Choice of Optimal Shift Parameter for the Intruder State Removal Techniques in Multireference Perturbation Theory

Assessment of State-Averaged Driven Similarity Renormalization Group on Vertical Excitation Energies: Optimal Flow Parameters and Applications to Nucleobases

We present a comprehensive excited-state benchmark for the state-averaged (SA) driven similarity renormalization group (DSRG) [Li, C.; Evangelista, F. A. J. Chem. Phys. 2018, 148, 124106]. Following the QUEST database [Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; Loos, P.-F. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2021, 11, e1517], 280 vertical transition energies of 35 medium-sized molecules are computed using the SA-DSRG derived second- and third-order perturbation theories (PT2/PT3) along with a nonperturbative approach [sq-LDSRG(2)]. Comparing to the theoretical best estimates, the optimal flow parameter is found to be 0.35 and 2.0 Eh-2 for SA-DSRG-PT2 and SA-DSRG-PT3, respectively. For SA-sq-LDSRG(2), a flow parameter of 1.5 Eh-2 provides converged equations without compromising the accuracy. We then assess the accuracy of the SA-DSRG hierarchy using these parameters. The SA-DSRG-PT2 scheme outperforms the level-shifted CASPT2 by 0.10 eV in mean absolute error (MAE), yet this accuracy is slightly inferior than that of CASPT2 with the ionization-potential-electron-affinity shift. Both SA-DSRG-PT3 and SA-sq-LDSRG(2) yield a MAE of 0.10 eV, which is comparable to that of CASPT3 (0.09 eV). Finally, we compute vertical excitation energies of several low-lying singlet states of nucleobases. The SA-sq-LDSRG(2) approach provides highly accurate results for π → π* excitations, while n → π* transitions are better described by SA-DSRG-PT3.

Regularized CASPT2: an Intruder-State-Free Approach

In this work we present a new approach to fix the intruder-state problem (ISP) in CASPT2 based on σ^p regularization. The resulting σ^p-CASPT2 method is compared to previous techniques, namely, the real and imaginary level shifts, on a theoretical basis and by performing a series of systematic calculations. The analysis is focused on two aspects, the effectiveness of σ^p-CASPT2 in removing the ISP and the sensitivity of the approach with respect to the input parameter. We found that σ^p-CASPT2 compares favorably with respect to previous approaches and that different versions, σ¹-CASPT2 and σ²-CASPT2, have different potential application domains. This analysis also reveals the unsuitability of the real level shift technique as a general way to avoid the intruder-state problem.

Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers

We present a formulation of the multiconfigurational (MC) wave function symmetry-adapted perturbation theory (SAPT). The method is applicable to noncovalent interactions between monomers which require a multiconfigurational description, in particular when the interacting system is strongly correlated or in an electronically excited state. SAPT(MC) is based on one- and two-particle reduced density matrices of the monomers and assumes the single-exchange approximation for the exchange energy contributions. Second-order terms are expressed through response properties from extended random phase approximation (ERPA). The dispersion components of SAPT(MC) have been introduced in our previous works [HapkaM.J. Chem. Theory Comput.2019, 15, 1016−102730525591; HapkaM.J. Chem. Theory Comput.2019, 15, 6712–672331670950]. SAPT(MC) is applied either with generalized valence bond perfect pairing (GVB) or with complete active space self-consistent field (CASSCF) treatment of the monomers. We discuss two model multireference systems: the H₂ ··· H₂ dimer in out-of-equilibrium geometries and interaction between the argon atom and excited state of ethylene. Using the C₂H₄* ··· Ar complex as an example, we examine second-order terms arising from negative transitions in the linear response function of an excited monomer. We demonstrate that the negative-transition terms must be accounted for to ensure qualitative prediction of induction and dispersion energies and develop a procedure allowing for their computation. Factors limiting the accuracy of SAPT(MC) are discussed in comparison with other second-order SAPT schemes on a data set of small single-reference dimers.

Approximations of density matrices in N-electron valence state second-order perturbation theory (NEVPT2). I. Revisiting the NEVPT2 construction

Over the last decade, the second-order N-electron valence state perturbation theory (NEVPT2) has developed into a widely used multireference perturbation method. To apply NEVPT2 to systems with large active spaces, the computational bottleneck is the construction of the fourth-order reduced density matrix. Both its generation and storage become quickly problematic beyond the usual maximum active space of about 15 active orbitals. To reduce the computational cost of handling fourth-order density matrices, the cumulant approximation (CU) has been proposed in several studies. A more conventional strategy to address the higher-order density matrices is the pre-screening approximation (PS), which is the default one in the ORCA program package since 2010. In the present work, the performance of the CU, PS, and extended PS (EPS) approximations for the fourth-order density matrices is compared. Following a pedagogical introduction to NEVPT2, contraction schemes, as well as the approximations to density matrices, and the intruder state problem are discussed. The CU approximation, while potentially leading to large computational savings, virtually always leads to intruder states. With the PS approximation, the computational savings are more modest. However, in conjunction with conservative cutoffs, it produces stable results. The EPS approximation to the fourth-order density matrices can reproduce very accurate NEVPT2 results without any intruder states. However, its computational cost is not much lower than that of the canonical algorithm. Moreover, we found that a good indicator of intrude states problems in any approximation to high order density matrices is the eigenspectra of the Koopmans matrices.

How Much Dispersion Energy Is Included in the Multiconfigurational Interaction Energy?

We demonstrate how to quantify the amount of dispersion interaction recovered by supermolecular calculations with the multiconfigurational self-consistent field (MCSCF) wave functions. For this purpose, we present a rigorous derivation which connects the portion of dispersion interaction captured by the assumed wave function model-the residual dispersion interaction-with the size of the active space. Based on the obtained expression for the residual dispersion contribution, we propose a dispersion correction for the MCSCF that avoids correlation double counting. Numerical demonstration for model four-electron dimers in both ground and excited states described with the complete active space self-consistent field (CASSCF) reference serves as a proof-of-concept for the method. Accurate results, largely independent of the size of the active space, are obtained. For many-electron systems, routine CASSCF interaction energy calculations recover a tiny fraction of the full second-order dispersion energy. We found that the residual dispersion is non-negligible only for purely dispersion-bound complexes.

Ab Initio Probing of the Ground State of Tetraradicals: Breakdown of Hund's Multiplicity Rule

The electronic structure of organic σ-type polyradical including 2,4,6-tridehydropyridine radical cation (246-TDHP) and three isomers of tetradehydrobenzene (TDHB) have been studied using a computationally robust and cost-effective second-order multireference perturbative model which provides a balanced treatment of nondynamic and dynamic contributions to the electron correlation problem in the ground or excited electronic states which are imperative for predicting structural properties (e.g., ground state multiplicity, energy gaps between high-spin and low-spin states, etc.) of polyradicals. Energy gaps are useful to capture insight into the degree of interaction between the radical sites. An important finding of this study is that the tetraradicals considered here possess singlet ground states, contrary to Hund's rule. Present findings are in close agreement with the available high-level ab initio estimates at attainable cost implying that a perturbative description of the systems is adequate. The impact of N⁺ on the nature of ground state for the 246-TDHP have also analyzed. The singlet-triplet energy gaps for 1245- and 1234-TDHB are smaller than for o-benzyne mainly due to the ring strain. 1235-TDHB is 14.42 and 11.05 kcal/mol lower in energy than 1245- and 1234-isomers, respectively. IVO-SSMRPT predicts ¹A₁-³B₂ and ¹A₁-⁵B₂ gaps of 25.84 and 105.15 kcal/mol, respectively for the 246-TDHP cation.

A simplified ab initio treatment of diradicaloid structures produced from stretching and breaking chemical bonds

With a proper choice of active spaces, the single root perturbation theory employing improved virtual orbitals can flawlessly describe the ground, excited, ionized, and dissociated states having varying degrees of degeneracy at the expense of low computational cost.

Modeling the high-energy electronic state manifold of adenine: Calibration for nonlinear electronic spectroscopy

Pump-probe electronic spectroscopy using femtosecond laser pulses has evolved into a standard tool for tracking ultrafast excited state dynamics. Its two-dimensional (2D) counterpart is becoming an increasingly available and promising technique for resolving many of the limitations of pump-probe caused by spectral congestion. The ability to simulate pump-probe and 2D spectra from ab initio computations would allow one to link mechanistic observables like molecular motions and the making/breaking of chemical bonds to experimental observables like excited state lifetimes and quantum yields. From a theoretical standpoint, the characterization of the electronic transitions in the visible (Vis)/ultraviolet (UV), which are excited via the interaction of a molecular system with the incoming pump/probe pulses, translates into the determination of a computationally challenging number of excited states (going over 100) even for small/medium sized systems. A protocol is therefore required to evaluate the fluctuations of spectral properties like transition energies and dipole moments as a function of the computational parameters and to estimate the effect of these fluctuations on the transient spectral appearance. In the present contribution such a protocol is presented within the framework of complete and restricted active space self-consistent field theory and its second-order perturbation theory extensions. The electronic excited states of adenine have been carefully characterized through a previously presented computational recipe [Nenov et al., Comput. Theor. Chem. 1040-1041, 295-303 (2014)]. A wise reduction of the level of theory has then been performed in order to obtain a computationally less demanding approach that is still able to reproduce the characteristic features of the reference data. Foreseeing the potentiality of 2D electronic spectroscopy to track polynucleotide ground and excited state dynamics, and in particular its expected ability to provide conformational dependent fingerprints in dimeric systems, the performances of the selected reduced level of calculations have been tested in the construction of 2D electronic spectra for the in vacuo adenine monomer and the unstacked adenine homodimer, thereby exciting the Lb/La transitions with the pump pulse pair and probing in the Vis to near ultraviolet spectral window.

Nonorthogonal orbital based n-body reduced density matrices and their applications to valence bond theory. III. Second-order perturbation theory using valence bond self-consistent field function as reference

Using the formulas and techniques developed in Papers I and II of this series, the recently developed second-order perturbation theory based on a valence bond self-consistent field reference function (VBPT2) has been extended by using the internally contracted correction wave function. This ansatz strongly reduces the size of the interaction space compared to the uncontracted wave function and thus improves the capability of the VBPT2 method dramatically. Test calculations show that internally contracted VBPT2 using only a small number of reference valence bond functions, can give results as accuracy as the VBPT2 method and other more sophisticated methods such as full configuration interaction and multireference configuration interaction.

A fundamental view of enthalpy–entropy compensation

There is no fundamental difference in enthalpy–entropy compensation between dispersion and electrostatics or between quantum and molecular mechanics.