Even‐tempered atomic orbitals. IV. Atomic orbital bases with pseudoscaling capability for molecular calculations

1973 ◽  
Vol 59 (11) ◽  
pp. 5966-5977 ◽  
Author(s):  
Richard D. Bardo ◽  
Klaus Ruedenberg
Keyword(s):  
Atomic Orbital ◽  
Atomic Orbitals ◽  
Molecular Calculations

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

From Atomic Orbitals to Molecular Orbitals and Chemical Bonds

2020 ◽  
pp. 150-187
Author(s):  
Jochen Autschbach
Keyword(s):  
Hydrogen Molecule ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Basis Set ◽  
Orbital Method ◽  
Chemical Bonds ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Generalized Matrix

It is shown how an aufbau principle for atoms arises from the Hartree-Fock (HF) treatment with increasing numbers of electrons. The Slater screening rules are introduced. The HF equations for general molecules are not separable in the spatial variables. This requires another approximation, such as the linear combination of atomic orbitals (LCAO) molecular orbital method. The orbitals of molecules are represented in a basis set of known functions, for example atomic orbital (AO)-like functions or plane waves. The HF equation then becomes a generalized matrix pseudo-eigenvalue problem. Solutions are obtained for the hydrogen molecule ion and H2 with a minimal AO basis. The Slater rule for 1s shells is rationalized via the optimal exponent in a minimal 1s basis. The nature of the chemical bond, and specifically the role of the kinetic energy in covalent bonding, are discussed in details with the example of the hydrogen molecule ion.

Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third-, fourth-, and fifth-row atoms

1992 ◽  
Vol 70 (2) ◽  
pp. 612-630 ◽  
Author(s):  
Walter J. Stevens ◽  
Morris Krauss ◽  
Harold Basch ◽  
Paul G. Jasien
Keyword(s):  
Atomic Orbital ◽  
Basis Sets ◽  
Excitation Energies ◽  
Effective Potentials ◽  
Hartree Fock ◽  
The Third ◽  
Atomic Excitation ◽  
Core Electrons ◽  
Atomic Wavefunctions ◽  
Molecular Calculations

Relativistic compact effective potentials (RCEP), which replace the atomic core electrons in molecular calculations, have been derived from numerical Dirac–Fock atomic wavefunctions using shape-consistent valence pseudo-orbitals and an optimizing procedure based on an energy-overlap functional. Potentials are presented for the third-, fourth-, and fifth-row atoms of the Periodic Table (excluding the lanthanide series). The efficiency of molecular calculations is enhanced by using compact Gaussian expansions (no more than three terms) to represent the radial components of the potentials, and energy-optimized, shared-exponent, contracted-Gaussian atomic orbital basis sets. Transferability of the potentials has been tested by comparing calculated atomic excitation energies and ionization potentials with values obtained from numerical relativistic Hartree–Fock calculations. For the alkali and alkaline earth atoms, core polarization potentials (CPP) have been derived which may be added to the RCEP to make possible accurate molecular calculations without explicitly including core-valence correlating configurations in the wavefunction. Keywords: model potentials, effective core potentials, transition metals, relativistic calculations.

STEREO PHOTOGRAPHY OF ATOMIC ARRANGEMENT AND ATOMIC-ORBITAL ANALYSIS BY TWO-DIMENSIONAL PHOTOELECTRON SPECTROSCOPY

2007 ◽  
Vol 14 (04) ◽  
pp. 637-643 ◽  
Author(s):  
FUMIHIKO MATSUI ◽  
TOMOHIRO MATSUSHITA ◽  
FANG ZHUN GUO ◽  
HIROSHI DAIMON
Keyword(s):  
Angular Momentum ◽  
Valence Band ◽  
Orbital Angular Momentum ◽  
Photoelectron Spectroscopy ◽  
Atomic Orbital ◽  
Incident Light ◽  
Atomic Orbitals ◽  
Angular Momentum Quantum Number ◽  
The Difference ◽  
Orbital Analysis

The circular dichroism of photoelectron forward focusing peak rotation around the incident-light axis reflects the orbital angular momentum of the excited core level and is inversely proportional to the distance between the emitter and scatterer atoms. This is the basis for the stereo photograph of the atomic arrangements. These rotations are also found in the case of the valence band excitation. The rotation for the 2pxy band of graphite was about twice those from 2s and 2pz bands, corresponding to the difference in the orbital angular momentum quantum number of each band. Simultaneously, photoelectron intensity from the bottom of the 2s band was observed at the Γ point of every other Brillouin zone reflecting the photoelectron structure factor that corresponds to the interference of photoelectron waves from 2s atomic orbitals within a unit cell. The origin of the dual behavior that appeared in the observation of a local angular momentum from a delocalized valence band is discussed.

A Relationship between the Sizes and Energies of Atomic Orbitals

1975 ◽  
Vol 53 (24) ◽  
pp. 3739-3746 ◽  
Author(s):  
R. Daudel ◽  
P. G. Mezey ◽  
J. D. Goddard ◽  
I. G. Csizmadia
Keyword(s):  
Atomic Orbital ◽  
Closed Shell ◽  
Electronic Energy ◽  
Simple Relationship ◽  
Atomic Orbitals ◽  
Total Electronic Energy ◽  
Simple Quantum ◽  
The Mean ◽  
Simply Connected ◽  
Relationship Of

An approximate relationship of the form[Formula: see text]where [Formula: see text] is the mean potential acting upon and V the mean volume of an electron in a closed shell of an atom has previously been proposed. This concept of a simple relationship between the sizes and energies of atomic orbitals which is predicted by simple quantum mechanical arguments has been further examined in this present work. The potential energy for a series of two electron atoms and ions has been replaced by the total electronic energy as these two quantities are simply connected by the virial theorem. For polyelectronic atoms, a quantity per electron pair which sums to the total electronic energy has been used. The volume of the ith atomic orbital[Formula: see text]has been calculated from its size as previously defined in terms of the spherical quadratic operator evaluated at the orbital centroid of charge. A relationship of the above form between the sizes and energies of atomic orbitals holds well for core orbitals but gradually deteriorates on going from the innermost (core) to outermost (valence) shell.

scholarly journals Prospective pedagogy for teaching chemical bonding for smart and sustainable learning

2014 ◽  
Vol 15 (4) ◽  
pp. 435-446 ◽  
Author(s):  
Harkirat S. Dhindsa ◽  
David F. Treagust
Keyword(s):  
Chemical Bonding ◽  
Teaching And Learning ◽  
Atomic Orbital ◽  
Chemical Compounds ◽  
Covalent Bonding ◽  
Classroom Observations ◽  
Atomic Orbitals ◽  
New Knowledge ◽  
Theoretical Paper ◽  
Psychology Of Learning

As an important subject in the curriculum, many students find chemistry concepts difficult to learn and understand. Chemical bonding especially is important in understanding the compositions of chemical compounds and related concepts and research has shown that students struggle with this concept. In this theoretical paper based on analysis of relevant science education research, textbooks, and our classroom observations and teaching experiences, the authors argue that the difficulty in learning chemical bonding concepts is associated with the sequence (ionic, covalent and polar covalent bonding) in which students are taught because this sequence receives little support from constructivist theories of learning. Consequently, the paper proposes a sequence to teach chemical bonding (covalent, polar covalent and ionic bonding) for effective and sustainable learning. In this sequence, the concepts are developed with minimum reorganisation of previously learned information, using a format which is claimed to be easy for students to learn. For teaching these concepts, the use of electronegativity and the overlap of atomic orbitals for all types of bonding have also been stressed. The proposed sequence and emphasis on electronegativity and atomic orbital overlap meets the criteria for teaching and learning of concepts based on the psychology of learning including the theory of constructivism necessitating the construction of new knowledge using related prior knowledge. It also provides a better linkage between the bonding concepts learned at secondary and tertiary levels. Considering these proposed advantages for teaching, this sequence is recommended for further research into effective and sustainable teaching.

Optimum atomic orbitals for molecular calculations A review

1972 ◽  
Vol 21 (94) ◽  
pp. 825-915 ◽  
Author(s):  
F.R. Burden ◽  
R.M. Wilson
Keyword(s):  
Atomic Orbitals ◽  
Molecular Calculations

scholarly journals Orbital Shaped Standing Waves Using Chladni Plates

2019 ◽  
Author(s):  
Eric Janusson ◽  
Johanne Penafiel ◽  
Andrew Macdonald ◽  
Shaun MacLean ◽  
Irina Paci ◽  
...  
Keyword(s):  
Standing Wave ◽  
Atomic Orbital ◽  
Three Dimensional ◽  
Standing Waves ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Cross Sectional ◽  
Atomic Orbitals ◽  
Chemistry Students

Chemistry students are often introduced to the concept of atomic orbitals with a representation of a one-dimensional standing wave. The classic example is the harmonic frequencies which produce standing waves on a guitar string; a concept which is easily replicated in class with a length of rope. From here, students are typically exposed to a more realistic three-dimensional model, which can often be difficult to visualize. Extrapolation from a two-dimensional model, such as the vibrational modes of a drumhead, can be used to convey the standing wave concept to students more easily. We have opted to use Chladni plates which may be tuned to give a two-dimensional standing wave which serves as a cross-sectional representation of atomic orbitals. The demonstration, intended for first year chemistry students, facilitates the examination of nodal and anti-nodal regions of a Chladni figure which students can then connect to the concept of quantum mechanical parameters and their relationship to atomic orbital shape.

Increased Valence or Electronic Hypervalence for Symmetrical Three-Centre Molecular Orbital Configurations

2007 ◽  
Vol 60 (9) ◽  
pp. 691 ◽  
Author(s):  
Richard D. Harcourt
Keyword(s):  
Molecular Orbital ◽  
Atomic Orbital ◽  
Additional Contribution ◽  
Electron Configuration ◽  
Electron Charge ◽  
Atomic Orbitals ◽  
Maximum Value ◽  
Orbital Configuration ◽  
The One ◽  
Increased Valence

With ψ1 = y + k1a + b, ψ2 = y – b, and ψ3 = y – k3a + b as Y–A and A–B bonding, non-bonding, and antibonding three-centre molecular orbitals for a symmetrical Y–A–B type bonding unit with overlapping atomic orbitals y, a, and b, it is deduced that the maximum value for the A atom valence, (VA = Vab + Vay), is (a) 4(3 – 2√2) = 0.6863 for the one-electron and five-electron configurations Φ(1) = (ψ1)1 and Φ(5) = (ψ1)2ψ2)2(ψ3)1; (b) 8(3 – 2√2) = 1.3726 for the two-electron and four-electron configurations Φ(2) = (ψ1)2 and Φ(4) = (ψ1)2(ψ2)2; and (c) 4/3 for the three-electron configuration Φ(3) = (ψ1)2(ψ2)1. Thus for each of the three-centre molecular orbital configurations, the A-atom can exhibit increased valence, or electronic hypervalence, relative to the valence for an A-atom in a two-centre molecular orbital configuration. When k1 ≠ 0 for Φ(1) and k3 ≠ 0 for Φ(5), the A-atom odd-electron charge is not equal to zero. This odd-electron charge is available for (fractional) electron-pair bonding to a fourth atom X, to give an additional contribution, Va, to the valence. The resulting maximum value for the A-atom valence (VA = Vab + Vay + Va) is equal to 1.2020 for each of Φ(1) and Φ(5). A-atom valencies are calculated for the three-centre bonding units for several molecules and ions. The expressions for VA = Vab + Vay were derived with atomic orbital overlap integrals omitted. The present paper shows how the theory is modified when these integrals are included.

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