Angular‐Momentum Conditions for a Correlated Wavefunction

Articles you may be interested in Angular-momentum conservative smoothed particle dynamics for incompressible viscous flows 1605 where q2 is the vibrational coordinate, P2 its conjugate momentum, and integration at the given ql-coordinate hypersurface is over a vibrational period. The vibra-tional energy equals lv, so that for a vibrationally adiabatic motion a portion of this energy, I(vt-vo), must go into translational energy along q\ where v t is the value of vibration frequency at the saddle point and Vo is that for the reactants. In the two calculations of Wall et al., cited above, I equaled !h and !h, respectively. loa It is possible, with the aid of analytical mechanics, to make a calculation of this tendency of A (quantum 15a Note added in proof: Further numerical calculations of tra-jectories in this system (with a different potential-energy surface) support this vibrational adiabaticity suggestion, not only for the rotation-free system but also, in contrast with earlier work, for the rotation-present one [ Sharma (private communication) J. mechanics) or I (classical mechanics) to be constant for the vibrational motion. Some calculations of this nature are now in progress. I6 Wall, Hiller, and Mazur have also made numerical calculations on classical-mechanical transmission coefficients for the case of rotating systems. I7 In this case the simple results described above for conversion of vibrational energy to energy useful for overcoming the barrier were apparently not obtained [see, however , Ref. 15(a) J,1t may be noted that in the activated-complex expression given by Eq. (IS) vibrational adi-abaticity was assumed only in the immediate vicinity of the activated complex, and not for all values of qi from region of reactants to that of products. We obtain the conditions under which a correlation wavefunction containing pair correlation functions for the 2pn electrons of C(SP, 'D, 'S), N(4S), O(SP), and Ne will be an eigenfunction of the orbital and spin angular-momentum operators. These pair functions contain quite general powers of electronic and interelectronic coordinates along with their variational parameters and should avoid the convergence difficulties of configuration interaction. In all these cases, except carbon which has just one pair of 2p electrons, one cannot obtain such a pair function, fli ;<'), just by minimizing its pair energy, Ei/ll, alone; i.e., minimizing the variational parameters of a 12.;<'). Minimization of one pair at a time corresponds to working with just a part of the correlation wavefunction which by itself cannot converge …