve of the 2³△_1g state have been recalculated (excluding 54 perturbed levels). The centrifugal distortion con-stant has been determined and agrees well with the value calculated based on standard empirical formulas. The hyperfine structure of the 2³△_1g state, which has not resolved in our sub-Doppler excitation spectra of the 2³△_1g state, has been interpreted with a preliminary simulation.     

A CI non-empirical pseudopotential calculation of the vertical valence excited states of the iodine molecule

The non-empirical atomic pseudopotential proposed by Durand and Barthelat has been used, together with the CIPSI algorithm for large scale CI, to calculate the vertical transition energies of the iodine molecule, in a valence extended (double-zeta + d) basis set. All the valence excited states were considered. The mixing of configurations is very important especially for the Σ⁺_g, Π_g and Π_u symmetries. The experimentally known transition energies are calculated within a 1 eV error, despite the lack of diffuse orbitals and spin-orbit interaction. Some qualitative Mulliken's estimates are discussed. A new ³Σ⁺_g state from the 10 σ_u → 11 σ_u single excitation is predicted in the 9 eV region.     

Electronic structure of the lithium molecular anion,Li2−

The electronic structure of the ground and excited states of the Li₂⁻ anion has been studied using optimized CI wavefunctions. The low-lying ²Σ_g⁺ state is of the Feshbach type and exhibits a near-degeneracy between ²Σ_g⁺ (υ′ = 0) of Li₂⁻ and ¹Σ_g⁺ (υ″ = 6) of Li₂. In contrast with the H₂⁻ system, we find a rich spectrum of low-lying resonant states for Li₂⁻.     

Low-lying states of cs22+

Using an MC SCF CI method, wavefunctions for the ground state ¹∑⁺_g and the excited states of the symmetries ¹∑⁺_g, ¹Π_g, and ¹Δ_g of the Cs²⁺₂ ionic system are generated. The potential curves for eleven ¹∑⁺_g twelve ¹Π_g, and six ¹Δ_g states are calculated. Results suggest a small charge-transfer cross section for the reaction CS⁺ + Cs⁺ → Cs CS²⁺.     

On Excited States of Alkyl Bridged [14] Annulenes

The linear dichroic absorption spectrum of 1,3,6,8-trans-15, 16-hexamethyl-dihydropyrene has been measured in stretched polyethylene at 77K, and CNDO-CI calculations with inclusion of singly and doubly excited configurations have been carried out on a series of alkyl bridged [14] annulenes with pyrene- and anthracene-shaped perimeters. Transitions to e_3g → e_4u type ¹B states are well described, and the results indicate that additional low-energy excited states originate from e_3g→ e_5g and e_2u → e_4u type configurations interacting strongly with doubly excited configurations of the e_3g, e_3g → e_4u, e_4u type. The second excited singlet state responsible for the weak transition observed between the ¹L bands may be assigned to one of these additional states, but it is probably of complex nature, similar to the ‘phantom’ state in linear polyenes.     

Electronic ground state of iron(II)porphyrin. Ab initio SCF and CI calculations and computed electron deformation densities

Ab initio SCF and CI calculations for the ³A_2g and ³E_g states of the iron(II)porphyrin both predict a ³A_2g ground state. The calculated electron density distribution around the iron atom and the deformation density maps are reported since they represent an important reference with regard to the determination of the ground state of FeP.     

AB initio and configuration interaction calculations for some σ → π* superexcited states of the trans-1,3-butadiene molecule

Some σ → π¹ superexcited states of the trans-1,3-butadiene molcule have been calculated in order to establish them as possible candidates for the 9.52 eV and 11.04 eV transitions observed in the electron impact spectra of this molecule. Four states have been solved self-consistently ( 7a_g→ 2a_u2a_gand 2b_g and 6b_u→ 2a_u, 2bg) and on the basis of extensive CI calculations of transition energies and oscillator strengths, we assign the 11.04 eV transition to the ¹B_g (6b_u→ 2a_u) state. The transition observed at 9.52 eV is more likely to be either a π (la_u) → π1 transition or the first member of a Rydberg series converging to the second ionization potential.     

Ab initio MRD CI calculations for the electron spectrum of the C3 radical

Calculations using the MRD CI method are reported for the ground and low lying excited states of C₃. Transitions from the 3σ_u, 4σ_g and 1π_u MO's into 1π_g are considered, as well as the 1π_u → 3s Rydberg species and the corresponding ionization, and good agreement with experimental data is obtained where comparison is possible. Potential curves calculated for the ground and (1π_u → 1π_g) ¹Σ⁺_u excited state are discussed.     

The externally contracted CI method applied to N2

An approximate multireference CI method is presented. By grouping together configurations with the same internal parts and freezing their relative weights by the use of perturbation theory, the number of variational parameters is drastically reduced. The loss of correlation energy is shown to be usually less than 2%, and the timing is less than one ordinary CI iteration. Examples from calculations on some states of the nitrogen atom and nitrogen molecule are given. The basis set convergence for the lowest excitation energy in the atom is very slow. Less than 50% of the correlation effect is obtained at the s, p, d limit. After the inclusion of ? functions this value is improved to 83%. The dissociation energies of the molecule also show slow basis set convergence with errors of 0.5 eV even after addition of ? functions. The bond distances are, howeever, accurately reproduced with errors of less than 0.005 Å for all the states. A qualitative discussion of predissociation in the a ¹Π_g and B ³Π_gstates caused by spin–orbit interaction with the ⁵Σ_g⁺ state, is finally presented. Rapidly oscillating lifetimes between the different vibrational states are predicted.     

A theoretical study on the ionization of tetrafluoroethylene with analysis of vibrational structure of the photoelectron spectra

Ab initio calculations have been performed to study on the molecular structures and the vibrational levels of the low-lying ionic states (²B_2u,²A_g,²B_2g,²B_3u,²A_u,²B_1g,²B_1u, and²B_3g) of tetrafluoroethylene. The equilibrium molecular structures and vibrational modes of these states are presented. The theoretical ionization intensity curves including the vibrational structures of the low-lying eight ionic states are also presented and compared with the photoelectron spectrum. Some new assignments of the photoelectron spectra are proposed.     

Potential energy curves for the X1∑ g, B1△g and B''''1∑ g states of C2 using MRCI and approximate CI methods

The potential energy curves for the X1∑ g, B1△g and B′1∑ g states of C2 have been studied by using MRCI and approximate CI methods, and are benchmarked against the calculations of full configuration interaction (FCI). The results obtained by MRCI method agree with the FCI very well, and even are accurate enough to compare other approximate methods as benchmark, when the calculations of FCI are not feasible. The approximate CI methods mentioned in this paper are reliable for treating chemical problems.     

1 Bu–2 Ag conical intersection in trans-butadiene: ultrafast dynamics and optical spectra

The potential-energy functions of the 1 ¹B_u and 2 ¹A_g excited valence states of trans-butadiene have been characterised by the CASPT2 method. Based on these ab initio data, a vibronic-coupling model describing the conical intersection of the 1 ¹B_u and 2 ¹A_g states has been constructed. UV resonance-Raman and absorption spectra have been calculated, employing the time-dependent approach. The time-dependent wave-packet calculations reproduce the expected ultrafast (≈30 fs) radiationless decay of the optically bright 1 ¹B_u state into the dark 2 ¹A_g state.     

MRD-CI ground state geometry and vertical spectrum of N3

CI calculations have been carried out for the prediction of the ground state geometry and of the vertical spectrum of N₃. The first three states are ²Π_g, ⁴Π_u and ²Σ⁺_u. The C_∞v correlation diagram for the first dissociation limits is discussed by taking into account possible nonadiabatic pathways.     

Light absorption by manganese pairs in KMgF3:Mn2+ through a vibronically induced exchange mechanism

Double excitations to ⁴E_g and ⁴A_1g states in manganese pairs of KMgF₃:Mn²⁺ have been studied spectroscopically. Three prominent sharp bands are observed in the low temperature absorption spectrum. These bands are displaced by about 400–500 cm^?1 to higher energies from the expected electronic origins. It is proposed that the observed pair transitions gain their intensity through a vibronically induced exchange mechanism. With this mechanism the symmetric double excitations ⁶A_1g⁶A_1g → ⁴E_gu⁴E_gu, ⁴E_gv⁴E_gv and ⁴A_1g⁴A_1g become allowed in addition to the transition ⁶A_1g⁶A_1g → ⁴E_gu⁴A_1g. Analogy to the spectrum of the linear dinuclear chromium complex [(NH₃)₅CrOCr(NH₃)₅]⁴⁺, where the same mechanism has been postulated, is demonstrated.     

Electronic absorption spectrum of Fe3+ doped in ammonium chloride single crystal

The electronic absorption spectrum of the Fe²⁺ ion doped in ammonium chloride has been studied at room and liquid air temperatures. The observed bands have been assigned transitions from the ground ⁶A_1g(S) state to the excited ⁴A_1g(⁴E_g), ⁴T_1g(G) and ⁴T_2g(G) states. The cubic field approximation with D_q = 675 cm^?1, B = 645 cm^?1 and C = 4.4 B is found to give a good fit to the observed band positions.It is further concluded that the site symmetry of the Fe³⁺ ion in the crystal is lowered from O_h to C_4v symmetry at liquid air temperature.     

Stabilization of a π double bond between two boron atoms: A theoretical approach

The low-lying states of HBBH, HBBNH₂ and H₂NBBNH₂ are investigated by means of ab initio CI calculations using a double-zeta + polarization basis set. Diborene is found to have a ³∑_g⁻ ground state. Replacement of hydrogen by amino groups on each side of the BB bond leads to an ethylene-like bond which corresponds to a ¹A_g state of D_2h symmetry. π back-donation by the amino lone pairs is responsible for the stabilization of this state.     

All-valence-electron CI treatment of the electronic spectrum of trans-butadiene

An all-valence-electron CI treatment is reported for the low-lying valence and Rydberg states of butadiene. All singly- and doubly-excited configurations relative to a series of the leading terms in a given CI expansion are taken into account, with resulting secular equation orders of as high as 150 000. The agreement between calculated and experimental transition energies is invariably better than 0.2 eV where comparison is possible, with all low-lying valence triplet and Rydberg singlet excited states being unambiguously assigned. The valence-shell excitation to the 2 ¹A_g species is concluded to correspond to the 7.06 eV band system, while the forbidden singlet—singlet transition reported by McDiarmid is assigned as x₂ → 3s. The possibility of an avoided crossing between Rydberg valence ¹B_u excited states having a determining influence on the appearance of the broad intense V₁—N absorption is also discussed.