Open‐Shell Wave Functions for Conjugated Hydrocarbons

1961 ◽  
Vol 34 (4) ◽  
pp. 1446-1447 ◽  
Author(s):  
J. R. Hoyland ◽  
Lionel Goodman
Keyword(s):  
Open Shell ◽  
Wave Functions ◽  
Conjugated Hydrocarbons

Short-range DFT energy correction to multiconfigurational wave functions for open-shell systems

2021 ◽  
Vol 154 (12) ◽  
pp. 124116
Author(s):  
José Aarón Rodríguez-Jiménez ◽  
Abel Carreras ◽  
David Casanova
Keyword(s):  
Short Range ◽  
Open Shell ◽  
Wave Functions ◽  
Energy Correction

Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules

2016 ◽  
Vol 120 (32) ◽  
pp. 6459-6466 ◽  
Author(s):  
Kenji Sugisaki ◽  
Satoru Yamamoto ◽  
Shigeaki Nakazawa ◽  
Kazuo Toyota ◽  
Kazunobu Sato ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Polynomial Time ◽  
Quantum Algorithm ◽  
Open Shell ◽  
Wave Functions ◽  
Quantum Computers ◽  
Time Quantum

scholarly journals General Framework for Calculating Spin–orbit Couplings Using Spinless One-Particle Density Matrices: Theory and Application to the Equation-of-Motion Coupled-Cluster Wave Functions

2019 ◽  
Author(s):  
Pavel Pokhilko ◽  
Evgeny Epifanovsky ◽  
Anna I. Krylov
Keyword(s):  
Degrees Of Freedom ◽  
Particle Density ◽  
Mean Field ◽  
Transition Density ◽  
Open Shell ◽  
Equation Of Motion ◽  
Wave Functions ◽  
Coupled Cluster ◽  
Spin Orbit ◽  
Matrix Elements

Standard implementations of non-relativistic excited-state calculations compute only one component of spin multiplets (i.e., Ms =0 triplets), however, matrix elements for all components are necessary for calculations of experimentally relevant spin-dependent quantities. To circumvent explicit calculations of all multiplet components, we employ Wigner–Eckart’s theorem. Applied to a reduced one-particle transition density matrix computed for a single multiplet component, Wigner–Eckart’s theorem generates all other spin–orbit matrix elements. In addition to computational efficiency, this approach also resolves the phase issue arising within Born–Oppenheimer’s separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculations of spin–orbit couplings using equation-of-motion coupled-cluster wave functions is presented. The two-electron contributions are included via the mean-field spin–orbit treatment. Intrinsic issues of constructing spin–orbit mean-field operators for open-shell references are discussed and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

Extension of Frozen Natural Orbital Approximation to Open-Shell References: Theory, Implementation, and Application to Single-Molecule Magnets

2019 ◽  
Author(s):  
Pavel Pokhilko ◽  
Daniil Izmodenov ◽  
Anna I. Krylov
Keyword(s):  
Density Matrix ◽  
Single Molecule ◽  
Open Shell ◽  
State Density ◽  
Molecular Orbitals ◽  
The State ◽  
Wave Functions ◽  
Virtual Space ◽  
Single Molecule Magnets ◽  
Natural Orbitals

Natural orbitals are often used in quantum chemistry to achieve a more compact representation of correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual-virtual block of the state density matrix instead of the canonical Hartree-Fock molecular orbitals results in smaller errors when the same fraction of virtual orbitals is frozen. This strategy, termed frozen natural orbitals (FNO) approach, has been successfully used to reduce the cost of state-specific coupled-cluster (CC) calculations, such as ground-state CC, as well as some multi-state methods, i.e., EOM-IP-CC (equation-of-motion CC method for ionization potentials). This contribution extends the FNO approach to the EOM-SF-CC ansatz (EOM-CC with spin-flip), which has been developed to describe certain multi-configurational wave-functions within the single-reference framework. In contrast to EOM-IP-CCSD, which describes open-shell target states by using a closed-shell reference, EOM-SF-CCSD relies on high-spin open-shell references (triplets, quartets, etc). Consequently, straightforward application of FNOs computed for an open-shell reference leads to an erratic behavior of the EOM-SF-CC energies and properties, which can be attributed to an inconsistent truncation of the α and β orbital spaces. A general solution to problems arising in the EOM-CC calculations utilizing open-shell references, termed OSFNO (open-shell FNO), is proposed. The OSFNO algo-rithm first identifies corresponding orbitals by means of singular value decomposition (SVD) of the overlap matrix of the α and β molecular orbitals and determines virtual orbitals corresponding to the singly occupied space. This is followed by SVD of the singlet part of the state density matrix in the remaining virtual orbital subspace. The so-computed FNOs preserve the spin purity of the open-shell orbital subspace to the extent allowed by the original reference thus facilitating a safe truncation of the virtual space. The performance of the OSFNO approximation in combination with different choices of reference orbitals is benchmarked for a set of diradicals and triradicals. For a set of di-copper single-molecule magnets, a conservative truncation criterion corresponding to a two-fold reduction of the virtual space in a triple-zeta basis leads to errors of 5–18 cm<sup>-1</sup> in the singlet–triplet gaps and errors of ∼2-3 cm<sup>-1</sup> in the spin–orbit coupling constants.

Open-shell ground state wave functions for linear polyacenes

1978 ◽  
Vol 82 (12) ◽  
pp. 1436-1438 ◽  
Author(s):  
John C. Schug ◽  
Byron H. Lengsfield ◽  
Dana A. Brewer
Keyword(s):  
Ground State ◽  
Open Shell ◽  
Wave Functions ◽  
State Wave
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