Size-intensive decomposition of orbital energy denominators

We introduce an alternative to Almlöf and Häser’s Laplace transform decomposition of orbital energy denominators used in obtaining reduced scaling algorithms in perturbation theory based methods. The new decomposition is based on the Cholesky decomposition of positive semidefinite matrices. We show that orbital denominators have a particular short and size-intensive Cholesky decomposition. The main advantage in using the Cholesky decomposition, besides the shorter expansion, is the systematic improvement of the results without the penalties encountered in the Laplace transform decomposition when changing the number of integration points in order to control the convergence. Applications will focus on the coupled-cluster singles and doubles model including connected triples corrections [CCSD(T)], and several numerical examples are discussed.Alfredo.Sá[email protected]

Reduced scaling in electronic structure calculations using Cholesky decompositions

We demonstrate that substantial computational savings are attainable in electronic structure calculations using a Cholesky decomposition of the two-electron integral matrix. In most cases, the computational effort involved calculating the Cholesky decomposition is less than the construction of one Fock matrix using a direct O(N2) [email protected]

Polarizability and optical rotation calculated from the approximate coupled cluster singles and doubles CC2 linear response theory using Cholesky decompositions

A new implementation of the approximate coupled cluster singles and doubles CC2 linear response model using Cholesky decomposition of the two-electron integrals is presented. Significantly reducing storage demands and computational effort without sacrificing accuracy compared to the conventional model, the algorithm is well suited for large-scale applications. Extensive basis set convergence studies are presented for the static and frequency-dependent electric dipole polarizability of benzene and C60, and for the optical rotation of CNOFH2 and (−)-trans-cyclooctene (TCO). The origin-dependence of the optical rotation is calculated and shown to persist for CC2 even at basis set [email protected]

Coupled cluster calculations of the vertical excitation energies of tetracyanoethylene

Coupled cluster linear-response formalism has been used to compute the vertical spectrum of ethylene and tetracyanoethylene (TCNE). We show that for both molecules the ππ∗ excitation 1A1g→1B1u of the experimental spectrum is not vertical nor the 0-0 transition. For TCNE this excitation is the only experimentally observed band. We have computed vertical excitations of 5.2 eV in gas phase and 5.1 eV in acetonitrile and estimated a lower bound for the 0-0 transition in the gas phase of 4.3 [email protected] ; [email protected]

The integral‐direct coupled cluster singles and doubles model

An efficient and highly vectorized implementation of the coupled cluster singles and doubles (CCSD) model using a direct atomic integral technique is presented. The minimal number of n6 processes has been implemented for the most time consuming terms and point group symmetry is used to further reduce operation counts and memory requirements. The significantly increased application range of the CCSD method is illustrated with sample calculations on several systems with more than 500 basis functions. Furthermore, we present the basic trends of an open ended algorithm and discuss the use of integral [email protected]

Calculation of size‐intensive transition moments from the coupled cluster singles and doubles linear response function

Coupled cluster singles and doubles linear response (CCLR) calculations have been carried out for excitation energies and dipole transition strengths for the lowest excitations in LiH, CH+, and C4 and the results compared with the results from a CI‐like approach to equation of motion coupled cluster (EOMCC). The transition strengths are similar in the two approaches for single molecule calculations on small systems. However, the CCLR approach gives size‐intensive dipole transition strengths, while the EOMCC formalism does not. Thus, EOMCC calculations can give unphysically dipole transition strengths, e.g., in EOMCC calculations on a sequence of noninteracting LiH systems we obtained a negative dipole strength for the lowest totally symmetric dipole allowed transition for 19 or more noninteracting LiH systems. The CCLR approach is shown to be a very attractive ‘‘black box’’ approach for the calculation of transition [email protected]

Assessment for the mean value total dressing method: Comparison with coupled cluster including triples methods for BF, NO+, CN+, C2, BeO, NH3, CH2, H2O, BH, HF, SiH2, Li2, LiNa, LiBe+, NeH+, and O3

Limited previous experience with the mean value total dressing (MVTD) method had shown that MVTD energies for closed shell systems are generally better than CCSD(T) ones compared to FCI. The method, previously published as total dressing 2′(td-2′), is based on the single reference intermediate Hamiltonian theory. It is not a CC method but deals in a great part with the same physical effects that CC methods that incorporate amplitudes of triples such as CCSDT or its CCSDT-1n approaches. A number of test calculations comparing to diverse CC methods, as well as FCI and experiment when available, have been performed. The tests concern equilibrium energies in NH3 and CH2, equilibrium energies and distances in some diatomics (BF, NO+, CN+, C2, BeO), different bond breaking situations (H2O, BH, HF, SiH2) and spectroscopic properties of different bonding conditions (Li2, LiNa, LiBe+, NeH+, and O3). The results are in general closer to the full CCSDT ones in the equilibrium regions and close to CCSDT-1 along most dissociation curves. A few exceptions to this rule are analyzed with the help of an approach to MVTD that does not take into account the effects of linked quadriexcitations. Such analysis suggests the interest of improving the treatment of effects of linked triples in the MVTD model. The separate contributions of linked and unlinked triples and quadruples are also analyzed for some of the above diatomics representing different behaviors of bond breaking. The interest of such analysis is illustrated in the NeH+ molecule. The MVTD results show, in general, a high quality, provided that the nature of the correlation problem does not become largely multiconfigurational, as occurs in multiple bond dissociation or in the asymmetric stretching of [email protected] ; [email protected] ; [email protected]

The CC3 model : An iterative coupled cluster approach including connected triples

An alternative derivation of many-body perturbation theory (MBPT) has been given, where a coupled cluster parametrization is used for the wave function and the method of undetermined Lagrange multipliers is applied to set up a variational coupled cluster energy expression. In this variational formulation, the nth-order amplitudes determine the energy to order 2n+1 and the nth-order multipliers determine the energy to order 2n+2. We have developed an iterative approximate coupled cluster singles, doubles, and triples model CC3, where the triples amplitudes are correct through second order and the singles amplitudes are treated without approximations due to the unique role of singles as approximate orbital relaxation parameters. The compact energy expressions obtained from the variational formulation exhibit in a simple way the relationship between CC3, CCSDT-1a [Lee et al., J. Chem. Phys. 81, 5906 (1984)] CCSDT-1b models [Urban et al., J. Chem. Phys. 83, 4041 (1985)], and the CCSD(T) model [Raghavachari et al., Chem. Phys. Lett. 157, 479 (1989)]. Sample calculations of total energies are presented for the molecules H2O, C2, CO, and C2H4. Comparisons are made with full CCSDT, CCSDT-1a, CCSDT-1b, CCSD(T), and full configuration interaction (FCI) results. These calculations demonstrate that CC3 and CCSD(T) give total energies of a similar quality. If results obtained by CC3 and CCSD(T) differ significantly, neither method can be trusted. In contrast to CCSD(T), time-dependent response functions can be obtained for [email protected]

Fast 3D Rotation Estimation of Fruits Using Spheroid Models

[EN] Automated fruit inspection using cameras involves the analysis of a collection of views of the same fruit obtained by rotating a fruit while it is transported. Conventionally, each view is analyzed independently. However, in order to get a global score of the fruit quality, it is necessary to match the defects between adjacent views to prevent counting them more than once and assert that the whole surface has been examined. To accomplish this goal, this paper estimates the 3D rotation undergone by the fruit using a single camera. A 3D model of the fruit geometry is needed to estimate the rotation. This paper proposes to model the fruit shape as a 3D spheroid. The spheroid size and pose in each view is estimated from the silhouettes of all views. Once the geometric model has been fitted, a single 3D rotation for each view transition is estimated. Once all rotations have been estimated, it is possible to use them to propagate defects to neighbor views or to even build a topographic map of the whole fruit surface, thus opening the possibility to analyze a single image (the map) instead of a collection of individual views. A large effort was made to make this method as fast as possible. Execution times are under 0.5 ms to estimate each 3D rotation on a standard I7 CPU using a single core.Albiol Colomer, AJ.; Albiol Colomer, A.; Sánchez De Merás, C. (2021). Fast 3D Rotation Estimation of Fruits Using Spheroid Models. Sensors. 21(6):1-24. https://doi.org/10.3390/s21062232S12421

Method specific Cholesky decomposition : Coulomb and exchange energies

We present a novel approach to the calculation of the Coulomb and exchange contributions to the total electronic energy in self consistent field and density functional theory. The numerical procedure is based on the Cholesky decomposition and involves decomposition of specific Hadamard product matrices that enter the energy expression. In this way, we determine an auxiliary basis and obtain a dramatic reduction in size as compared to the resolution of identity (RI) method. Although the auxiliary basis is determined from the energy expression, we have complete control of the errors in the gradient or Fock matrix. Another important advantage of this method specific Cholesky decomposition is that the exchange energy and Fock matrix can be evaluated with a linear scaling effort contrary to the RI method or standard Cholesky decomposition of the two-electron integral matrix. The methods presented show the same scaling properties as the so-called local density fitting methods, but with full error [email protected]