The pseudospectral (PS) method for self-consistent-field calculations is extended for use in generalized valence-bond calculations and is used to calculate singlet-triplet excitation energies in methylene, silylene, and ethylene molecules and bond dissociation and twisting energies in ethylene. We find that the PS calculations lead to an accuracy in total energies of <0.1 kcallmol and excitation energies to <0.01 kcallmol for all systems. With effective core potentials on Si, we find greatly improved accuracy for PS.
A recent suggestion by G. Chen and W. A. Goddard (1) for electron pairing in hightemperature superconducting oxides reintroduced the concept of magnon exchange as a replacement for the standard BardeenCooper-Schrieffer (BCS) phonon exchange (2). This suggestion received considerable attention because [on the basis of microscopic calculations (1, 3) for small clusters] it provided precise estimates of the various superconducting transition temperatures Tc in the cuprate ceramics and calculated an upper bound T"x = 232 K. We show that, within the Chen-Goddard mechanism, the estimates of Tc are incorrect because Chen and Goddard use an equation for Tc appropriate only for weak coupling and that their Tc"'a is spurious, as there is no upper bound when the correct expression is used.The Chen-Goddard calculation makes use of the weak-coupling BCS model (2) Tc = 1.13 ToeI-X McMillan (4) augmented the weak coupling BCS expression in Eq. 1 to include renormalization. This results in the constant prefactor changing from 1.13 to 0.69, and X being replaced by X* = X/(1 + X). This change, valid for X < -1.5, is significant (2) where a = 0.25 gives the correct McMillan limit. For A = 3.52, Tc = 58 K.The estimate of Tcmax = 232 K is a spurious result, derived from the weak coupling expression (Eq. 1). If Eq. 2 is used, at the large A limit we recover the Allen-Dynes (7) limiting expression Tc = 0.18 Jdd1X112, and Tc has no upper bound as X -* oo. Within the Chen-Goddard mechanism, estimates of Tc should be changed from 114 K, 174 K, and 232 K to 21 K, 58 K, and oo, respectively.At this time it is generally accepted that the identity of the exchange boson for the superconducting pairing electrons in the oxides is still an open question. Phonons, excitons, plasmons, and magnons are among the candidates (8), and there are more. In all cases the appearance of a superconducting instability (9) in the original (normal) state has to compete against other, usually energetically more favorable, instabilities. For the magnon exchange mechanism the dominating instability is normally another magnetic phase, for example, ferromagnetism, spiral spin arrangements, or spin glasses.If the superconducting state is stable in some temperature range, then a T"ax may possibly exist if X in the exponent and the prefactor lJddl of Eq. 2 are both renormalized.It is notoriously difficult to predict the existence of new superconductors and to calculate Tc, even for conventional electronphonon coupling (10), because large changes in Tc are usually found for small changes in coupling. Hence the proposal by Chen and Goddard to test their theory with the use of microscopic electronic calculations of their material parameters is very attractive. However, the cluster calculations of Guo et al. (3) give at best rough estimates of the electrical parameters on the scale needed.
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