Cluster perturbation theory. VI. Ground-state energy series using the Lagrangian

Abstract

In this paper, we derive alternative cluster perturbation series to the energy cluster perturbation (ECP) series of Paper I. The ECP series were derived using the standard coupled cluster energy framework. Here, we use the coupled cluster Lagrangian framework to derive the Lagrangian cluster perturbation (LCP) series and show that a slightly modified order concept means that the ECP and the LCP series become identical. Using the Lagrangian, we also derive a perturbation series where total cluster amplitudes and multipliers are determined through the same orders as dictated by the 2n+1/2n+2 rule, the VCP series. The VCP energies have errors that are bilinear in the errors of the total cluster amplitudes and multipliers. Test calculations have been performed for S(D) and SD(T) orbital excitation spaces. The convergence of the test calculations can be divided into two groups. The first group contains molecules that exhibit a slow monotonic geometric convergence pattern in both orbital spaces. The second group, containing the rest of the molecules, exhibits a fast low order convergence. For the S(D) calculations, the deviations in fourth order from the coupled cluster singles and doubles energy are below 1.3 per cent for the LCP series and 0.3 per cent for the VCP series, respectively. For the SD(T) calculations, the second group hardly shows any difference between the low order convergence of the three series ECP, LCP, and LCP and at fourth order the deviations from the triples correlation energy are less than 1 per cent.

High throughput screening of norbornadiene/quadricyclane derivates for molecular solar thermal energy storage

“…We have performed a small control investigation by selecting three molecules with the best xTB predicted properties, and three molecules with the worst xTB predicted properties. We have compared the xTB and DFT results for these six molecules with calculations performed at a higher-level of theory, namely, the variational method 49 for single point energies and excitation energy calculations using the CPS(D-3) model 50,51 on the DFT optimized geometries. The three best (worst) molecules according to xTB are denoted 1, 2, and 3 (−1, −2, and −3).…”

“…The developed screening procedure based on xTB methods can clearly be utilized for designing MOST molecules having optimal properties for actual MOST devices. We observed that molecules that performed the best in the screening procedure were performing extremely well when we utilized accurate quantum mechanical methods such as the variational method 49 and the CPS(D-3) model. 50,51 We also note that recent work reaches similar conclusions concerning the use of TB methods that the methods can be used for screening and designing MOST systems.…”

“…For a few handpicked systems, we did Cluster Perturbation (CP) theory calculations in order to facilitate a comparison of the xTB and DFT results to results of CCSD quality. We performed single-point energy calculations using the variational L CPSðDÀ4Þ method 49 and excitation energy calculations using the CPS(D-3) model 50,51 on the DFT optimized geometries. The CP calculations were carried out in a local development version of LS-Dalton 52 using the 6-311G(d) [46][47][48] basis set for energy calculations and the 6-311 + G(d) [46][47][48] basis set for excitation energies to align the calculations with the corresponding DFT calculations.…”

Prospects of Improving Molecular Solar Energy Storage of the Norbornadiene/Quadricyclane System through Bridgehead Modifications

“…Calculations have been performed in Gaussian16 . This methodology is chosen as earlier studies have shown good performance for both NBD/QC and BOD/TCO systems. , Subsequently, we refine the electronic energy of the determined structures using the newly developed cluster perturbation theory CPS­(D-4) model in LSDalton, ,, which provides energies of CCSD quality at a low cost, while we utilize the vibrational and entropic energy contributions of the DFT calculations. The resulting storage energies are given in Table .…”

Tensor Hypercontraction of Cluster Perturbation Theory: Quartic Scaling Perturbation Series for the Coupled Cluster Singles and Doubles Ground-State Energies

“…The result of this is that the error relative to the CCSD energy in the obtained energy is bilinear in the errors of the approximate parameters, while the error obtained in the incremental formulation is linear in the errors of the amplitudes and multipliers. For a detailed derivation and analysis of these energy models, we refer the reader to previous studies 72 that give full derivations of these models.…”