A toolchain for the automatic generation of computer codes for correlated wavefunction calculations

A perspective on the future of quantum chemical software: the example of the ORCA program package

The field of computational chemistry has made an impressive impact on contemporary chemical research. In order to carry out computational studies on actual systems, sophisticated software is required in form of large-scale quantum chemical program packages. Given the enormous diversity and complexity of the methods that need to be implementation in such packages, it is evident that these software pieces are very large (millions of code lines) and extremely complex. Most of the packages in widespread use by the computational chemistry community have had a development history of decades. Given the rapid progress in the hardware and a lack of resources (time, workforce, money), it is not possible to keep redesigning these program packages from scratch in order to keep up with the ever more quickly shifting hardware landscape. In this perspective, some aspects of the multitude of challenges that the developer community faces are discussed. While the task at hand - to ensure that quantum chemical program packages can keep evolving and make best use of the available hardware - is daunting, there are also new evolving opportunities. The problems and potential cures are discussed with the example of the ORCA package that has been developed in our research group.

Efficient Spin-Adapted Implementation of Multireference Algebraic Diagrammatic Construction Theory. I. Core-Ionized States and X-ray Photoelectron Spectra

We present an efficient implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulating core-ionized states and X-ray photoelectron spectra (XPS). Taking advantage of spin adaptation, automatic code generation, and density fitting, our implementation can perform calculations for molecules with more than 1500 molecular orbitals, incorporating static and dynamic correlation in the ground and excited electronic states. We demonstrate the capabilities of MR-ADC methods by simulating the XPS spectra of substituted ferrocene complexes and azobenzene isomers. For the ground electronic states of these molecules, the XPS spectra computed using the extended second-order MR-ADC method (MR-ADC(2)-X) are in a very good agreement with available experimental results. We further show that MR-ADC can be used as a tool for interpreting or predicting the results of time-resolved XPS measurements by simulating the core ionization spectra of azobenzene along its photoisomerization, including the XPS signatures of excited states and the minimum energy conical intersection. This work is the first in a series of publications reporting the efficient implementations of MR-ADC methods.

Code generation in ORCA: progress, efficiency and tight integration

An improved version of ORCA's automated generator environment (ORCA-AGE II) is presented. The algorithmic improvements and the move to C++ as the programming language lead to a performance gain of up to two orders of magnitude compared to the previously developed PYTHON toolchain. Additionally, the restructured modular design allows for far more complex code engines to be implemented readily. Importantly, we have realised an extremely tight integration with the ORCA host program. This allows for a workflow in which only the wavefunction Ansatz is part of the source code repository while all actual high-level code is generated automatically, inserted at the appropriate place in the host program before it is compiled and linked together with the hand written code parts. This construction ensures longevity and uniform code quality. Furthermore the new developments allow ORCA-AGE II to generate parallelised production-level code for highly complex theories, such as fully internally contracted multireference coupled-cluster theory (fic-MRCC) with an enormous number of contributing tensor contractions. We also discuss the automated implementation of nuclear gradients for arbitrary theories. All these improvements enable the implementation of theories that are too complex for the human mind and also reduce development times by orders of magnitude. We hope that this work enables researchers to concentrate on the intellectual content of the theories they develop rather than be concerned with technical details of the implementation.

Kinetics of the Reactions of Chlorinated Very Short-Lived Substances (VSLSs) with Chlorine Atoms

Chlorinated very short-lived substances (VSLSs), which are not controlled by the Montreal Protocol, are of current concern with regard to recovery of stratospheric ozone. Further study is needed on the temperature dependences of chlorinated VSLSs relevant to atmospheric conditions. Here, the kinetics of chlorinated VSLSs, such as chloroform (CHCl3), dichloromethane (CH2Cl2), dichloroethane (CH2ClCH2Cl), and trichloroethene (C2HCl3) reacting with chlorine atoms, were investigated between 180 and 400 K, expanding the range of temperatures relative to previous studies. RRKM/Master Equation and Canonical Variational Transition State Theory were utilized to calculate the rate coefficients using the MultiWell suite of programs. CCSD(T), QCISD(T), and M062X with aug-cc-pV(T+d)Z levels of theory were used to calculate the kinetic parameters. Arrhenius equations obtained from fits to the calculated rate coefficients are k1 = (2.66 ± 0.7) × 10-12 exp [(-927 ± 131)/T] cm3 molecule-1 s-1, k2 = (8.99 ± 0.3) × 10-12 exp [(-957 ± 19)/T] cm3 molecule-1 s-1, k3 = (1.51 ± 0.16) × 10-11 exp [(-714 ± 54)/T] cm3 molecule-1 s-1, and k4 = (9.17 ± 1.8) × 10-12 exp [(612 ± 101)/T] cm3 molecule-1 s-1 for the reactions of CHCl3, CH2Cl2, CH2ClCH2Cl, and C2HCl3 with Cl atoms, respectively. The rate coefficients for the reactions of chlorinated VSLSs with Cl atoms from this study are compared with the most recent recommended values from the NASA/JPL and IUPAC evaluations and with literature values. The reactivity trends of the reactions are discussed.

Automatic derivation of many-body theories based on general Fermi vacua

This paper describes Wick&d, an implementation of the algebra of second-quantized operators normal ordered with respect to general correlated references and the corresponding Wick theorem [D. Mukherjee, Chem. Phys. Lett. 274, 561 (1997) and W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997)]. Wick&d employs a compact representation of operators and a backtracking algorithm to efficiently evaluate Wick contractions. Since Wick&d can handle both fully and partially contracted terms, it can be applied to both projective and Fock-space many-body formalisms. To demonstrate the usefulness of  Wick&d, we use it to evaluate the single-reference coupled cluster equations up to octuple excitations and report an automated derivation and implementation of the second-order driven similarity renormalization group multireference perturbation theory.

A time-dependent density functional theory study of a fluorescent probe to detect hydroxyl radicals: Inhibiting the twisted intramolecular charge-transfer process

Due to the relevance to excited-state processes, sensing mechanisms of fluorescent probes were difficult to study directly by experimental methods. This work investigated theoretically the sensing mechanism of a reported bifunctional fluorescent probe to detect intracellular hydroxyl radicals and their environmental viscosity (J. Am. Chem. Soc. 2019, 141, 18301). Calculations were performed at the B3P86/TZVP/SMD level using density functional theory and time-dependent density functional theory. The transition from the ground-state (S₀) to the first singlet excited state (S₁) was calculated to have the largest oscillation strength for the probe. The wavelength that corresponded to the S₀-S₁ vertical excitation energy (427 nm) agreed well with the maximum absorption band at 400 nm in the ultraviolet-visible spectra. Theoretical results showed that the probe had two distinct geometries in the S₀ and S₁ states, respectively. This difference was caused by the different distributions of frontier molecular orbitals that were involved in the S₀-S₁ transition and corresponds to a twisted intramolecular charge transfer. The S₁-state potential energy curve of the probe molecule confirmed that the twisted intramolecular charge transfer could proceed spontaneously with a potential barrier of only 12.20 kJ/mol. This result provided an irradiative approach for the probe molecule to dissipate the S₁-state energy, which explained its fluorescence quenching. In contrast, the hydroxyl oxidation reaction changed frontier molecular orbitals of the probe molecule, which made its S₁ state a local S₁ state with a strong fluorescence emission. Precisely due to the mechanism, the hydroxyl radicals could be detected by changes in the fluorescence signal of the probe molecule.

Approximations of density matrices in N-electron valence state second-order perturbation theory (NEVPT2). II. The full rank NEVPT2 (FR-NEVPT2) formulation

In Paper I, the performances of pre-screening (PS), extended PS (EPS), and cumulant (CU) approximations to the fourth-order density matrix were examined in the context of second-order N-electron valence state perturbation theory (NEVPT2). It has been found that the CU, PS, and even EPS approximations with loose thresholds may introduce intruder states. In the present work, the origin of these "false intruder" states introduced by approximated density matrices is discussed. Canonical NEVPT2 implementations employ a rank reduction trick. By analyzing its residual error, we find that the omission of the rank reduction leads to a more stable multireference perturbation theory for incomplete active space reference wave functions. Such a full rank (FR)-NEVPT2 formulation is equivalent to the conventional NEVPT2 method for the complete active space self-consistent field/complete active space configuration interaction reference wave function. A major drawback of the FR-NEVPT2 formulation is the necessity of the fifth-order density matrix. To avoid the construction of the high-order density matrices, the combination of the FR-NEVPT2 with the CU approximation is studied. However, we find that the CU approximation remains problematic as it still introduces intruder states. The question of how to robustly and efficiently perform internally contracted multireference perturbation theories with approximate densities remains a challenging field of investigation.

A multireference coupled-electron pair approximation combined with complete-active space perturbation theory in local pair-natural orbital framework

The Complete-Active Space Second-order Perturbation Theory (CASPT2) has been one of the most widely-used methods for reliably calculating electronic structures of multireference systems. Because of its lowest level treatment of dynamic correlation, it has a high computational feasibility; however, its accuracy in some cases falls short of needs. Here, as a simple yet higher-order alternative, we introduce a hybrid theory of the CASPT2 and a multireference variant of the Coupled-Electron Pair Approximation (CEPA), which is a class of high level correlation theory. A central feature of our theory (CEPT2) is to use the two underlying theories for describing different divisions of correlation components based on the full internal contraction framework. The external components, which usually give a major contribution to the dynamic correlation, are intensively described using the CEPA Ansatz, while the rests are treated at the CASPT2 level. Furthermore, to drastically reduce the computational demands, we have incorporated the pair-natural orbital (PNO) method into our multireference implementations. This development, thus, requires highly complex derivations and coding, while it has been largely facilitated with an automatic expression and code generation technique. To highlight the accuracy of the CEPT2 approach and to assess the errors caused by the PNO truncation, benchmark calculations are shown on small- to medium-size molecules, illustrating the high accuracy of the present CEPT2 model. By tightening the truncation thresholds, the PNO-CEPT2 energy converges toward the canonical counterpart and is more accurate than that of PNO-CASPT2 as long as the same truncation thresholds are used.

Diagrammatic Coupled Cluster Monte Carlo

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker-Campbell-Hausdorff expansion of the similarity-transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach-diagCCMC-allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.

Novel strategy to implement active-space coupled-cluster methods

A new approach is presented for the efficient implementation of coupled-cluster (CC) methods including higher excitations based on a molecular orbital space partitioned into active and inactive orbitals. In the new framework, the string representation of amplitudes and intermediates is used as long as it is beneficial, but the contractions are evaluated as matrix products. Using a new diagrammatic technique, the CC equations are represented in a compact form due to the string notations we introduced. As an application of these ideas, a new automated implementation of the single-reference-based multi-reference CC equations is presented for arbitrary excitation levels. The new program can be considered as an improvement over the previous implementations in many respects; e.g., diagram contributions are evaluated by efficient vectorized subroutines. Timings for test calculations for various complete active-space problems are presented. As an application of the new code, the weak interactions in the Be dimer were studied.