arXiv subjects

Devin A. Matthews

Publications and source records attributed to Devin A. Matthews.

At least 37 records · Page 2Linked to original sources

arXiv2023

Transition moments for STEOM-CCSD with core triples

Similarity transformed equation-of-motion coupled cluster theory (STEOM-CC) is an alternative approach to equation-of-motion coupled cluster theory for excited states (EOMEE-CC) which uses a second similarity transformation of the Hamiltonian, followed by diagonalization in a small (CI singles-like) excitation space, even when single and double excitations are included in the transformation. In addition to vertical excitation energies, transition moments measure the strength of the interactions between states determining absorption, emission, and other processes. In STEOM-CCSD, transition moments are calculated in a straight-forward manner as biorthogonal expectation values using both the left- and right-hand solutions, with the main difference from EOMEE-CC being the inclusion of the transformation operator. We recently developed an extension of STEOM-CCSD to core excitations, CVS-STEOM-CCSD+cT, which includes triple excitations and the well-known core-valence separation for the core ionization potential calculations. In this work, we derived transition moments for core-excited states with core triple excitations, including both ground-to-core-excited and valence-to-core-excited transitions. The improvement of the computed transition moments of the CVS-STEOM-CCSD+cT method is compared to standard CVS-STEOMEE-CCSD and CVS-EOMEE-CCSD for our previously published small molecule benchmark set.

physics.chem-ph↗

arXiv2023

Ab Initio Investigation of Intramolecular Charge Transfer States in DMABN by Calculation of Excited State X-ray Absorption Spectra

Dual fluorescence in 4-(dimethylamino)benzonitrile (DMABN) and its derivatives in polar solvents has been studied extensively for the past several decades. An intramolecular charge transfer (ICT) minimum on the excited state potential energy surface, in addition to the localized low-energy (LE) minimum, has been proposed as a mechanism for this dual fluorescence, with large geometric relaxation and molecular orbital reorganization a key feature of the ICT pathway. Herein, we have used both equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD) and time-dependent density functional (TDDFT) methods to investigate the landscape of excited state potential energy surfaces across a number of geometric conformations proposed as ICT structures. In order to correlate these geometries and valence excited states in terms of potential experimental observables, we have calculated the nitrogen K-edge ground and excited state absorption spectra for each of the predicted "signpost" structures, and identified several key spectral features which could be used to interpret a future time-resolved x-ray absorption experiment.

physics.chem-ph↗

arXiv2022

Theoretical Investigation of The X-Ray Stark Effect in Small Molecules

We have studied the Stark effect in the soft x-ray region for various small molecules by calculating the field-dependent x-ray absorption spectra. This effect is explained in terms of the response of molecular orbitals (core and valence), the molecular dipole moment, and the molecular geometry to the applied electric field. A number of consistent trends are observed linking the computed shifts in absorption energies and intensities with specific features of the molecular electronic structure. We find that both the virtual molecular orbitals (valence and/or Rydberg) as well as the core orbitals contribute to observed trends in a complementary fashion. This initial study highlights the potential impact of x-ray Stark spectroscopy as a tool to study electronic structure and environmental perturbations at a sub-molecular scale.

physics.chem-ph↗

arXiv2022

A Mountaineering Strategy to Excited States: Revising Reference Values with EOM-CC4

In the framework of the computational determination of highly-accurate vertical excitation energies in small organic compounds, we explore the possibilities offered by the equation-of-motion formalism relying on the approximate fourth-order coupled-cluster (CC) method, CC4. We demonstrate, using an extended set of more than 200 reference values based on CC including up to quadruples excitations (CCSDTQ), that CC4 is an excellent approximation to CCSDTQ for excited states with a dominant contribution from single excitations with an average deviation as small as $0.003$ eV. We next assess the accuracy of several additive basis set correction schemes, in which vertical excitation energies obtained with a compact basis set and a high-order CC method are corrected with lower-order CC calculations performed in larger basis sets. Such strategies are found to be overall very beneficial, though their accuracy depend significantly on the actual scheme. Finally, CC4 is employed to improve several theoretical best estimates of the QUEST database for molecules containing between four and six (non-hydrogen) atoms, for which previous estimates were computed at the CCSDT level.

physics.chem-ph↗

arXiv2022

Transition-Potential Coupled Cluster II: Optimization of the Core Orbital Occupation Number

The issue of orbital relaxation in computational core-hole spectroscopy, specifically x-ray absorption, has been a major problem for methods such as equation-of-motion coupled cluster with singles and doubles (EOM-CCSD). The transition-potential coupled cluster (TP-CC) method is utilized to address this problem by including an explicit treatment of orbital relaxation via the use of reference orbitals with a fractional core occupation number. The value of the fractional occupation parameter $λ$ was optimized for both TP-CCSD and XTP-CCSD methods in an element-specific manner due to the differences in atomic charge and energy scale. Additionally, TP-CCSD calculations using the optimized parameters were performed for the K-edge absorption spectra of gas-phase adenine and thymine. TP-CCSD reproduces the valence region well and requires smaller overall energy shifts in comparison to EOM-CCSD, while also improving on the relative position and intensities of several absorption peaks.

physics.chem-ph↗

arXiv2022

Accurate core-excited states via inclusion of core triple excitations in similarity-transformed EOM theory

The phenomenon of orbital relaxation upon excitation of core electrons is a major problem in the linear-response treatment of core-hole spectroscopies. Rather than addressing relaxation through direct dynamical correlation of the excited state via equation-of-motion coupled cluster theory (EOMEE-CC), we extend the alternative similarity-transformed equation-of-motion coupled cluster theory (STEOMEE-CC) by including the core-valence separation (CVS) and correlation of triple excitations only within the calculation of core ionization energies. This new method, CVS-STEOMEE-CCSD+cT, significantly improves on CVS-EOMEE-CCSD and unmodified CVS-STEOMEE-CCSD when compared to full CVS-EOM-CCSDT for K-edge core-excitation energies of a set of small molecules. The improvement in both absolute and relative (shifted) peak positions is nearly as good as for transition-potential coupled cluster (TP-CC), which includes an explicit treatment of orbital relaxation, and CVS-EOMEE-CCSD*, which includes a perturbative treatment of triple excitations.

physics.chem-ph↗

arXiv2021

How accurate are EOM-CC4 vertical excitation energies?

We report the first investigation of the performance of EOM-CC4 -- an approximate equation-of-motion coupled-cluster model which includes iterative quadruple excitations -- for vertical excitation energies in molecular systems. By considering a set of 28 excited states in 10 small molecules for which we have computed CCSDTQP and FCI reference energies, we show that, in the case of excited states with a dominant contribution from the single excitations, CC4 yields excitation energies with sub-kJ~mol$^{-1}$ accuracy (i.e., error below $0.01$ eV), in very close agreement with its more expensive CCSDTQ parent. Therefore, if one aims at high accuracy, CC4 stands as a highly competitive approximate method to model molecular excited states, with a significant improvement over both CC3 and CCSDT. Our results also evidence that, although the same qualitative conclusions hold, one cannot reach the same level of accuracy for transitions with a dominant contribution from the double excitations.

physics.chem-ph↗

arXiv2021

A Critical Analysis of Least-Squares Tensor Hypercontraction Applied to MP3

The least-squares tensor hypercontraction (LS-THC) approach is a promising method of reducing the high polynomial scaling of wavefunction methods, for example those based on many-body perturbation theory or coupled cluster. Here, we focus on LS-THC-MP3, and identify four variants with differing error and efficiency characteristics. The performance of LS-THC-MP3 is analyzed for regular test systems with up to 40 first-row atoms. We also analyze the size-extensivity/size-consistency and grid- and basis set-dependence of LS-THC-MP3. Overall, the errors observed are favorably small in comparison with standard density fitting, and a more streamlined method of generating grids via pruning is suggested. Practical crossover (the point at which LS-THC-MP3 is cheaper than the canonical method) is achieved around 240 correlated electrons. Despite several drawbacks of LS-THC that have been identified: a small but non-zero size-consistency error, poor description of angular correlation, and potentially large increase of error with basis set size, the results show that LS-THC has significant potential for practical application to MP3 and other wavefunction methods.

physics.chem-ph↗

arXiv2020

Transition-Potential Coupled Cluster

The problem of orbital relaxation in computational core-hole spectroscopies, including x-ray absorption and x-ray photoionization, has long plagued linear response approaches, including equation-of-motion coupled cluster with singles and doubles (EOM-CCSD). Instead of addressing this problem by including additional electron correlation, we propose an explicit treatment of orbital relaxation via the use of "transition potential" reference orbitals, leading to a transition-potential coupled cluster (TP-CC) family of methods. One member of this family in particular, TP-CCSD(1/2), is found to essentially eliminate the orbital relaxation error and achieve the same level of accuracy for core-hole spectra as is typically expected of EOM-CCSD in the valence region. These results show that very accurate x-ray absorption spectra for molecules with first-row atoms can be computed at a cost essentially the same as that for EOM-CCSD.

physics.chem-ph↗

arXiv2020

Analytic Gradients of Approximate Coupled Cluster Methods with Quadruple Excitations

The analytic gradient theory for both iterative and non-iterative coupled-cluster approximations that include connected quadruple excitations is presented. These methods include, in particular, CCSDT(Q), which is an analog of the well-known CCSD(T) method which starts from the full CCSDT method rather than CCSD. The resulting methods are implemented in the CFOUR program suite, and pilot applications are presented for the equilibrium geometries and harmonic vibrational frequencies of the simplest Criegee intermediate, CH$_2$OO, as well as to the isomerization pathway between dimethylcarbene and propene. While all methods are seen to approximate the full CCSDTQ results well for "well-behaved" systems, the more difficult case of the Criegee intermediate shows that CCSDT(Q), as well as certain iterative approximations, display problematic behavior.

physics.chem-ph↗

arXiv2020

Accelerating the Convergence of Higher-Order Coupled Cluster Methods II: Coupled Cluster $Λ$ Equations and Dynamic Damping

The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $Λ$ equations. The sub-iteration procedure for the $Λ$ equations is found to be highly similar to that for the amplitude equations, and to exhibit a similar improvement in rate of convergence relative to extrapolation of all $\hat{T}$ or $\hatΛ$ amplitudes using DIIS. A method of dynamic damping is also presented which is found to effectively recover rapid convergence in the case of oscillatory behavior in the amplitude or $Λ$ equations. Together, these techniques allow for the convergence of both the amplitude and $Λ$ equations necessary for the calculation of analytic gradients and properties of higher-order coupled cluster methods without the high memory or disk I/O cost of full DIIS extrapolation.

physics.chem-ph↗

arXiv2020

EOM-CC Methods with Approximate Triple Excitations for NEXAFS and XPS

A number of iterative and perturbative approximations to the full equation-of-motion coupled cluster method with single, double, and triple excitations (EOM-CCSDT) are evaluated in the context of calculating the K-edge core-excitation and core-ionization energies of several small molecules. Several of these methods are found to accurately reproduce the full EOM-CCSDT energies well, in particular the EOM-CCSD* method which, when using the core-valence separation (CVS) ansatz, scales rigorously with the sixth power of molecular size. The EOM-CCSDR(3) method, which has been used previously to include triples effects in a cost-effective manner was found to perform rather poorly, although the precise cause has not been determined. These results highlight that very accurate NEXAFS and XPS spectra for molecules with first-row atoms can be computed at a cost not much larger than that for EOM-CCSD.

physics.chem-ph↗

arXiv2019

Improved Grid Optimization and Fitting in Least Squares Tensor Hypercontraction

A new method for generating fitting grids for least-squares tensor hypercontraction (LS-THC) is presented. This method draws inspiration from the related interpolative separable density fitting (ISDF) technique, but uses only a pivoted Cholesky decomposition of the metric matrix, S, already computed as a matter of course in LS-THC. The size and quality of the resulting grid is controlled by a user-defined cutoff parameter and the size of the starting grid. Additionally, the Cholesky-based method provides an alternative and possible more numerically stable method for performing the least-squares fit. The quality of the grids produced is evaluated for LS-DF-THC-MP2 calculations on retinal and benzene, the former with a large starting grid and small cc-pVDZ basis set, and the latter with a wide range of grids and basis sets. The error and grid size is found to be well-controlled by either the cutoff parameter (with a large starting grid) or the starting grid size (with a tight cutoff) and highly predictable. The Cholesky-based method is also able to generate unique grids tailored to different charge distributions, for example the (ab|, (ai|, and (ij| distributions that arise in the molecular orbital integrals. While only the (ai| grid directly affects the MP2 energy, the relative sizes of the other grids are examined.

physics.chem-ph↗

arXiv2017

High-Performance Tensor Contraction without Transposition

Tensor computations--in particular tensor contraction (TC)--are important kernels in many scientific computing applications. Due to the fundamental similarity of TC to matrix multiplication (MM) and to the availability of optimized implementations such as the BLAS, tensor operations have traditionally been implemented in terms of BLAS operations, incurring both a performance and a storage overhead. Instead, we implement TC using the flexible BLIS framework, which allows for transposition (reshaping) of the tensor to be fused with internal partitioning and packing operations, requiring no explicit transposition operations or additional workspace. This implementation, TBLIS, achieves performance approaching that of MM, and in some cases considerably higher than that of traditional TC. Our implementation supports multithreading using an approach identical to that used for MM in BLIS, with similar performance characteristics. The complexity of managing tensor-to-matrix transformations is also handled automatically in our approach, greatly simplifying its use in scientific applications.

cs.MS↗

arXiv2017

Strassen's Algorithm for Tensor Contraction

Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and practice, extending it to accelerate TC has not been previously pursued. Thus, we believe this to be the first paper to demonstrate how one can in practice speed up tensor contraction with Strassen's algorithm. By adopting a Block-Scatter-Matrix format, a novel matrix-centric tensor layout, we can conceptually view TC as GEMM for a general stride storage, with an implicit tensor-to-matrix transformation. This insight enables us to tailor a recent state-of-the-art implementation of Strassen's algorithm to TC, avoiding explicit transpositions (permutations) and extra workspace, and reducing the overhead of memory movement that is incurred. Performance benefits are demonstrated with a performance model as well as in practice on modern single core, multicore, and distributed memory parallel architectures, achieving up to 1.3x speedup. The resulting implementations can serve as a drop-in replacement for various applications with significant speedup.

cs.MS↗

arXiv2017

Convergence of coupled cluster perturbation theory

The convergence of a recently proposed coupled cluster (CC) family of perturbation series [Eriksen, J. J. et al., J. Chem. Phys. 140, 064108 (2014)], in which the energetic difference between two CC models - a low-level parent and a high-level target model - is expanded in orders of the Møller-Plesset (MP) fluctuation potential, is investigated for four prototypical closed-shell systems (Ne, singlet methylene, distorted HF, and the fluoride anion) in standard and augmented basis sets. In these investigations, energy corrections of the various series have been calculated to high orders and their convergence radii determined by probing for possible front- and back-door intruder states, the existence of which would make the series divergent. In summary, we conclude how it is primarily the choice of target state, and not the choice of parent state, which ultimately governs the convergence behavior of a given series. For example, restricting the target state to, say, triple or quadruple excitations might remove intruders present in series that target the full configuration interaction (FCI) limit, such as the standard MP series. Furthermore, we find that whereas a CC perturbation series might converge within standard correlation consistent basis sets, it may start to diverge whenever these become augmented by diffuse functions, similar to the MP case. However, unlike for the MP case, such potential divergences are not found to invalidate the practical use of the low-order corrections of the CC perturbation series.

physics.chem-ph↗

arXiv2016

Generating Families of Practical Fast Matrix Multiplication Algorithms

Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due to the increased cost of memory movement, which is particularly noticeable for non-square matrices. Such implementations also require considerable workspace and modifications to the standard BLAS interface. We propose a code generator framework to automatically implement a large family of FMM algorithms suitable for multiplications of arbitrary matrix sizes and shapes. By representing FMM with a triple of matrices [U,V,W] that capture the linear combinations of submatrices that are formed, we can use the Kronecker product to define a multi-level representation of Strassen-like algorithms. Incorporating the matrix additions that must be performed for Strassen-like algorithms into the inherent packing and micro-kernel operations inside GEMM avoids extra workspace and reduces the cost of memory movement. Adopting the same loop structures as high-performance GEMM implementations allows parallelization of all FMM algorithms with simple but efficient data parallelism without the overhead of task parallelism. We present a simple performance model for general FMM algorithms and compare actual performance of 20+ FMM algorithms to modeled predictions. Our implementations demonstrate a performance benefit over conventional GEMM on single core and multi-core systems. This study shows that Strassen-like fast matrix multiplication can be incorporated into libraries for practical use.

cs.MS↗

arXiv2016

Assessment of the accuracy of coupled cluster perturbation theory for open-shell systems. II. Quadruples expansions

We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell atoms and organic radicals to the description of quadruple excitations. Namely, the second- through sixth-order models of the recently proposed CCSDT(Q-n) quadruples series [J. Chem. Phys. 140, 064108 (2014)] are compared to the prominent CCSDT(Q) and lambda-CCSDT(Q) models. From a comparison of the models in terms of their recovery of total CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find that the performance of the CCSDT(Q-n) models is independent of the reference used (unrestricted or restricted (open-shell) Hartree-Fock), in contrast to the CCSDT(Q) and lambda-CCSDT(Q) models, for which the accuracy is strongly dependent on the spin of the molecular ground state. By further comparing the ability of the models to recover relative CCSDTQ atomization energies, the discrepancy between them is found to be even more pronounced, stressing how a balanced description of both closed- and open-shell species - as found in the CCSDT(Q-n) models - is indeed of paramount importance if any perturbative CC model is to be of chemical relevance for high-accuracy applications. In particular, the third-order CCSDT(Q-3) model is found to offer an encouraging alternative to the existing choices of quadruples models used in modern computational thermochemistry, since the model is still only of moderate cost, albeit markedly more costly than, e.g., the CCSDT(Q) and lambda-CCSDT(Q) models.

physics.chem-ph↗