A study investigated the multiconfiguration self-consistent field and multireference configuration interaction methods and applications to the field of chemistry. These methods are applicable to ...arbitrary electronics states and molecular configurations.
Understanding the properties of electronically excited states is a challenging task that becomes increasingly important for numerous applications in chemistry, molecular physics, molecular biology, ...and materials science. A substantial impact is exerted by the fascinating progress in time-resolved spectroscopy, which leads to a strongly growing demand for theoretical methods to describe the characteristic features of excited states accurately. Whereas for electronic ground state problems of stable molecules the quantum chemical methodology is now so well developed that informed nonexperts can use it efficiently, the situation is entirely different concerning the investigation of excited states. This review is devoted to a specific class of approaches, usually denoted as multireference (MR) methods, the generality of which is needed for solving many spectroscopic or photodynamical problems. However, the understanding and proper application of these MR methods is often found to be difficult due to their complexity and their computational cost. The purpose of this review is to provide an overview of the most important facts about the different theoretical approaches available and to present by means of a collection of characteristic examples useful information, which can guide the reader in performing their own applications.
In this paper, benchmark results are presented on Coupled Cluster calculation of singlet excitation energies and the corresponding oscillator strength. The test set of Thiel et al. (Schreiber, M.; ...Silva, M. R. J.; Sauer, S. P. A.; Thiel, W. J. Chem. Phys. 2008, 128, 134110) has been used, and the earlier results have been extended by CC3 oscillator strength for the whole set, CC3 excitation energies for larger molecules, and CCSDT results for some small molecules. Accuracy of the members of the hierarchy CC2-CCSD-CC3-CCSDT has been analyzed. The results show that both CC2 and CCSD are quite accurate and the difference to CC3 excitations energies is typically not larger than 0.2–0.3 eV. While the mean deviation of the CC2 results is close to zero, CCSD systematically overshoots the CC3 results by about 0.2 eV. The standard deviation is, however, somewhat smaller for CCSD, that is, the latter method provides more systematic results. Still, only a few cases could be identified were the absolute value of the error is over 0.3 eV in case of CC2. The results are even better for CCSD, with the exception of uracil, where surprisingly large error of the excitation energies have been found for two of the four lowest n–π* transitions. Both LR (Linear Response) and EOM (Equation of Motion) style oscillator strengths have been calculated. The former is more accurate at both CC2 and CCSD levels, but the difference between them is only 1–2% in case of CCSD. The error of the CC2 oscillator strength are substantially larger than that of CCSD but qualitatively still correct.
Benchmark calculations with the Spin-Component-Scaled CC2 variants SCS-CC2 and SOS-CC2 are presented for the electronically excited valence and Rydberg states of small- and medium-sized molecules. ...Besides the vertical excitation energies and excited state gradients, the potential energy surfaces are also investigated via scans following the forces that act in the Franck–Condon region. The results are compared to the regular CC2 ones, as well as higher level methods CCSD, CCSD(T)(a)*, and CCSDT. The results indicate that a large fraction of the flaws of CC2 revealed by earlier studies disappears if spin-component scaling is employed. This makes these variants attractive alternatives of their unscaled counterparts, offering competitive accuracy of vertical excitation energies of both valence and Rydberg type states and reliable potential energy surfaces, while also maintaining a low-power-scaling computational cost with the system size.
We present a comprehensive statistical analysis on the accuracy of various excited state Coupled Cluster methods, accentuating the effect of diffuse basis sets on vertical excitation energies of ...valence and Rydberg-type states. Many popular approximate doubles and triples methods are benchmarked with basis sets up to aug-cc-pVTZ, with high level EOM-CCSDT results used as reference. The results reveal a serious deficiency of CC2 linear response and CIS(D) techniques in the description of Rydberg states, a feature not shown by the EOM-CCSD(2) and EOM-CCSD variants. The CC3 theory proves to be an accurate choice among the iterative approximate triples methods, while the novel perturbation-based CCSD(T)(a)* variant turns out to be the best way to include the effect of triple excitations in a noniterative way.
In a recent paper of this journal ( Tajti ; Szalay . J. Chem. Theory Comput. 2019, 15, 5523 ), we have shown that failures of the CC2 method to describe Rydberg excited states as well as potential ...energy surfaces of certain valence excited states can be cured by spin-component scaled (SCS) versions SCS-CC2 and SOS-CC2 to a large extent. In this paper, the related and popular second-order algebraic diagrammatic construction (ADC(2)) method and its SCS variants are inspected with the previously established methodology. The results reflect the similarity of the CC2 and ADC(2) models, showing identical problems in the case of the canonical form and the same improvement when spin-component scaling is applied.
The numerous existing publications on benchmarking quantum chemistry methods for excited states rarely include Charge Transfer (CT) states, although many interesting phenomena in, e.g., biochemistry ...and material physics involve the transfer of electrons between fragments of the system. Therefore, it is timely to test the accuracy of quantum chemical methods for CT states, as well. In this study we first propose a new benchmark set consisting of dimers having low-energy CT states. On this set, the vertical excitation energy has been calculated with Coupled Cluster methods including triple excitations (CC3, CCSDT-3, CCSD(T)(a)*), as well as with methods including full or approximate doubles (CCSD, STEOM-CCSD, CC2, ADC(2), EOM-CCSD(2)). The results show that the popular CC2 and ADC(2) methods are much less accurate for CT states than for valence states. On the other hand, EOM-CCSD seems to have similar systematic overestimation of the excitation energies for both types of states. Among the triples methods the novel EOM-CCSD(T)(a)* method including noniterative triple excitations is found to stand out with its consistently good performance for all types of states, delivering essentially EOM-CCSDT quality results.
The molecular level understanding of electronic transport properties depends on the reliable theoretical description of charge-transfer (CT)-type electronic states. In this paper, the performance of ...spin-component-scaled variants of the popular CC2 and ADC(2) methods is evaluated for CT states, following benchmark strategies of earlier studies that revealed a compromised accuracy of the unmodified models. In addition to statistics on the accuracy of vertical excitation energies at equilibrium and infinite separation of bimolecular complexes, potential energy surfaces of the ammonia–fluorine complex are also reported. The results show the capability of spin-component-scaled approaches to reduce the large errors of their regular counterparts to a significant extent, outperforming even the coupled-cluster single and double method in many cases. The cost-effective scaled-opposite-spin variants are found to provide a remarkably good agreement with the CCSDT-3 reference data, thereby being recommended methods of choice in the study of charge-transfer states.
Describing electronically excited states of molecules accurately poses a challenging problem for theoretical methods. Popular second order techniques like Linear Response CC2 (CC2-LR), Partitioned ...Equation-of-Motion MBPT(2) (P-EOM-MBPT(2)), or Equation-of-Motion CCSD(2) (EOM-CCSD(2)) often produce results that are controversial and are ill-balanced with their accuracy on valence and Rydberg type states. In this study, we connect the theory of these methods and, to investigate the origin of their different behavior, establish a series of intermediate variants. The accuracy of these on excitation energies of singlet valence and Rydberg electronic states is benchmarked on a large sample against high-accuracy Linear Response CC3 references. The results reveal the role of individual terms of the second order similarity transformed Hamiltonian, and the reason for the bad performance of CC2-LR in the description of Rydberg states. We also clarify the importance of the T̂ 1 transformation employed in the CC2 procedure, which is found to be very small for vertical excitation energies.
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