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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
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Published on: April 8, 2020

Ab initio quantum dynamics using coupled-cluster.

Simen Kvaal1

  • 1University of Oslo, Centre of Mathematics for Applications, N-0316 Oslo, Norway. simen.kvaal@cma.uio.no

The Journal of Chemical Physics
|May 23, 2012
PubMed
Summary
This summary is machine-generated.

We introduce orbital-adaptive time-dependent coupled-cluster, a new method for quantum mechanics that overcomes the curse of dimensionality. This flexible approach scales polynomially, enabling accurate simulations for larger systems.

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Area of Science:

  • Quantum Mechanics
  • Computational Chemistry
  • Theoretical Physics

Background:

  • The curse of dimensionality (COD) severely limits ab initio quantum mechanics methods for systems with many particles.
  • Coupled-cluster (CC) methods offer polynomial scaling for stationary problems, overcoming COD.
  • Existing time-dependent methods struggle with scalability for complex quantum systems.

Purpose of the Study:

  • To develop a novel, computationally efficient method for solving the time-dependent Schrödinger equation.
  • To generalize the coupled-cluster (CC) approach to the time domain.
  • To create a flexible, polynomially scaling approximation for quantum dynamics.

Main Methods:

  • Generalization of the coupled-cluster (CC) method to the time domain.
  • Incorporation of adaptive single-particle functions for enhanced flexibility.
  • Development of orbital-adaptive time-dependent coupled-cluster (OATDCC) as a hierarchy of approximations.
  • Comparison with the multi-configurational time-dependent Hartree (MCTDH) method.

Main Results:

  • The proposed method inherits size-consistency and extensivity from the CC formalism.
  • OATDCC provides a polynomially scaling approximation to the time-dependent Schrödinger equation.
  • Demonstrated flexibility through adaptive single-particle functions.
  • Numerical experiments validate the method's applicability.

Conclusions:

  • Orbital-adaptive time-dependent coupled-cluster (OATDCC) effectively addresses the curse of dimensionality in quantum dynamics.
  • The method offers a scalable and accurate alternative to existing time-dependent approaches.
  • OATDCC represents a significant advancement for ab initio quantum mechanical simulations.