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Bivariational Approximations in Quantum Mechanics and Applications to Quantum Chemistry

Objective

The standard variational principles (VPs) are cornerstones of quantum mechanics, and one can hardly overestimate their usefulness as tools for generating approximations to the time-independent and
time-dependent Schröodinger equations. The aim of the proposal is to study and apply a generalization of these, the bivariational principles (BIVPs), which arise naturally when one does not assume a priori that the system Hamiltonian is Hermitian. This unconventional approach may have transformative impact on development of ab initio methodology, both for electronic structure and dynamics.

The first objective is to establish the mathematical foundation for the BIVPs. This opens up a whole new axis of method development for ab initio approaches. For instance, it is a largely ignored fact that the popular traditional coupled cluster (TCC) method can be neatly formulated with the BIVPs, and TCC is both polynomially scaling with the number of electrons and size-consistent. No “variational” method enjoys these properties simultaneously, indeed this seems to be incompatible with the standard VPs.

Armed with the BIVPs, the project aims to develop new and understand existing ab initio methods. The second objective is thus a systematic multireference coupled cluster theory (MRCC) based on the BIVPs. This
is in itself a novel approach that carries large potential benefits and impact. The third and last objective is an implementation of a new coupled-cluster type method where the orbitals are bivariational
parameters. This gives a size-consistent hierarchy of approximations to multiconfiguration
Hartree--Fock.

The PI's broad contact with and background in scientific disciplines such as applied mathematics and nuclear physics in addition to quantum chemistry increases the feasibility of the project.

Field of science

  • /natural sciences/physical sciences/nuclear physics
  • /natural sciences/physical sciences/quantum physics
  • /natural sciences/mathematics
  • /natural sciences/chemical sciences/physical chemistry/quantum chemistry

Call for proposal

ERC-2014-STG
See other projects for this call

Funding Scheme

ERC-STG - Starting Grant

Host institution

UNIVERSITETET I OSLO
Address
Problemveien 5-7
0313 Oslo
Norway
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 499 572

Beneficiaries (1)

UNIVERSITETET I OSLO
Norway
EU contribution
€ 1 499 572
Address
Problemveien 5-7
0313 Oslo
Activity type
Higher or Secondary Education Establishments