Perturbation Theory

Digital quantum simulation of molecular vibrations

“…Moreover, we expect that the UVCC ansatz will deal better with problems of strong static correlation than the VCC ansatz, as the former can easily be used with multi-reference states. This echoes the way in which the UCC ansatz can be used with multi-reference states,56 while it is typically more difficult when using the canonical CC method 1…”

“…We can solve for the electronic energy levels of the system as a function of the nuclear positions, which enables us to map out potential energy surfaces for the system. A number of approximate classical methods have been developed to solve this problem,1,39 as well as several quantum algorithms 8,40–42. These electronic potential surfaces can then be viewed as the nuclear potential, determining the vibrational energy levels.…”

“…The most accurate simulations require a full quantum mechanical treatment—which is exponentially costly for classical computers. While many approximations have been developed to solve this problem, they are often not sufficiently accurate 1. One possible route to more accurate simulations is to use quantum computers.…”

Density matrix renormalization group pair-density functional theory (DMRG-PDFT): singlet–triplet gaps in polyacenes and polyacetylenes

“…The non-relativistic electronic Hamiltonian may be written in second quantization as81where p, q, r, and s denote molecular orbitals, h pq and g pqrs are one- and two-electron integrals, respectively, E pq is the singlet excitation operator, and e pqrs is the two-electron excitation operator. The excitation operators can be written in terms of creation and annihilation operators aswhere Greek letters label the spin functions associated with the molecular orbitals p, q, r, and s. The electronic energy for eigenstate | Ψ 〉 is expressed as is expressed aswhere V NN is the nuclear–nuclear repulsion energy; D pq and d pqrs are the elements of one-electron and two-electron reduced density matrices (RDMs), respectively.…”

Realistic theory of electronic correlations in nanoscopic systems

“…One would be the quantum chemical approach to attack the full system including all interactions using a truncated configuration interaction or similar approach to account for the correlation effects [59]. The other one, more popular among physicists, is to "truncate" the problem already at the level of the Hamiltonian and then solve the remainder as exactly as possible.…”