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The application of the recent theories of Liu and Marcus [J. Chem. Phys. 63, 272 (1975)] and Coombe and Snider [J. Chem. Phys. 67, 2659 (1977)] for the experimental determination of the relaxation parameters T1 and T2 from line shape measurements in zero Stark field is examined. In the first part of the paper it is shown that power‐broadened absorption lines in zero field may be fit to a single Lorentzian line shape from which a combined parameter qT1/T2 may be obtained. The new parameter q, which is determined by the distribution of populations of the m components of the levels under conditions of partial saturation, is defined and related to results of previous work. In the second part of the paper expressions for T1−1 and T2−1 for the zero‐field and non‐zero‐field cases are derived in terms of time correlation integrals of a random perturbation. It is shown that a close connection exists between T1−1u1 and T2−1 in zero field and certain averages of these quantities over the m states for nonzero field. From the comparisons it is seen that precise values of these parameters may provide additional information about the collision process.

This paper is divided into four parts: The first part (Sec. I) contains a brief review of different assumptions made by several authors for the numerical values of the free Mn2+ ion parameters. It is shown that if only the Racah parameters B and C are taken into account, then the Orgel‐Griffith choice B=960 cm−1, C=3325 cm−1 seems to be the best one. Tanabe and Sugano's figures lead to errors as high as 3800 cm−1. Adding only the Racah‐Trees correction α does not seriously improve the fitting of levels 4G, 4D, and 4F because a singular set of equations is then obtained. An exact experimental agreement can be obtained for all quartet levels by simultaneously using the Racah‐Trees correction α and the seniority correction β. The best fit values of the adjustable parameters relevant to the Mn2+ ion are given; it is found that α and β do not differ very much from Shadni's values. Section II deals with the well‐known use of the two normalization parameters Nt, Ne for describing covalent bonding. A routine method is developed for performing these calculations by using the three traces of the 4E, 4T1, and 4T2 matrices (if experimentally available). The interest of using these traces, rather than the energies of individual levels, lies in the fact that the energy sum of 4E(4G) and 4E(4D) levels deviates only slightly from a linear function of the Koide and Pryce covalency parameter, while the energy sum of 4T1 and 4T2 levels does not depend on any assumption upon Dq. This method is extensively applied in Sec. IV. In Sec. III is an attempt to obtain condensed analytical expressions by means of Lohr's INDO approximation for covalent bonding. These expressions allow some discussion about the validity of the method described above: It is shown that the use of the conventional Dq formalism can still be justified (with a suitable modified value of Dq) when only the metal‐ligand interaction is taken into account, but it is no longer correct if the ligand‐ligand terms are introduced in the calculation. In Sec. IV, we have used the ``method of traces'' described in Sec. II for deriving tables of covalency and normalization parameters for several manganese‐containing crystals: MnF2, MnCl2, MnBr2, NaCl:Mn, &cellip; . We found that the accuracy of the experimental results presently available is in some cases very poor and new measurements by means of more modern techniques are needed. Specifically, an error as high as 6000 cm−1 has been found on the 4T1(4P) level in Pappalardo's classical paper on MnCl2. Nevertheless, the Dq values we obtain are in the right order Dq(MNBr2)

Using the computational procedure established in the previous paper, configuration interaction calculations have been performed for the 3Σg−, 3Σu−, 3Πg, 1Πg, and 1Σg+ symmetries of O2. The lowest diabatic Rydberg state for each symmetry is presented. Vibrational energy levels of the 1Πg Rydberg state are given. The extent of Rydberg–valence interaction is discussed and the 3Σu− state is compared with a previous calculation.

The Raman spectrum of phosphorus pentachloride III, which is obtained by squeezing the ordinary phase II to a few kilobars (see preceding paper), has been recorded at ∼100 K and zero pressure. The ratio of the integrated intensities of the PCl4+ and PCl6− ions is much smaller in phase III than in phase II, showing that the ionization PCl6−→PCl4++2Cl− occurs in the solid at the transition. It appears to be the first example of a pressure‐induced ionizing dissociation in a solid. Phase III is similar to, but apparently not identical with, a phase obtained by subliming phase II and condensing the vapor at, apparently, room temperature. The implications of this transformation for the synthesis of inorganic compounds is briefly discussed.

In this paper, the adiabatic relaxation theory is applied to investigate the origin of rare‐earth fluorescence quenching involving multiphonon transitions. The energy level schemes for BaCl2:Sm2+ and BaBr2:Sm2+ have been obtained from the observed fluorescence spectra. The phonon cutoff frequencies, 210 and 140 cm−1 for BaCl2 and BaBr2, respectively, have been determined from vibronic sidebands. From the observed temperature dependence of the fluorescence intensities and lifetimes, it is shown that the 5D1 and 5D0 levels are thermally quenched through radiationless excitation to the 4f55d band and that the population of the 5D0 level from 5D1 involves the 4f55d band as an intermediary. This indirect f (→d) →f relaxation mechanism appears to have resulted from the proximity and relatively large displacement between the adiabatical surfaces of the low‐lying 4f55d and the 5D1 states of Sm2+ in BaCl2 and BaBr2.

The fluorescent sulfur LII,III emission spectra have been quantitatively measured and analyzed for the relative strengths (radiative yields) of the allowed transitions, and for the corresponding emission linewidths. These were investigated for the sulfur compounds in the solid, vapor, and gas states—Na2SO4, K2SO4, CdSO4, Na2SO3, K2SO3, C4H4S, H2S, SO2, and SF6. The S LII,III spectra for the solid compounds (all strongly ionic) revealed essentially the same localized molecular orbital character about a central sulfur atom as for the molecular compounds—showing no significant influence of the cations and no evidence of crystal band structure. The measured molecular orbital energies and radiative yields were found to be generally consistent with the eigenvalue and eigenvector calculations based upon current CNDO and abinitio molecular orbital approximation methods. The measured sulfur LII,III spectra for the compounds reported in this paper have been interpreted according to the valence orbital configuration as obtained from the CNDO/2 method. This is done while recognizing that other reported molecular orbital calculations on these molecules often indicate different orderings. The molecular orbital energies as derived from the LII,III spectra have also been compared with those obtained from photoelectron spectroscopy, demonstrating, generally, very good agreement between these two methods. Because the LII,III spectra for second row elements probe the 3s and the 3d character of the valence band and the Kβ spectra probe the 3p character of the valence band, it has been found very useful to combine the results of these x‐ray emission techniques in order to gain a complete analysis of valence band electronic populations and symmetries. It has been shown that the LII,III emission analysis can be a uniquely powerful tool for the determination of the role of the 3d atomic orbital in the chemical bonding of the second‐row elements.

The spin–orbit contribution to the zero‐field splitting (ZFS) in the CH2O 3A2(n→π*) state is evaluated using the full Breit–Pauli Hamiltonian. All calculations are carried out at the planar ground state geometry using a double‐zeta plus polarization basis of contracted Gaussian‐lobe functions augmented with diffuse s and p functions. Configuration–interaction wavefunctions, constructed using the 3A2 canonical orbitals, are used to describe the 3A2 state and all states coupling to it via the spin–orbit Hamiltonian. The excitation energies and oscillator strengths obtained from these wavefunctions are in good agreement with other theoretical calculations and with experiment. Of the 12 states considered in the second‐order perturbation theory treatment of the spin–orbit interaction, the 1A1 ground and the nearby 3A1(π→π*) states were the most important. Rydberg states were observed to have very small spin–orbit matrix elements and consequently to have little effect on the ZFS. The spin–orbit contributions to the ZFS parameters D and E were −0.224 and 0.009 cm−1, respectively, which when added to the spin–spin contribution obtained in an earlier paper [S. R. Langhoff, S. T. Elbert, E. R. Davidson, Int. J. Quantum Chem. 7, 999 (1973)] give total values of D=0.314 cm−1 and E=0.04 cm−1. These results are larger than the best experimental results of D=0.141 cm−1 and E=0.02 cm−1, determined by Birss etal. [F. W. Birss, R. Y. Dong, and D. A. Ramsay, Chem. Phys. Lett. 18, 11 (1973)] from a rotational analysis of the 0+←0 bands of the 3A2←1A1 transition. An extensive calculation was also undertaken to assess the degree of convergence in the second‐order perturbation theory treatment. The contribution of the lowest 100 singlet and triplet states of A1, B1, and B2 symmetry were considered where each state was described by a 100‐term CI wavefunction. This calculation gives a spin–orbit contribution to D of −0.221 cm−1 essentially identical to the previous result providing evidence that the second‐order treatment has indeed converged. The radiative lifetimes of the three sublevels of the triplet state were determined using the same representations for the manifold of electronic states. In the high temperature limit, the radiative lifetime was determined to be between 0.02 and 0.06 sec, somewhat longer than the estimated experimental value of 0.01 sec. The mutual perturbation of the 1A1 ground and 3A2 states and the perturbation of the 3A2 state by the 1A1(π→π*) state were determined to be most important in determining the lifetime. These results ensure that the emitted light is polarized primarily along the carbon–oxygen bond in agreement with experiment. A critical examination of the quantitative validity of the numerical results is presented to assess the reliability of the theoretically determined lifetimes.

This paper reports an abinitio CI calculation of the radiationless decay of the formaldehyde 1A2 state. First we derive quantitative conditions, which a basis set must satisfy if it is to be used for describing radiationless decay. We checked these conditions for the formaldehyde molecule and found them to be satisfied for the adiabatic Born–Oppenheimer set used in the calculation. We then derive a general equation for the coupling elements resulting from this basis set. With the method used, rotational coupling could be treated completely equivalent with vibrational coupling; this rotational coupling turned out to be not important in formaldehyde however. The coupling elements for D2CO are a factor 10 smaller than the corresponding ones in H2CO. The results of the calculation show, that the internal conversion in formaldehyde is an example of the so‐called resonance case. Therefore the decay cannot be described by the model proposed by Yeung and Moore, where S1→S0 internal conversion is the rate determining step in the photodissociation. Finally, we discuss the applicability of the ’’golden rule’’ in describing radiationless decay.

This paper reports an abinitio CI calculation of the radiative 1A1→1A2 transition of H2CO and D2CO. Throughout the calculation the electronic wavefunctions and transition moments are explicitly calculated as functions of the nuclear geometry, contrary to the conventional Herzberg–Teller approach. The evaluation of the vibrational wavefunctions and integrals was made numerically. The results show that the excited state frequency for mode 3 has to be reassigned and that the calculated vibrational structure agrees well with the experimental intensities.

We present the most exhaustive theoretical studies to date of the nature of the lowest (ππ*) singlet state of vertical C2H4. Basis sets as large as double zeta plus polarization plus diffuse functions were used in conjunction with large scale configuration interaction, including as many as 7064 1B1u configurations, constructed from 31 898 Slater determinants. The lowest total energy obtained was −78.0284 hartree, significantly lower than any previous variational result. A key to determining the spatial extent of the vertical V state was provided in the important paper by McMurchie and Davidson, who showed how critical it is that the CI wavefunction be invariant to transformations within the π* (b3u) orbital space. However the actual value of 〈ψ‖Σi x2i‖ψ〉 obtained here, ∼27 a.u., is somewhat larger than that of McMurchie and Davidson. We conclude that the V state is intermediate in its spatial extent between valence and Rydberg character. However, it is also seen that variational energies are veryinsensitive to the value of 〈x2〉 predicted. That is, by raising the vertical excitation energy of the V state by only 0.1 eV, the intermediate spatial extent suggested by the variational principal becomes markedly more valencelike. The latter observation serves to explain the experimental spectra of Miron, Raz, and Jortner.

In this paper we consider the problem of intramolecular vibrational energy flow from a conventional bond to a van der Waals bond in a linear AB–CD van der Waals molecule, where AB and CD are conventional diatomics. A model for collinear vibrational predissociation of AB–CD on a single ground state potential surface was developed. The vibrational predissociation of a van der Waals heterodimer, consisting of a pair of distinct diatomics, can be described in terms of a simple exponential decay of a single discrete zero order state which corresponds to excited bond modes, into a dissociative continuum. The dependence on the vibrational predissociation rate of the heterodimer on the parameters of the molecular bonds and of the van der Waals bond is elucidated. The details of the intramolecular dynamics of a homodimer, consisting of a pair of identical diatomics, are determined by the excitation conditions. Optical infrared short time excitation is expected to result in a coherent, in phase, superposition of degenerate bond modes, which will subsequently exhibit a simple exponential time evolution, the decay rate being determined by the resonance width. Collisional excitation of the dimer is expected to result in an incoherent initial superposition of degenerate bond modes, the subsequent time evolution being determined by the discrete–discrete coupling and by the widths of the metastable states. Model calculations were performed for the nuclear dynamics of collisionally excited linear halogen dimers A2⋅⋅⋅A2(A=F, Cl, Br, I). The linear (Cl2)2, (Br2)2, and (I2)2 dimers are characterized by negligibly small discrete–discrete coupling terms whereupon the nuclear dynamics of these van der Waals molecules is determined by exponential decay due to vibrational predissociation, without direct energy exchange between the bond modes. For the (F2)2 linear dimer the discrete–discrete coupling terms overwhelm the widths of the resonances and the system will exhibit efficient direct energy exchange between the molecular bond modes before the occurrence of vibrational predissociation. Model calculations for the vibrational predissociation lifetimes for the halogen dimers reveal remarkably long lifetimes, which can be accounted for in terms of the energy gap law for vibrational predissociation. Our results account for the ineffective process of intramolecular vibrational energy flow discovered by Dixon and Herschbach in the (Cl2)2 dimer.