Explicitly correlated wave functions of the ground state and the lowest quintuplet state of the carbon atom

Abstract

Variational, nonrelativisitic energies have been calculated for the ground state ( 3 P g ) and the lowest quintuplet state ( 5 S u ) of the carbon atom, with wavefunctions expressed in the basis of symmetry-projected, explicitly correlated Gaussian (ECG) lobe functions. New exact limits of these energies have been estimated, amounting to −37.844906(4) and −37.691751(2) hartree. With finite nuclear masses and leading, scalar relativistic corrections included, respective experimental excitation energy of 12 C has been reproduced with accuracy of about 7 cm −1 .

Chemical Bonding in the C2 Molecule

“…In the first case, the resulting multiplicity is still a triplet, but in the second case, all four electrons have an identical spin; this provides a quintet high-spin state, and the electrons prefer a tetrahedral arrangement. It is noteworthy that the energy of the 5 S u state is only 4.2 eV higher than the energy of the 3 P g state [64]; this is roughly half of the difference of the orbital energies. Although excitation energy must be provided, the repulsion energy in the high-spin state is considerably reduced, first, because the Coulomb repulsion of the electrons in the 2s AO, which are not Fermi correlated, is reduced, and moreover the Coulomb repulsion of four tetrahedrally arranged electrons is minimal in the spherical shell.…”

Potential Energy Curves of the Low-Lying Five 1Σ+ and 1Π States of a CH+ Molecule Based on the Free Complement - Local Schrödinger Equation Theory and the Chemical Formula Theory

“…The H-square errors were mostly less than 0.05, which indicated their sufficient accuracies of the calculated wave functions. In the literature of accurate calculations, − the explicitly correlated Gaussian (ECG) methods provided very accurate variational energies, , but their applications would be limited to small systems. The calculations of the diffusion Monte Carlo (DMC) method by Needs et al also gave the accurate total energies of both ground states of C + and C atoms .…”

“…Boldface means satisfying chemical accuracy, i.e., |Δ E | < 1 kcal/mol. d Refs , . e Estimated by the absolute ground-state energies plus the NIST experimental excitation energies (the value of the lowest J state was used) f Ref . g Ref . h Ref . i Ref . j ref . k Difference of the excitation energy from the experimental excitation energies. Boldface means |Δ EX | < 0.03 eV. l NIST experimental excitation energies (the value of the lowest J state was used) with converted eV units. …”

Deformed Explicitly Correlated Gaussians

“…In the first one the Gaussian centers are shifted, which introduces nonspherical components into the basis functions 59,78,85,86,100,128 . The advantage of this approach is that the calculation of the matrix elements remain simple, and the disadvantage is that the desired angular momentum has to be built-in 59,77,129 or has to be projected out 78,85 .…”