Atom orbitals
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Understanding Atomic Orbitals in Molecules
Introduction to Atomic Orbitals in Molecules
Atomic orbitals (AOs) are fundamental concepts in quantum chemistry, representing regions in an atom where electrons are likely to be found. When atoms form molecules, these orbitals interact and combine to form molecular orbitals (MOs). Recent research has provided new insights into the nature and behavior of atomic orbitals within molecules, enhancing our understanding of molecular bonding and electronic structure.
Quantum-Mechanical Theory of Atomic Orbitals
A rigorous definition of atomic orbitals in molecules (AOIMs) has been developed, which is universally applicable to wave functions from various electronic structure calculations. This definition ensures that AOIMs are continuous and orthonormal, making them suitable for accurately representing individual molecular orbitals and strongly occupied natural orbitals. The coefficients of these linear combinations are notably insensitive to the quality of basis sets used, making AOIMs particularly useful for describing bonding in diverse chemical systems 1.
Effective Atomic Orbitals and Topological Atoms
Effective atomic orbitals have been realized within the framework of Bader's atoms in molecules theory. This approach retrieves a proper set of orthonormalized numerical atomic orbitals from any type of calculation, with occupation numbers summing up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Typically, only a limited number of effective atomic orbitals exhibit significant occupation numbers, corresponding to atomic hybrids resembling the core and valence shells of the atom. This method allows for an accurate representation of molecular orbitals as linear combinations of these orthonormalized atomic orbitals 4.
Variational Optimization of Atomic Orbitals
A practical method for variationally optimizing numerical atomic orbitals used in density functional calculations has been presented. This optimization significantly reduces computational effort while maintaining high accuracy. The optimized orbitals reproduce results calculated by a larger number of unoptimized orbitals, making them suitable for large-scale electronic structure calculations 59.
Gaussian Expansions of Slater-Type Atomic Orbitals
The use of Gaussian expansions to represent Slater-type atomic orbitals has been shown to lead to rapid convergence of atomization energies, atomic populations, and electric dipole moments. This method uses common Gaussian exponents shared between Slater-type 2s and 2p functions, providing a standard set of scale factors for molecular calculations. These optimized exponents are nearly independent of the number of Gaussian functions, making them adequate for calculating total and atomization energies 3.
Automated Construction of Molecular Active Spaces
The atomic valence active space (AVAS) technique constructs active molecular orbitals capable of describing all relevant electronic configurations from a targeted set of atomic valence orbitals. This method simplifies multiconfiguration and multireference electronic structure calculations, making them easier to execute and reproduce. AVAS is particularly useful in transition-metal chemistry and bond dissociation processes 7.
Orthogonal Atomic Orbitals
Orthogonal atomic orbitals, introduced by Wannier and Lowdin, do not simplify the non-orthogonality problem in the Heitler-London method. However, they are suitable for complete perturbation calculations, providing a convenient alternative to linear combination of atomic orbitals (LCAO) methods 8.
Conclusion
Recent advancements in the understanding and application of atomic orbitals in molecules have significantly enhanced our ability to describe and predict molecular behavior. From rigorous definitions and effective atomic orbitals to variational optimization and automated construction of active spaces, these developments provide powerful tools for quantum chemistry and molecular physics. These insights not only improve computational efficiency but also deepen our understanding of molecular bonding and electronic structure.
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Atomic orbitals in molecules
This new definition of atomic orbitals in molecules (AOIMs) is universally applicable and provides a continuous and orthonormal representation of molecular orbitals and strongly occupied natural orbitals, making them suitable for compact description of bonding in diverse chemical systems.
Atomic orbital search: A novel metaheuristic algorithm
The Atomic Orbital Search (AOS) algorithm provides outstanding results in solving mathematical and engineering design problems compared to other metaheuristic algorithms.
Highly CitedSelf‐Consistent Molecular‐Orbital Methods. I. Use of Gaussian Expansions of Slater‐Type Atomic Orbitals
Using Gaussian expansions of Slater-type atomic orbitals in self-consistent molecular-orbital calculations leads to accurate values for atomization energies, atomic populations, and electric dipole moments, with a standard set of values for molecular calculations.
Highly CitedThe atomic orbitals of the topological atom.
Effective atomic orbitals can accurately reproduce the original Quantum Theory of Atoms in Molecules (QTAIM) atomic populations, with a limited number of orbitals showing significant occupation numbers.
Variationally optimized atomic orbitals for large-scale electronic structures
Optimized atomic orbitals for density functional calculations reduce computational effort and maintain high accuracy while maintaining convergent results in large-scale electronic structures.
Highly CitedAre there atomic orbitals in a molecule?
Effective atomic orbitals in molecules can be calculated using the "fuzzy atoms" method, allowing for a more accurate representation of molecular orbitals.
Automated Construction of Molecular Active Spaces from Atomic Valence Orbitals.
The atomic valence active space (AVAS) technique simplifies multireference electronic structure calculations in transition-metal chemistry and bond dissociation processes, making them easier to execute and reproduce.
Highly CitedNote on Orthogonal Atomic Orbitals
Orthogonal atomic orbitals do not solve the non-orthogonality problem in the Heitler-London method, but are suitable for complete perturbation calculations.
Highly CitedNumerical atomic basis orbitals from H to Kr
Optimized orbitals from H to Kr significantly reduce computational efforts while maintaining high accuracy, making them suitable for large scale DFT calculations.
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