Also Formula electronic structure

Fischer-type carbene complexes, generally characterized by the formula (CO)5M=C(X)R (M=Cr, Mo, W X=7r-donor substitutent, R=alkyl, aryl or unsaturated alkenyl and alkynyl), have been known now for about 40 years. They have been widely used in synthetic reactions [37,51-58] and show a very good reactivity especially in cycloaddition reactions [59-64]. As described above, Fischer-type carbene complexes are characterized by a formal metal-carbon double bond to a low-valent transition metal which is usually stabilized by 7r-acceptor substituents such as CO, PPh3 or Cp. The electronic structure of the metal-carbene bond is of great interest because it determines the reactivity of the complex [65-68]. Several theoretical studies have addressed this problem by means of semiempirical [69-73], Hartree-Fock (HF) [74-79] and post-HF [80-83] calculations and lately also by density functional theory (DFT) calculations [67, 84-94]. Often these studies also compared Fischer-type and... 

As mentioned in Section II.A, the Pgl process is ideal for the application of the optical model. This is clear in the classical and semiclassical Pgl theory,24,25 for which opacity and cross-section formulas are completely equivalent to those given earlier in this chapter. The quantal optical model is also rigorously related to the elastic component of the quantal Pgl theory. Miller49 has shown that T(r), identified in Pgl as the autoionization width of the excited electronic state, may be accurately obtained by a standard Born-Oppenheimer electronic structure calculation as... 

The analyses of H. Davy, and J. L. Gay Lussac and L. J. Thenard show that nitric oxide has the empirical composition NO. This formula agrees with the physical properties of the gas. Oxygen is bivalent, hence the nitrogen in nitric oxide also behaves as a bivalent element 0=N but nitrogen is usually ter-or quinque-valent, so that nitric oxide is usually considered to be an unsaturated compound. No evidence of the existence of 0=N—N=0 has been observed. C. Weltzien considers that the radicle NO is sometimes univalent, and sometimes bivalent. J. C. Thomlinson s calculations of the thermochemical eq. of nitrogen in nitric oxide favoured the assumption that the oxygen is quinquevalent. E. Muller discussed this subject and E. C. Stoner, and C. D. Niven, the electronic structure. 

The chemical properties Of phosphine.—H. Davy10 analyzed the gas, but his sample must have been mixed with so much hydrogen as to render his result useless for determining the composition of the gas. The analyses of H. Rose, J. B. A. Dumas, and U. J. J. Leverrier agree with the empirical formula PH3 and the vapour density determinations previously indicated show that this is also the mol. formula. A. O. Rankine discussed the structure of the molecules of the family of trihydrides H. Remy, and H. Henstock, the electronic structure and G. W. F. Holroyd gave... 

The best understood oxo-metallo-bis(dithiolenes) possess the general formula [MO(dithiolene)2]". Although dioxo [M02(dithiolene)2]2 (33, 34, 70, 314, 391-393) and desoxo [MX(dithiolene)2] (X = OR, SR, or SeR) (58, 327, 394) complexes have also been studied, considerably less is known of their spectroscopic properties and electronic structures. Therefore, they will not be... 

The electronic structures of the three solvent molecules have been examined at the same level and the dipole and quadrupole moments evaluated so that the dipole, dipole gradient and quadrupole fields can be included in the discrete simulation. Calculations of the dipole moment of the isolated pNA molecule have also been made for use in the EFISH formula. 

Intuitively, it seems evident that this kind of hierarchic interrelation should be entered into the structure of chemical sets, with not only the nudei but also the electrons of the partides composing them being taken into account. Let us consider now a major structural theme in coordination chemistry - the evolution of dusters having the general formula BL. Each duster is formed from a central atom of the element E bonded to a number of ligands L (n is the coordination number) and each is characterized by a certain formal... 

From the point of view of a computational chemist, one of the most appreciated strengths of the polarization propagator approach is that, although being generally applicable to many fields in physics, it also delivers efficient, computationally tractable formulas for specific applications. Today we see implementations of the theory for virtually all standard electronic structure methods in quantum chemistry, and the implementations include both linear and nonlinear response functions. The double-bracket notation is the most commonly used one in the literature, and, in analogy with Eq. (5), the response functions are defined by the expansion... 

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