The predissociation of Li2 b3Πu by a3Σ+u

⁶Li₂ 1³Δ_g(F₁) → b³Π_u(F₁v = 0–11) rotationally resolved fluorescence spectra are recorded following perturbation-facilitated optical—optical double resonance excitation of 1³Δ_g via spin—orbit mixed A¹Σ⁺_u ∼ b³Π_u(F₁e) intermediate levels. The f-symmetry Λ-components of b³Π_u(F₁) are broadened above the 0.05 cm⁻¹ detection threshold owing to predissociation by the vibrational continuum of the a³Σ⁺_u state. The observed v = 0–11, N = 31f level widths were used to determine the potential energy curve for the Li₂ a³Σ⁺_u state in the region 2.35 < R < 2.60 Å and 11200 < E < 14900 cm⁻¹ (relative to E = 0 at the minimum of X¹Σ⁺_g). The a³Σ⁺_u ∼ b³Π_u curve crossing is at R = 2.57 Å and E = 11246 cm⁻¹ and the electronic part of the − BN·LL-uncoupling matrix element is 〈b Π¦L⁺ ¦aΣ〉 = 1.216H at an R-centroid Rv_bϵ_a = 2.61Å.     

Vibronic coupling between the lowest electronic states of biphenyl

Vibronic coupling among the lowest excited states of biphenyl have been computed by a CNDO/S Hamiltonian in a floating-orbital scheme. The v₆(b_1u) and v₆(b_2u) modes are the most active in coupling 1B_3g with the L_a, B_a and B_b states. The v₁(b_1u) mode induces a sizable coupling between the quasi-degenerate 1B_3g and 1B_2u states. The computed induced intensities agree with those of false origins in fluorescence.     

Trans-N2F2 and cis-N2F2: A green's function calculation on their photoelectron spectra

The vertical valence ionization potentials of trans-N₂F₂ and cis-N₂F₂ have been computed by a many-body Green function method. For trans-N₂F₂ the agreement with experiment is very satisfactory in general and the calculations permit an analysis and assignment of the experimental photoelectron spectrum. The ionization potentials of cis-N₂F₂ are predictions. The ordering of the ionization potential is for trans-N₂F₂ 5ag(n₊), 2a_u(π), 4b_u(n_?), 4ag, 1b_g(π), 1a_u(π), 3b_u, 3a_g, 2b_u and for cis-N₂F₂ 4b₂ (n_?), 2b₁ (π) + 5a₁(n+), 3b₂, 1a₂ (π), 1b₁(π), 4a₁, 3a₁, 2b2, n₊ and n_? denote lone pairs on the N atoms except for the 4b_u(n_?) orbital which has the largest contribution from the F atoms.     

Charge-transfer complexes of meso-substituted porphines

Charge-transfer (CT) complexes of 5,10,15,20-tetramethyl-21H,23H-porphine [H₂(tmp)] and 5,10,15,20-tetraphenyl-21H,23H-porphine [H₂(tpp)] have been prepared with TCNQ-type (TCNQ = 7,7,8,8-tetracyanoquinodimethane) acceptors. The complexes crystallize in a mixed-stacked structure. The electronic state of the complexes has been investigated by combining structural geometry information of the acceptors with vibrational spectroscopy data. The complexes were found to possess neutral ground states. The difference between the donor oxidation potential and the acceptor reduction potential (ΔE) also supports this designation of their electronic states. The CT absorption energy shows a linear correlation with ΔE, which is expected for CT complexes in their neutral ground states. The frontier orbitals of the porphyrin donor that participate in the CT interactions have been examined by calculating the overlap integral between the donor occupied molecular orbitals and acceptor LUMO in the complexes. In the H₂(tmp) and H₂(tpp) complexes, a_2u- and a_1u-type porphyrin HOMO and next-HOMO, respectively, are suggested to both be contributors to the establishment of π–π* CT interactions and formation of the complex.     

Low temperature luminescence spectra of the d10s2 complexes Cs2MX6 (M = Se,Te and X = Cl,Br). The Jahn—Teller effect in the Γ−4(3T1u) excited state

The emission spectra of the title compounds in microcrystalline form have been measured at 10 K. The extensive vibrational progression in the e_g mode is indicative of a tetragonal Jahn—Teller distortion in the Γ^?₄(³T_1u) excited state. The vibronic coupling of a threefold electronic state with a doubly degenerate e_g mode (T—e coupling), linear in the nuclear coordinates, has been reinvestigated considering spin—orbit coupling up to second order perturbation on energy levels which result from an a¹_1gt¹_1u electron configuration. For an estimation of Jahn—Teller coupling constants, the intensity distributions in the progressions were compared with the theoretical line shape functions which were obtained from a model which also permits the determination of potential energy minima and vibrational fundamentals of the excited state. The unusually large increase in the e_g vibrational frequency compared to the ground state is due to Jahn-Teller forces which distort the potential surface, yielding steeper excited state energy curves.     

Isomorphism in electron-pair densities of atoms

The spherically averaged electron-pair intracule (relative motion) h(u) and extracule (center-of-mass motion) d(R) densities are a couple of densities which characterize the motion of electron pairs in atomic systems. We study a generalized electron-pair density (q; a, b) that represents the probability density function for the magnitude of two-electron vector a r _j +b r _k of any pair of electrons j and k to be q, where a and b are nonzero real numbers. In particular, h(u)=g(u;1, −1) and d(R) = . It is shown that the scaling property of the Dirac delta function and the inversion symmetry of orbitals in atoms due to the central force field generate several isomorphic relations in the electron-pair density (q; a, b) with respect to the two parameters a and b. The approximate isomorphism d(R)≅8h(2R) known in the literature between the intracule and extracule densities is a special case of the present results. Received: 24 May 2000 / Accepted: 18 July 2000 / Published online: 27 September 2000     

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.     

The impact of higher polarization basis sets on molecular ab initio results.: III. The ground state of Cl2 in comparison with other diatomics

The ground state potential curve of Cl₂ has been computed near R_c by means of the SCF, MC SCF, CI(SD), and the recently proposed CPF methods. The convergence of the total energy, of D_c and R_c is studied with the aid of computations for various basis sets which include up to three d, two f and one g set. Higher polarization functions have a larger effect than for F₂ for all methods, the g set still affects D_c by 0.15 eV and R_c by 0.02 a₀ on the CPF level. The most elaborate calculation, on the CPF [7,4,3,2,1] level, yields D_c and R_c with an accuracy of 0.08 eV and 0.02 a₀. The same accuracy is obtained for the MC-178 CAS SCF treatment employing a 2d1f polarization basis set. The present results allow us to order the polarization functions according to their relative importance as: d⁽¹⁾ > f⁽¹⁾ > d⁽²⁾ > f⁽²⁾ = d⁽³⁾ > g⁽¹⁾ for the SCF and d⁽¹⁾ > f⁽¹⁾ > d⁽²⁾ > g⁽¹⁾ > f⁽²⁾ = d⁽³⁾ for methods including external correlation. CI(SD) or CPF. A comparison of the results for N₂, F₂, P₂, and Cl₂ shows the higher polarization functions d⁽³⁾, f⁽²⁾, g⁽¹⁾ to contribute 0.1 (F₂) to 0.3 eV (F₂, Cl₂) to D_c and affect R_c by 0.005 a₀ (N₂) to 0.01 7 a₀ (P₂).We have focused our attention mainly on the impact of the atomic basis set incompleteness on the accuracy of results obtained from various methods of computation. Cl₂ turns out to be more demanding than the first-row counterpart F₂ on all levels of theory, which is mainly due to the slower angular convergence rate for E, D_c and R_c (for Cl₂), tables 2 and 3. The more pronounced influence of higher polarization functions is already noticed on the SCF and MC SCF level: f⁽¹⁾ increases D_c by 0.18 eV and reduces R_c by 0.052 a₀ on the MC-178 level for Cl₂, table 6, typical corresponding results for F₂ are only 0.04 eV and 0.013 a₀ [1]. CAS SCF calculations furthermore appear to require larger active spaces for Cl₂, as discussed in section 3.3.On the CI(SD) or CPF level — which aim to account for the entire external correlation — one even finds a pronounced influence of the first g set which contributes ≈ 0.15 eV to D_c and reduces R_c by ≈ 0.02 a₀ (on the CPF level, table 3), the corresponding effects for F₂ were only ≈ 0.04 eV and 0.01 a₀ [1]. The 2d1f polarization basis, which will remain the “standard” large basis for treatments of tri- and tetraatomic molecules, appears to underestimate D_c by still 0.5 eV and to overestimate R_c by ≈ 0.02 a₀ for P₂ and Cl₂, table 7, and probably all molecules in-between. This conclusion emerges from the cumulative effect of adding d⁽³⁾, f⁽²⁾ and g⁽¹⁾ which amounts already to 0.3 eV and 0.015 a₀, table 7.     

Assignment of the vibrational bands of the B1u ← A1g transition in solid benzene films

Low temperature absorption spectra of benzene films were observed in the ¹B_1u ← ¹A_1g transition region. The origins of the two progressions of the totally symmetric vibration v₂(a_1g) are assigned to the crystal-field-induced 0—0 transition and to the false origin 0 + v_1g(e_2g).     

Molecular structure and conformation of gaseous chloroacetyl chloride as determined by electron diffraction

Chloroacetyl chloride is studied by gas-phase electron diffraction at nozzle-tip tempera- tures of 18, 110 and 215°C. The molecules exist as a mixture of anti and gauche confor- mers with the anti form the more stable. The composition (mole fraction) of the vapor with uncertainties estimated at 2σ is found to be 0.770 (0.070), 0.673 (0.086) and 0.572 (0.086) at 18, 110 and 215°C, respectively. These values correspond to an energy difference with estimated standard deviation ΔE^o = E^o_g -E^o_a = 1.3 ± 0.4 kcal mol^?1 and an entropy difference ΔS^o = S^o_g -S^o_a = 0.7 ± 1.1 cal mol^?1 K^?1. Certain of the diffraction results permit the evaluation of an approximate torsional potential function of the form 2V = V₁(1 - cos φ) + V₂(1 - cos 2φ) + V₃(1 - cos 3φ); the results are V₁ = 1.19 ± 0.33, V₂ = 0.56 ± 0.20 and V₃ = 0.94 ± 0.12, all in kcal mol^?1. The results for the distance (r_a), angle (_∠α) and r.m.s. amplitude parameters obtained at the three temperatures are entirely consistent. At 18°C the more important parameters are, with estimated uncertainties of 2σ, r(C-H) = 1.062(0.030) Å, r(CO) = 1.182(0.004) Å, r(C-C) = 1.521(0.009) Å. r(CO-Cl) = 1.772(0.016) Å, r(CH₂-Cl) = 1.782(0.018) Å, ∠C-C-0 = 126.9(0.9)°, ∠CH₂-CO-C1 = 110.0(0.7)°,∠CO-CH₂-C1 = 112.9(1–7)°, ∠H-C-H = 109.5° (assumed), ∠φ (gauche torsion angle relative to 0° for the anti form) = 116.4(7.7)°, δ (r.m.s. amplitude of torsional vibration in the anti conformer) == 17.5(4.2)°.     

Fourier spectrometry investigation of the 1 3Σg+ →a 3Σu+ transition of the 7Li2 molecule

The 1 ³Σ_g⁺ → a ³Σ_u⁺ transition in the ⁷Li₂ molecule has been observed in the 8200–10 000 cm⁻¹ region with a high resolution Fourier spectrometer. Rotational analysis of 1 ⩽ υ′ ⩽ 7 of 1 ³Σ_g⁺ and 0 ⩽ υ″ ⩽ 7 of a ³Σ_u⁺ has been carried out. We found D_e(a ³Σ_u⁺) = 332.5 ± 1.0 cm⁻¹ that gives T_e(a ³Σ_u⁺) = 8184.3 ± 1.5 cm⁻¹ and D_e(1 ³Σ_g⁺) = 7090.4 ± 1.5 cm⁻¹ with T_e = 16330 ± 2 cm⁻¹.     

Outer valence orbital momentum distributions of carbon dioxide by binary (e,2e) spectroscopy

The outer valence orbital momentum distributions of CO₂ have been reinvestigated using a high momentum resolution (0.1 a_o^?1 fwhm) binary (e,2e) spectrometer operated at 1200 eV impact energy under the non-coplanar symmetric scattering condition. Generally good agreement of the measured momentum distributions with theoretical momentum distributions calculated using literature SCF double-zeta quality wavefunctions has been obtained for the 1π_g, (1π_u + 3σ_u) and 4σ_g orbitals. Although there is a reasonable agreement of the measured momentum distributions with earlier low momentum resolution (0.4 a_o^?1 fwhm) non-coplanar measurements at 400 eV impact energy reported by Cook and Brion, given the large differences in the momentum resolutions much more definitive results are obtained in the present study. In particular, the significantly higher momentum resolution clearly shows the mixed s-p character of the 4σ_g orbital. The present study also gives a much better agreement with theory in the case of the 4σ_g momentum distribution. For each orbital the calculated and where possible the experimentally determined spherically averaged momentum distributions are compared and contrasted with their respective two-dimensional momentum and position density maps. These together with three-dimensional surface plots at selected constant density values of the four outermost orbitals are used to provide a detailed comparison of momentum-space bonding and orbital properties with their more familiar position-space counterparts in the CO₂ triatomic molecule. The calculated momentum-space density contour maps of the core orbitals exhibit rather large density oscillations and the feasibility of future experiments is discussed.     

Symmetry of the dissociation of hydrogen: angular dependence of the doppler profile of the excited hydrogen atom (n = 4) produced in e-H2 collisions

The angular dependence of the Doppler profile of the Balmer-β line indicates that the asymmetry parameter, b, is positive and the polarization of the electric vector, J_p, is 0.7 ± 0.1 for the formation of H¹(n=4) from H₂. Thus, H¹(n=4) is produced in a parallel transition, and the transition moment of H¹ lies along the dissociation axis. This result suggests that the intermediate states for the fast and anisotropic H¹(n=4) atoms should be of the type ¹Σ⁺_u(2pσ_u)(n/σ_g).     

Nucleophilic substitution reactions of acetylides on substituted tricarbonyl(η6-fluoroarene)chromium and reactions of tricarbonyl[η6-(2-trimethylsilylethynyl)toluene]chromium and tricarbonyl[η6-(p-ethynyl-phenylethynyl)benzene]chromium with dicobalt octacarbonyl

Nucleophilic substitution reactions of various acetylides on substituted tricarbonyl(η⁶-fluoroarene)chromiums were pursued. The reaction presumably underwent a more complicated mechanism rather than the direct substitution on the fluorine-bearing carbon. The organometallic compounds (η⁶-C₆H₃R¹R²R³)Cr(CO)₃ (R¹: CC–C₆H₄CH₃, R²: o-Me, R³: H (5a), R¹: CC–C₆H₄CH₃, R²: o-OMe, R³: H (6a), R¹: CC–C₆H₄CH₃, R²: m-OMe, R³: H (6b), R¹: CCPh, R²: o-Me, R³: o-OMe (8b), R¹: CCPh, R²: m-Me, R³: m-OMe (8c), R¹: CCSiMe₃, R²: o-Me, R³: H (9a), R¹: CC–C₆H₄CCH, R²: H, R³: H (12), R¹: CC–C₆H₄CCH, R²: o-Me, R³: H (13)) as well as the organometallic dimmer [{(η⁶-o-Me-C₆H₄)Cr(CO)₃(di-ethynyl)] (di-ethynyl: CC–C₆H₄CC (14)) have been synthesized from nucleophilic substitution reactions of tricarbonyl(η⁶-fluoroarene)(chromium) compounds with suitable acetylides. The products have been characterized by spectroscopic means. In addition, (8b) and (8c) were characterized by X-ray diffraction studies. Further reactions of (9a) and (12) with appropriate amount of Co₂(CO)₈ yielded μ-alkyne bridged bimetallic complexes, Co₂(CO)₆{μ-Me₃SiCC–(o-tolueneCr(CO)₃} (10) and (Co₂(CO)₆)₂{μ-HCC–C₆H₄–CC–(benzene)Cr(CO)₃)}(15), respectively. Both (10) and (15) were characterized by spectroscopic means as well as single crystal X-ray crystallography. The core of these molecules is quasi-tetrahedron containing a Co₂C₂ unit. A two-dicobalt-fragments coordinated di-enyls complex, (Co₂(CO)₆)₂{μ-HCC–C₆H₄–CC–H} (17), was synthesized from the reaction of 1,3-diethynylbenzene with Co₂(CO)₈. Crystallographic studies of (17) also show that it exhibits a distorted Co₂C₂ quasi-tetrahedral geometry.     

The importance of ground-state vibronic mixing in molecular Raman scattering

We consider Albrecht's theory for Raman scattering of fundamentals in the far and pre-resonance regions. Destructive interferences inherent to the A and B terms augment the conventionally suppressed C term dramatically. Raman excitation profiles for the ν₁(a_1g) and ν₆(e_2g fundamentals in benzene can be well fitted with theoretical C-term profiles involving the ¹E_1u(π-π^*) state at 1800 A.     

Theoretical study of the electronic transition moment for the d 3IIga 3IIu band system of the C2 molecule

Large scale ab initio SCF and CI calculations are employed to study the potential curves for the d ³II_g, a ³II_u and X¹Σ⁺_g states of the C₂ radical. The electronic transition moment R_e′e″ for the Swan bands (d ³II_ga ³II_u) is calculated in various AO and MO basis sets as a function of the internuclear CC distance. The form of the Σ|R_e′e″|² curve is in very good agreement with that obtained recently from measurements of Danylewych and Nicholls and Tatarczyk et al.; the calculated value for Σ|R_e′e″² at 2.44 bohr is found to be 5.2 au² compared to the most recent experimental values of |R_e(r_oo)|² = 3.57 au² of Tatarczyk et al.     

Modified Gaussian functions and their use in quantum chemistry. I. Integrals

A modified Gaussian function g(u, v, w, a, R ) = const s(a, R ) is considered where l = u + v + w, s (a, R ) is a 1s-type Gaussian function centered at R , a is the coefficient in the exponent of the 1 s Gaussian function and X, Y, Z are components of R . General formulae are derived for overlap integrals, kinetic energy integrals, nuclear attraction integrals, and electron repulsion integrals, valid for any l. The formulae are much simpler than those derived by Huzinaga for Cartesian Gaussian functions.     

The structure of 1-chloro-1-silabicyclo(2.2.2)octane as determined by gas-phase electron diffraction

The structure of 1 -chloro-1 -si labicyclo( 2.2.2 )octane is determined by gas-phase electron diffraction. The molecule is found to have a large amplitude twisting motion with a double minimum quartic potential function of the form V(φ) = V_o[1 + (φ/φ_o)⁴ - 2(φ/φ_o)²]. Least-squares analysis of the experimental data gives values of 1.4(0.8) kcal mole^? for V_o and 17.5(2.5)° for φ_o. Other structural parameters for the “quasi-C_3v” cage-like molecule include: r_g(Si-Cl) = 2.061(3) Å, r_g(Si-C) = 1.863(3) Å, r_g(C-C_av) = 1.559(2) Å, and r_g(C-H_av) = 1.098(7) Å. Several valence angles exhibit large deviations from tetrahedral values, e.g. ∠Cl-Si-C₂ = 114.6(0.2)°, ∠Si-C₂-C₃ = 105.8(0.4)°, ∠C₂-C₃-C₄ = 114.2(1.2)°, ∠C-₃-C₄-C₅ = 111.4(0.8)° and ∠C₂-Si-C₆= 103.9(0.2)°. Many of the structural features in this strained polycyclic compound. Including the nature of the quartic potential function, can be rationalized in terms of a simple molecular mechanics model. A new method for the calculation of an analytical Jacobian of the intensity function with respect to parameters of the potential function is also discussed.     

Second-order perturbation theory for the angular pair correlation function in molecular fluids

Second-order perturbation theory is used to calculate spherical harmonic coefficients of the angular pair correlation function g(rω₁ω₂) for a liquid in which the molecules interact with a pair potential that is the sum of Lennard-Jones and quadrupole-quadrupole parts. The theory is compared with both molecular dynamics results and with the predictions of the GMF ≡ LHNC, QHNC and first-order perturbation theories. Second-order perturbation theory gives excellent results for the harmonic coefficient g(224,r), but is poorer for g(222,r) and g(202,r).     

The electronic absorption spectra of the alkyl-substituted derivatives of bis(benzene)chromium(0) in the vapour phase

The UV and visible absorption spectra of (arene)₂chromium(0) (arene = benzene (I), toluene (II), ethylbenzene (III), cumene (IV), tert-butylbenzene (V), mesitylene (VI) in the vapour phase have been investigated. Four band systems A,B,C and D are revealed in the spectra. The bands of the system with the shortest wavelengths, D, represent the Rydberg series. The first ionisation potentials IP_a1g, 5.18 and 5.01 eV respectively. The Rydberg bands correspond to the allowed electrodipole transitions from the highest occupied molecular orbital (MO) a_1g to the vacant MO of either the a_2u or e_1u type.System C corresponds to the intense band of the solution spectra. The electronic transition e_2g → e_2g obviously makes a great contribution to this system. System B is assigned to the transition from a_1g to vacant a_2u or e_1u MO, which can be Rydberg orbitals. System A can be assigned to the a_1g → e_2u transition or to the Rydberg transition, which is forbidden in the D_6h point group but becomes allowed upon reduction of symmetry.