P561: Uses for valence virtual orbitals

Author: Michael W. Schmidt, Iowa State University, USA

Co-Author:

Date: 8/5/14

Time: 3:40 PM4:00 PM

Room: MAN 123

Related Symposium: S36

Valence Virtual Orbitals (VVOs) can be extracted from the unoccupied orbital space of any kind of SCF (or limited MCSCF) calculation. VVOs will be shown to be antibonding (two or more center) combinations of atomic orbitals. The Fock (or Kohn-Sham) operator’s expectation values assigns an energy value to each VVO. Thus the lowest VVO (LVVO) is a semi-quantitative realization of the LUMO concept. The shapes and the approximate energies of all VVOs are found to be independent of the working basis set for the MO calculation. Applications to molecules such as ferrocene or buckmisterfullerene demonstrate that a full MO diagram may be constructed using the LVVO, the LVVO+1, and so on, together with the usual occupied orbitals. A further application of the VVO lies in their prediction of excited state orbitals, for valence-type excited states. A pedantic, but useful, application is the preparation of starting orbitals and even suggests an automated active space design for multi-reference calculations. User input is trivial: one keyword causes the generation of VVOs. The process requires no expert knowledge, as the number of VVOs sought is based on counting s-block atoms as having only a valence s orbital, transition metals as having valence s and d, and main group atoms as being valence s and p elements. Elements up to Xenon may be used in the program’s present state.

P560: Construction of valence virtual orbitals

Author: Michael W. Schmidt, Iowa State University, USA

Co-Author:

Date: 8/5/14

Time: 3:05 PM3:25 PM

Room: MAN 123

Related Symposium: S36

The orbitals of the atoms in a molecule form various antibonding molecular orbitals (MOs), as well as the bonding MOs. This idea led directly to the frontier orbital theory of Fukui, and a very widespread use of the HOMO and LUMO concept (highest occupied, lowest unoccupied MO). Although the HOMO and lower energy occupied orbitals of today’s quantum chemistry calculations remain suitable for qualitative interpretations (for example, ionization potentials), the LUMO has been lost. At one time only a minimal basis set could be used in a quantum chemistry calculation, whose unoccupied orbitals were assuredly atomic in character, and chemically relevant. However, today’s calculations employ basis sets with multiple basis functions for the atomic orbitals, extended by polarization and diffuse augmentations. The relatively few valence antibonding orbitals have been lost in a sea of far less meaningful unoccupied orbitals, representing the continuum of states associated with a detached electron, as well as Rydberg or other states. Fortunately, a simple mathematical procedure can extract Valence Virtual Orbitals from the largely uninteresting valence space. Chemical applications of these VVOs will be discussed in a related presentation at this same meeting.

P444: Energetic order of atomic orbitals: Observed values versus textbook stories

Author: W. H. Eugen Schwarz, Theoretical Chemistry Center, Department of Chemistry, Tsinghua University, Beijing 100084, China (Presented by Michael W. Schmidt, Ames Laboratory, Iowa State University)

Co-Author: Jun Li, Tsinghua University, China

Date: 8/5/14

Time: 10:35 AM10:55 AM

Room: MAN 123

Related Symposium: S36

Any ‘atoms first in chemistry’ approach must begin with the shapes and energies of the atomic orbitals. The concept of atomic orbits and their energetic order in poly-electronic atoms was introduced by N. Bohr. In his widely published Noble lecture, he not only derived the spin-orbit split term energies Enlj of the core and valence shells of ‘all’ light and heavy elements from the diverse observed spectra, but also plotted the orbital orders correctly already since 1922. The common order is rather hydrogen-like. However, due to the strong shielding of the nuclear charge by the inner core electrons at the beginning of periods n = 4, 5, 6, 7 (i.e., the heavy s-block elements), the common hydrogenic orbital order (n-2)f < (n-1)d < ns becomes inverted to ns < (n-1)d < (n-2)f. Remarkably, the chemical community chose the latter exceptional orbital energy order as the standard order, and teaches it up to present times. The textbooks must then combine it with several further inconsistencies of logic and facts and ‘exceptions from the rules’ to achieve agreement with chemical deductions. We propose to teach the observed standard orbital order, which then does not require further mental maneuvers. For undergraduate students, one may just communicate this fact in general chemistry. At the graduate level, the exceptional orbital order in the first two groups of the periodic table can be theoretically explained by the nuclear shielding effect, which must be mentioned anyhow in connection with the s-p-d splitting.

P445: Atoms first, but correctly: Consistent explanation of the periodic law

Author: W. H. Eugen Schwarz, Theoretical Chemistry Center, Department of Chemistry, Tsinghua University, Beijing 100084, China (Presented by Michael W. Schmidt, Ames Laboratory, Iowa State University)

Co-Author: Jun Li, Tsinghua University, China

Date: 8/5/14

Time: 11:10 AM11:30 AM

Room: MAN 123

Related Symposium: S36

The operational definition (Boyle 1661) and discovery of the mass of chemical elements (Lavoisier et al. 1787) called for a systematic ordering that was empirically achieved in the 1860s (Meyer, Mendeleyev, and many others). A logical explanation of the basic Periodic Law of chemistry is still missing today, despite the availability of sufficient theoretical concepts (since Bohr 1922, et al.). The periodicity of the elements is based on the periodicity of valency, i.e. of the number of holes in a strongly-bound atomic noble-gas core shell, or of weakly-bound valence electrons energetically high above the core. The particularly different groups of the halogens, noble gases, and alkali metals form the backbone of the periodic system. The origin is the particularly large orbital energy gap above the low-lying 1s2 and np6 noble-gas shells, and below the much more loosely-bound (n+1)s, nd and (n-1)f valence shells. The appearance and position of the large orbital energy gap is due to the shielding of the nuclear attraction of the more and less core-penetrating valence orbitals. We propose to teach the observed orbital energy gaps. One can then, in the 2010s, for the first time rationalize a) the structure and backbone of the periodic system, and b) why the p6 shell is special whereas the s2, d10 and f14 shells are not. For undergraduate students, one may just communicate this fact, while the theoretical explanation through nuclear shielding arguments can be taught to graduate students and beyond.