Two- and one-photon absorption spectra of aqueous thiocyanate anion highlight the role of symmetry in the condensed phase.

We present the two-photon absorption (2PA) spectrum of aqueous thiocyanate calculated using high-level quantum-chemistry methods. The 2PA spectrum is compared to the one-photon absorption (1PA) spectrum computed using the same computational protocol. Although the two spectra probe the same set of electronic states, the intensity patterns are different, leading to an apparent red-shift of the 2PA spectrum relative to the 1PA spectrum. The presented analysis explains the intensity patterns and attributes the differences between the 1PA and 2PA spectra to the native symmetry of isolated SCN - , which influences the spectra in the low-symmetry solvated environment. The native symmetry also manifests itself in variations of the polarization ratio (e.g., parallel vs. perpendicular cross sections) across the spectrum. The presented results highlight the potential of 2PA spectroscopy and high-level quantum-chemistry methods in studies of condensed-phase phenomena.

Theory, implementation, and disappointing results for two-photon absorption cross sections within the doubly electron-attached equation-of-motion coupled-cluster framework.

The equation-of-motion coupled-cluster singles and doubles method with double electron attachment (EOM-DEA-CCSD) is capable of computing reliable energies, wave functions, and first-order properties of excited states in diradicals and polyenes that have a significant doubly excited character with respect to the ground state, without the need for including the computationally expensive triple excitations. Here, we extend the capabilities of the EOM-DEA-CCSD method to the calculations of a multiphoton property, two-photon absorption (2PA) cross sections. Closed-form expressions for the 2PA cross sections are derived within the expectation-value approach using response wave functions. We analyze the performance of this new implementation by comparing the EOM-DEA-CCSD energies and 2PA cross sections with those computed using the CC3 quadratic response theory approach. As benchmark systems, we consider transitions to the states with doubly excited character in twisted ethene and in polyenes, for which EOM-EE-CCSD (EOM-CCSD for excitation energies) performs poorly. The EOM-DEA-CCSD 2PA cross sections are comparable with the CC3 results for twisted ethene; however, the discrepancies between the two methods are large for hexatriene. The observed trends are explained by configurational analysis of the 2PA channels.

The orbital picture of the first dipole hyperpolarizability from many-body response theory.

We present an approach for obtaining a molecular orbital picture of the first dipole hyperpolarizability (ß) from correlated many-body electronic structure methods. Ab initio calculations of ß rely on quadratic response theory, which recasts the sum-over-all-states expression of ß into a closed-form expression by calculating a handful of first- and second-order response states; for resonantly enhanced ß, damped response theory is used. These response states are then used to construct second-order response reduced one-particle density matrices (1PDMs), which, upon visualization in terms of natural orbitals (NOs), facilitate a rigorous and black-box mapping of the underlying electronic structure with ß. We explain the interpretation of different components of the response 1PDMs and the corresponding NOs within both the undamped and damped response theory framework. We illustrate the utility of this new tool by deconstructing ß for cis-difluoroethene, para-nitroaniline, and hemibonded OH· + H2O complex, computed within the framework of coupled-cluster singles and doubles response theory, in terms of the underlying response 1PDMs and NOs for a range of frequencies.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core-valence separation.

We present a novel approach for computing resonant inelastic X-ray scattering (RIXS) cross sections within the equation-of-motion coupled-cluster (EOM-CC) framework. The approach is based on recasting the sum-over-states expressions for RIXS moments into closed-form expressions by using damped response theory. Damped response formalism allows one to circumvent problems of divergent behavior of response equations in the resonant regime. However, the convergence of response equations in the X-ray frequency range is often erratic due to the electronically metastable (i.e., resonant) nature of the virtual core-excited states embedded in the valence ionization continuum. We circumvent this problematic behavior by extending the core-valence separation (CVS) scheme, which decouples the valence-excited and core-excited configurations of the excitation manifold, into the response domain. The accuracy of the CVS-enabled damped response theory, implemented within the EOM-EE-CCSD (EOM-CC for excitation energies with single and double excitations) framework, is assessed by comparison against standard damped EOM-EE-CCSD response calculations. The capabilities of the new approach are illustrated by calculations of RIXS cross sections for benzene and benzene radical cation.

Correction: How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core-valence separation.

Correction for 'How to stay out of trouble in RIXS calculations within equation-of-motion coupled-cluster damped response theory? Safe hitchhiking in the excitation manifold by means of core-valence separation' by Kaushik D. Nanda et al., Phys. Chem. Chem. Phys., 2020, 22, 2629-2641, DOI: .

Cherry-picking resolvents: A general strategy for convergent coupled-cluster damped response calculations of core-level spectra.

Damped linear response calculations within the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) framework usually diverge in the x-ray regime. This divergent behavior stems from the valence ionization continuum in which the x-ray response states are embedded. Here, we introduce a general strategy for removing the continuum from the response manifold while preserving important spectral properties of the model Hamiltonian. The strategy is based on decoupling the core and valence Fock spaces using the core-valence separation (CVS) scheme combined with separate (approximate) treatment of the core and valence resolvents. We illustrate this approach with the calculations of resonant inelastic x-ray scattering (RIXS) spectra of benzene and para-nitroaniline using EOM-CCSD wave functions and several choices of resolvents, which differ in their treatment of the valence manifold. The method shows robust convergence and extends the previously introduced CVS-EOM-CCSD RIXS scheme to systems for which valence contributions to the total cross section are important, such as the push-pull chromophores with charge-transfer states.

A simple molecular orbital picture of RIXS distilled from many-body damped response theory.

Ab initio calculations of resonant inelastic x-ray scattering (RIXS) often rely on damped response theory, which prevents the divergence of response solutions in the resonant regime. Within the damped response theory formalism, RIXS moments are expressed as the sum over all electronic states of the system [sum-over-states (SOS) expressions]. By invoking resonance arguments, this expression can be reduced to a few terms, an approximation commonly exploited for the interpretation of computed cross sections. We present an alternative approach: a rigorous formalism for deriving a simple molecular orbital picture of the RIXS process from many-body calculations using the damped response theory. In practical implementations, the SOS expressions of RIXS moments are recast in terms of matrix elements between the zero-order wave functions and first-order frequency-dependent response wave functions of the initial and final states such that the RIXS moments can be evaluated using complex response one-particle transition density matrices (1PTDMs). Visualization of these 1PTDMs connects the RIXS process with the changes in electronic density. We demonstrate that the real and imaginary components of the response 1PTDMs can be interpreted as contributions of the undamped off-resonance and damped near-resonance SOS terms, respectively. By analyzing these 1PTDMs in terms of natural transition orbitals, we derive a rigorous, black-box mapping of the RIXS process into a molecular orbital picture. We illustrate the utility of the new tool by analyzing RIXS transitions in the OH radical, benzene, para-nitroaniline, and 4-amino-4'-nitrostilbene. These examples highlight the significance of both the near-resonance and off-resonance channels.

The effect of polarizable environment on two-photon absorption cross sections characterized by the equation-of-motion coupled-cluster singles and doubles method combined with the effective fragment potential approach.

We report an extension of a hybrid polarizable embedding method incorporating solvent effects in the calculations of two-photon absorption (2PA) cross sections. We employ the equation-of-motion coupled-cluster singles and doubles method for excitation energies (EOM-EE-CCSD) for the quantum region and the effective fragment potential (EFP) method for the classical region. We also introduce a rigorous metric based on 2PA transition densities for assessing the domain of applicability of QM/MM (quantum mechanics/molecular mechanics) schemes for calculating 2PA cross sections. We investigate the impact of the environment on the 2PA cross sections of low-lying transitions in microhydrated clusters of para-nitroaniline, thymine, and the deprotonated anionic chromophore of photoactive yellow protein (PYPb). We assess the performance of EOM-EE-CCSD/EFP by comparing the 2PA cross sections against full QM calculations as well as against the non-polarizable QM/MM electrostatic embedding approach. We demonstrate that the performance of QM/EFP improves when few explicit solvent molecules are included in the QM subsystem. We correlate the errors in the 2PA cross sections with the errors in the key electronic properties-identified by the analysis of 2PA natural transition orbitals and 2PA transition densities-such as excitation energies, transition moments, and dipole-moment differences between the initial and final states. Finally, using aqueous PYPb, we investigate the convergence of 2PA cross sections to bulk values.

Communication: The pole structure of the dynamical polarizability tensor in equation-of-motion coupled-cluster theory.

In this letter, we investigate the pole structure of dynamical polarizabilities computed within the equation-of-motion coupled-cluster (EOM-CC) theory. We show, both theoretically and numerically, that approximate EOM-CC schemes such as, for example, the EOM-CC singles and doubles model exhibit an incorrect pole structure in which the poles that reflect the excitations from the target state (i.e., the EOM-CC state) are supplemented by artificial poles due to excitations from the CC reference state. These artificial poles can be avoided by skipping the amplitude response and reverting to a sum-over-states formulation. While numerical results are generally in favor of such a solution, its major drawback is that this scheme violates size extensivity.

Effect of the diradical character on static polarizabilities and two-photon absorption cross sections: A closer look with spin-flip equation-of-motion coupled-cluster singles and doubles method.

We present static polarizabilities and two-photon absorption (2PA) cross sections for the low-lying electronic states of prototypical diradicals such as benzynes and analogues of m-xylylene and p-quinodimethane computed with the spin-flip equation-of-motion coupled-cluster singles and doubles (EOM-SF-CCSD) method. The static polarizabilities were calculated as analytic second derivatives of the EOM energies, and the 2PA cross sections were calculated using the expectation-value approach. We explain the trends in the nonlinear responses of the SF target states by constructing few-states models based on truncated sum-over-states expressions for these nonlinear properties. By using a Huckel-type treatment of the frontier molecular orbitals that host the unpaired electrons, we rationalize the trends in the dipole interactions between the SF target states relevant in the few-states models. We demonstrate the correlation between the nonlinear responses of these electronic states and the diradical character.

Static polarizabilities for excited states within the spin-conserving and spin-flipping equation-of-motion coupled-cluster singles and doubles formalism: Theory, implementation, and benchmarks.

We present the theory and implementation for calculating static polarizabilities within the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) framework for electronically excited states and its spin-flip variant. We evaluate the second derivatives of the EOM-CCSD Lagrangian with respect to electric-field perturbations. The relaxation of reference molecular orbitals is not included. In our approach, the wave function amplitudes satisfy the 2n + 1 rule and the amplitude-response Lagrange multipliers satisfy the 2n + 2 rule. The new implementation is validated against finite-field and CCSD response-theory calculations of the excited-state polarizabilities of pyrimidine and s-tetrazine. We use the new method to compute static polarizabilities of different types of electronic states (valence, charge-transfer, singlets, and triplets) in open- and closed-shell systems (uracil, p-nitroaniline, methylene, and p-benzyne). We also present an alternative approach for calculating excited-state static polarizabilities as expectation values by using the EOM-CCSD wave functions and energies in the polarizability expression for an exact state. We find that this computationally less demanding approach may show differences up to ∼30% relative to the excited-state polarizabilities computed using the analytic-derivative formalism.

Two-photon absorption cross sections within equation-of-motion coupled-cluster formalism using resolution-of-the-identity and Cholesky decomposition representations: Theory, implementation, and benchmarks.

The equation-of-motion coupled-cluster (EOM-CC) methods provide a robust description of electronically excited states and their properties. Here, we present a formalism for two-photon absorption (2PA) cross sections for the equation-of-motion for excitation energies CC with single and double substitutions (EOM-CC for electronically excited states with single and double substitutions) wave functions. Rather than the response theory formulation, we employ the expectation-value approach which is commonly used within EOM-CC, configuration interaction, and algebraic diagrammatic construction frameworks. In addition to canonical implementation, we also exploit resolution-of-the-identity (RI) and Cholesky decomposition (CD) for the electron-repulsion integrals to reduce memory requirements and to increase parallel efficiency. The new methods are benchmarked against the CCSD and CC3 response theories for several small molecules. We found that the expectation-value 2PA cross sections are within 5% from the quadratic response CCSD values. The RI and CD approximations lead to small errors relative to the canonical implementation (less than 4%) while affording computational savings. RI/CD successfully address the well-known issue of large basis set requirements for 2PA cross sections calculations. The capabilities of the new code are illustrated by calculations of the 2PA cross sections for model chromophores of the photoactive yellow and green fluorescent proteins.

Prediction of organic molecular crystal geometries from MP2-level fragment quantum mechanical/molecular mechanical calculations.

The fragment-based hybrid many-body interaction (HMBI) model provides a computationally affordable means of applying electronic structure wavefunction methods to molecular crystals. It combines a quantum mechanical treatment of individual molecules in the unit cell and their short-range pairwise interactions with a polarizable molecular mechanics force-field treatment of long-range and many-body interactions. Here, we report the implementation of analytic nuclear gradients for the periodic model to enable full relaxation of both the atomic positions and crystal lattice parameters. Using a set of five, chemically diverse molecular crystals, we compare the quality of the HMBI MP2/aug-cc-pVDZ-level structures with those obtained from dispersion-corrected periodic density functional theory, B3LYP-D*, and from the Amoeba polarizable force field. The MP2-level structures largely agree with the experimental lattice parameters to within 2%, and the root-mean-square deviations in the atomic coordinates are less than 0.2 Å. These MP2 structures are almost as good as those predicted from periodic B3LYP-D*/TZP and are significantly better than those obtained with B3LYP-D*/6-31G(d,p) or with the Amoeba force field.

Cherry-Picking Resolvents: Recovering the Valence Contribution in X-ray Two-Photon Absorption within the Core-Valence-Separated Equation-of-Motion Coupled-Cluster Response Theory.

Calculations of first-order response wave functions in the X-ray regime often diverge within correlated frameworks such as equation-of-motion coupled-cluster singles and doubles (EOM-CCSD), a consequence of the coupling with the valence ionization continuum. Here, we extend our strategy of introducing a hierarchy of approximations to the EOM-EE-CCSD resolvent (or, inversely, the model Hamiltonian) involved in the response equations for the calculation of X-ray two-photon absorption (X2PA) cross sections. We exploit the frozen-core core-valence separation (fc-CVS) scheme to first decouple the core and valence Fock spaces, followed by a separate approximate treatment of the valence resolvent. We demonstrate the robust convergence of X-ray response calculations within this framework and compare X2PA spectra of small benchmark molecules with the previously reported density functional theory results.

Probing Molecular Chirality of Ground and Electronically Excited States in the UV-vis and X-ray Regimes: An EOM-CCSD Study.

We present several strategies for computing electronic circular dichroism (CD) spectra across different frequency ranges at the equation-of-motion coupled-cluster singles and doubles level of theory. CD spectra of both ground and electronically excited states are discussed. For selected cases, the approach is compared with coupled-cluster linear response results as well as time-dependent density functional theory. The extension of the theory to include the effect of spin-orbit coupling is presented and illustrated by calculations of X-ray CD spectra at the L-edge.

Visualizing the Contributions of Virtual States to Two-Photon Absorption Cross Sections by Natural Transition Orbitals of Response Transition Density Matrices.

Observables such as two-photon absorption cross sections cannot be computed from the wave functions of initial and final states alone because of their nonlinear nature. Rather, they depend on the entire manifold of the excited states, which follows from the familiar sum-over-states expressions of second- and higher-order properties. Consequently, the interpretation of the computed nonlinear optical properties in terms of molecular orbitals is not straightforward and usually relies on approximate few-states models. Here, we show that the two-photon absorption (2PA) transitions can be visualized using response one-particle transition density matrices, which are defined as transition density matrices between the zero-order and first-order perturbed states. We also extend the concept of natural transition orbitals to 2PA transitions. We illustrate the utility of this new tool, which provides a rigorous black box alternative to traditional qualitative few-states analysis, by considering 2PA transitions in ethylene, trans-stilbene, and para-nitroaniline.

Predicting finite-temperature properties of crystalline carbon dioxide from first principles with quantitative accuracy.

Molecular crystal structures, thermodynamics, and mechanical properties can vary substantially with temperature, and predicting these temperature-dependencies correctly is important for many practical applications in the pharmaceutical industry and other fields. However, most electronic structure predictions of molecular crystal properties neglect temperature and/or thermal expansion, leading to potentially erroneous results. Here, we demonstrate that by combining large basis set second-order Møller-Plesset (MP2) or even coupled cluster singles, doubles, and perturbative triples (CCSD(T)) electronic structure calculations with a quasiharmonic treatment of thermal expansion, experimentally observable properties such as the unit cell volume, heat capacity, enthalpy, entropy, sublimation point and bulk modulus of phase I crystalline carbon dioxide can be predicted in excellent agreement with experiment over a broad range of temperatures. These results point toward a promising future for ab initio prediction of molecular crystal properties at real-world temperatures and pressures.