Abstract
We present a pilot application of the recently proposed quasi-variational coupled cluster method to the energies, polarizabilities, and second hyperpolarizabilities of model hydrogen chains. Relative to other single-reference methods of equivalent computational complexity, we demonstrate this method to be highly robust and especially useful when traditional coupled cluster theory fails to perform adequately. In particular, our results indicate it to be a suitable method for the black-box treatment of multiradicals, making it of widespread general interest and applicability.
I. INTRODUCTION
II. THEORY
III. METHODOLOGY
IV. RESULTS AND DISCUSSION
A. The model
B. The model
C. The model
D. The C_{2h} H_{4} model
E. The model
F. Towards the metal-insulator transition:
G. Comparison with UHF-CCSD
V. CONCLUDING REMARKS
Key Topics
- Polarizability
- 29.0
- Wave functions
- 16.0
- Statistical properties
- 11.0
- Coupled cluster
- 10.0
- Electron correlation calculations
- 7.0
G02F1/35
Figures
Clockwise from top-left, the D_{∞h}, C_{2v}, D_{2h}, and C_{2h} H_{4} models.
Clockwise from top-left, the D_{∞h}, C_{2v}, D_{2h}, and C_{2h} H_{4} models.
Calculated energies of the D_{∞h} H_{4} model with R _{1} = R _{2} and the aug-cc-pVDZ basis.
Calculated energies of the D_{∞h} H_{4} model with R _{1} = R _{2} and the aug-cc-pVDZ basis.
Calculated potential energy curves for the C_{2v} H_{4} model with R = 2.25 Å, and with the aug-cc-pVDZ basis.
Calculated potential energy curves for the C_{2v} H_{4} model with R = 2.25 Å, and with the aug-cc-pVDZ basis.
Calculated potential energy curves for the D_{2h} H_{4} model with R = 1.75 Å, and with the aug-cc-pVDZ basis.
Calculated potential energy curves for the D_{2h} H_{4} model with R = 1.75 Å, and with the aug-cc-pVDZ basis.
Calculated second hyperpolarizabilities perpendicular to the plane of the D_{2h} H_{4} model with R = 1.75 Å, and with the aug-cc-pVDZ basis
Calculated second hyperpolarizabilities perpendicular to the plane of the D_{2h} H_{4} model with R = 1.75 Å, and with the aug-cc-pVDZ basis
Calculated potential energy curves for the C_{2h} H_{4} model with R = 2.0 Å, and with the aug-cc-pVDZ basis.
Calculated potential energy curves for the C_{2h} H_{4} model with R = 2.0 Å, and with the aug-cc-pVDZ basis.
Calculated polarizabilities perpendicular to the plane of the C_{2h} H_{4} model with R = 2.0 Å, and with the aug-cc-pVDZ basis.
Calculated polarizabilities perpendicular to the plane of the C_{2h} H_{4} model with R = 2.0 Å, and with the aug-cc-pVDZ basis.
Calculated potential energy curves for the D_{∞h} H_{6} model with R _{1} = R _{2} and with the aug-cc-pVDZ basis.
Calculated potential energy curves for the D_{∞h} H_{6} model with R _{1} = R _{2} and with the aug-cc-pVDZ basis.
Calculated polarizabilities for the D_{∞h} H_{6} model with R _{1} = R _{2} and with the aug-cc-pVDZ basis.
Calculated polarizabilities for the D_{∞h} H_{6} model with R _{1} = R _{2} and with the aug-cc-pVDZ basis.
Calculated second hyperpolarizabilities for the D_{∞h} H_{6} model with R _{1} = R _{2} and with the aug-cc-pVDZ basis.
Calculated second hyperpolarizabilities for the D_{∞h} H_{6} model with R _{1} = R _{2} and with the aug-cc-pVDZ basis.
Calculated energies of the D_{∞h} H_{10} model with R _{1} = R _{2} and the STO-3G basis.
Calculated energies of the D_{∞h} H_{10} model with R _{1} = R _{2} and the STO-3G basis.
Calculated longitudinal polarizabilities of the D_{∞h} H_{10} model with R _{1} = R _{2} and the STO-3G basis.
Calculated longitudinal polarizabilities of the D_{∞h} H_{10} model with R _{1} = R _{2} and the STO-3G basis.
Calculated longitudinal second hyperpolarizabilities of the D_{∞h} H_{10} model with R _{1} = R _{2} and the STO-3G basis.
Calculated longitudinal second hyperpolarizabilities of the D_{∞h} H_{10} model with R _{1} = R _{2} and the STO-3G basis.
Errors relative to FCI for calculated energies of the D_{∞h} H_{4} model with R _{1} = R _{2} and the cc-pVDZ basis.
Errors relative to FCI for calculated energies of the D_{∞h} H_{4} model with R _{1} = R _{2} and the cc-pVDZ basis.
Tables
Calculated energies, polarizabilities, and second hyperpolarizabilities for a selection of geometries of the various model hydrogen systems with the aug-cc-pVDZ basis. All quantities are in atomic units, and calculated with either the FCI (H_{4}) or MRAQCC (H_{6}) methods.
Calculated energies, polarizabilities, and second hyperpolarizabilities for a selection of geometries of the various model hydrogen systems with the aug-cc-pVDZ basis. All quantities are in atomic units, and calculated with either the FCI (H_{4}) or MRAQCC (H_{6}) methods.
Errors relative to FCI for calculated energies of, and polarizabilities perpendicular to the D_{∞h} H_{4} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R _{1}, R _{2})}, where R _{1} ∈ {1.0, 1.5, 2.0, 2.5, 3.0}Å and R _{2} ∈ {1.0, 1.75, 2.5, 3.25, 4.0}Å.^{a}
Errors relative to FCI for calculated energies of, and polarizabilities perpendicular to the D_{∞h} H_{4} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R _{1}, R _{2})}, where R _{1} ∈ {1.0, 1.5, 2.0, 2.5, 3.0}Å and R _{2} ∈ {1.0, 1.75, 2.5, 3.25, 4.0}Å.^{a}
Errors relative to FCI for calculated energies, and polarizabilities perpendicular to the plane, in the C_{2v} H_{4} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R, θ)}, where R ∈ {2.25, 2.5, 2.75, 3.0, 3.25}Å and θ ∈ {0, ±2, ±4, ±6, ±8}°.
Errors relative to FCI for calculated energies, and polarizabilities perpendicular to the plane, in the C_{2v} H_{4} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R, θ)}, where R ∈ {2.25, 2.5, 2.75, 3.0, 3.25}Å and θ ∈ {0, ±2, ±4, ±6, ±8}°.
Errors relative to FCI for calculated energies of, and polarizabilities perpendicular to the D_{2h} H_{4} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R, θ)}, where R ∈ {1.0, 1.75, 2.0, 2.25}Å and θ ∈ {70, 72, 74, 76, 78, 80, 82, 84, 86, 87, 88, 89}°.
Errors relative to FCI for calculated energies of, and polarizabilities perpendicular to the D_{2h} H_{4} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R, θ)}, where R ∈ {1.0, 1.75, 2.0, 2.25}Å and θ ∈ {70, 72, 74, 76, 78, 80, 82, 84, 86, 87, 88, 89}°.
Errors relative to FCI for calculated energies of, and polarizabilities perpendicular to the C_{2h} H_{4} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R, θ)}, where R ∈ {1.0, 1.5, 2.0, 2.5, 3.0}Å and θ ∈ {− 15, 0, 15, 30, 45, 60, 75, 90}°.
Errors relative to FCI for calculated energies of, and polarizabilities perpendicular to the C_{2h} H_{4} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R, θ)}, where R ∈ {1.0, 1.5, 2.0, 2.5, 3.0}Å and θ ∈ {− 15, 0, 15, 30, 45, 60, 75, 90}°.
Errors relative to MRAQCC for calculated energies of, and polarizabilities perpendicular to the D_{∞h} H_{6} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R _{1}, R _{2})}, where R _{1}, R _{2} ∈ {1.0, 1.2, 1.4, 1.6, 1.8}Å.
Errors relative to MRAQCC for calculated energies of, and polarizabilities perpendicular to the D_{∞h} H_{6} model with the aug-cc-pVDZ basis. Results were obtained from the set of points {(R _{1}, R _{2})}, where R _{1}, R _{2} ∈ {1.0, 1.2, 1.4, 1.6, 1.8}Å.
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