Electronic Structure. Internuclear Distance

Experimental Results. The analogues of the red and infrared atmospheric oxygen bands [1, pp. 278/9] were discovered in the emission spectrum of NF produced and excited by a discharge through Ar-NF3. The green emission at 529 nm was identified with the forbidden b transition [3, 4], the near-IR emission at 874 nm with the forbidden a A  

Theoretical Results. A survey of ab initio SCF-MO (restricted Hartree-Fock) and configuration interaction (Cl) calculations for NF in the three lowest states X 2 , a A, and b 2 is presented in Table 15, p. 273. It contains the total molecular energies Ej and the corresponding (calculated or experimental) bond lengths r, and, for sake of completeness, a listing of other molecular data obtained from the respective wavefunctions. 

In addition to the results given in Table 15, bond lengths for NF(X 2 ) were calculated with various basis sets (STO-3G, 3-21G, 6-31G ) using the restricted and unrestricted Hartree-Fock procedures (RHF and UHF) and Moller-Plesset perturbation theory at second and third order (MP2 and MP3) (re between 1.30 and 1.39 A) [26] and with the 6-31G basis set using UHF, Cl, MP2, and MP3 methods (re between 1.30 and 1.33 A) [27]. Geometry optimizations were carried out for NF(X 32-)(RHF, 4-31G basis) [28] and for NF(X a A, b 2- ) (large Cl calculations, no details) [29]. 

The most commonly used abbreviations and symbols are given in Table 7, p. 235. - MRD Cl = multi-reference double-excitation Cl, full CI = CI without configuration selection. AH = reaction enthalpy, A = electron affinity, cOe, cOeXe, Be, ae = vibrational and rotational constants, D = dissociation energy. - Publications [22] and [23] give identical results the excited state, however, is labeled a A in [22] and b 2 in [23], the latter obviously in view of the discovery of the b X emission spectrum, see note added in proof in [23]. - Calculated Ej minima at 2.44 a.u. (=1.291 A) for X and 2.43 a.u. (=1.286 A) for a A or b 2- . 

The few semiempirical studies dealt with the molecular correlation energy of NF (X 2, b 2 ) (effective-pair correlation method) [30], the bond lengths of NF(X 2, a A) (MNDO approximation) [31], the bond lengths of singlet and triplet NF (CNDO, INDO) [32], the valence MO energies of NF(X 2 ) (CNDO) [33], and the populations in singlet and triplet NF (CNDO, INDO) [34] and NF(X 2 ) (extended Huckel method) [35]. 

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These surfaces are all based on some combination of ab initio electronic structure calculations plus fitting. The AD and BM surfaces are based respectively in whole or in part on extended-basis-set single-configuration self-consistent-field calculations, whereas the RB and RBST calculations are based on calculations including electron correlation by Moller-Plesset fourth-order perturbation theory. For the rigid-rotator calculations R., the intramolecular internuclear distances R- and R ... 

Fig. 3.13 Left-hand panel The electronic structure of an sp-valent diatomic molecule as a function of the internuclear separation. Labels Et and Ep mark the positions of the free-atomic valence s and p levels respectively and = ( s + p). The quantity Rx is the distance at which the and upper tr9 levels cross. The region between the upper and lower n levels has been shaded to emphasize the increase in their separation with decreasing distance that is responsible for this crossing. Right-hand panel The self-consistent local density approximation electronic structure for C2 and Si2 whose equilibrium internuclear separations are marked by RCz and RSa respectively. (After Harris 1984.)...

We may attempt to make a rough quantitative statement about the bond type in these molecules by the use of the values of their electric dipole moments. For the hydrogen halogenides only very small electric dipole moments would be expected in case that the bonds were purely covalent. For the ionic structure H+X-, on the other hand, moments approximating the product of the electronic charge and the internuclear separations would be expected. (Some reduction would result from polarization of the anion by the cation this we neglect.) In Table 3-1 are given values of the equilibrium internuclear distances r0, the electric moments er0 calculated for the ionic structure H+X , the observed values of the electric moments /, and the ratios of these to the values of er0.ls These ratios may be interpreted in a simple... 

A full theoretical treatment of Pgl within the Born-Oppenheimer approximation involves two stages. First, the potentials V (R), V+(R), and the width T(f ) of the initial state must be calculated in electronic-structure calculations at different values of the internuclear distance R—within the range relevant for an actual collision at a certain collision energy—and then, in the second stage the quantities observable in an experiment (e.g., cross sections, energy and angular distributions of electrons) must be calculated from the functions V+(R), V+(R), and T(f ), taking into account the dynamics of the heavy-particle collisions. 

Pure rotational spectroscopy in the microwave or far IR regions joins electron diffraction as one of the two principal methods for the accurate determination of structural parameters of molecules in the gas phase. The relative merits of the two techniques should therefore be summarised. Microwave spectroscopy usually requires sample partial pressures some two orders of magnitude greater than those needed for electron diffraction, which limits its applicability where substances of low volatility are under scrutiny. Compared with electron diffraction, microwave spectra yield fewer experimental parameters more parameters can be obtained by resort to isotopic substitution, because the replacement of, say, 160 by lsO will affect the rotational constants (unless the O atom is at the centre of the molecule, where the rotational axes coincide) without significantly changing the structural parameters. The microwave spectrum of a very complex molecule of low symmetry may defy complete analysis. But the microwave lines are much sharper than the peaks in the radial distribution function obtained by electron diffraction, so that for a fairly simple molecule whose structure can be determined completely, microwave spectroscopy yields more accurate parameters. Thus internuclear distances can often be measured with uncertainties of the order of 0.001 pm, compared with (at best) 0.1 pm with electron diffraction. If the sample is a mixture of gaseous species (perhaps two or more isomers in equilibrium), it may be possible to unravel the lines due to the different components in the microwave spectrum, but such resolution is more difficult to accomplish with electron diffraction. 

According to a complete X-ray diffraction analysis, Se6 consists of ring molecules with the molecular symmetry of Dzd the crystal and molecular parameters are listed in Table II (17) and the crystal structure is shown in Fig. 2. Refinement by the least squares method resulted in the following atomic parameters of the single atom in the asymmetric unit x = 0.1602 0.00048, y = 0.20227 0.00047, z = 0.12045 0.00120 calculated density, 4.71 g/cm3. An earlier investigation of selenium vapor by electron diffraction led to an internuclear distance of 234 1 pm and an average bond angle of 102 0.5° for the chairlike cyclic Se6 molecule (23). 

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