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# Reduced‐scaling coupled cluster response theory: Challenges and opportunities

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We review the current state of reduced‐scaling electron correlation methods, particularly coupled‐cluster theory for the simulation and prediction of molecular response properties. The successes of local‐coupled‐cluster and related approaches are well known for reaction energies, thermodynamic constants, dipole moments, and so forth—properties that depend primarily on the quality of the ground‐state wave function. However, much more challenging are higher‐order properties such as polarizabilities, hyperpolarizabilities, optical rotations, magnetizabilities, and others that also require accurate representation of the derivative of the wave function to external electromagnetic fields. We discuss a range of methods for improving the correlation domains of such perturbed wave functions, including the use of “perturbation‐aware” natural orbitals that are customized for the property of interest. In addition, we consider the viability and potential of promising, but still‐emerging methods such as stochastic and real‐time coupled‐cluster approaches, for which the localizability of the field‐dependent wave function may be more controllable than for conventional response theory. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy Software > Quantum Chemistry
The CCSD/aDZ (a) dynamic polarizability and (b) specific rotation of the (P)‐(H2)7 helix at 589 nm using both the PNO and PNO++ schemes as a function of the T2 ratio (see text)
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The CCSD/aDZ (a) dynamic polarizability and (b) specific rotation of the (P)‐(H2)7 helix at 589 nm using the FVNO and FVNO++ schemes as a function of percentage of virtual space removed
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Spatial extent (〈r2〉) of virtual orbitals of H2O2 vs. virtual CMO orbital energy (left‐hand axis) and virtual NO occupation number (right‐hand axis); (b) CCSD/aDZ polarizabilities of H2O2 in both FVNO and FVNO(M) schemes as a function of the number of virtual orbitals removed
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Errors in the CCSD (a) correlation energy and (b) polarizability of H2O2 in both CMO and NO bases as a function of the number of virtual orbitals removed
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Statistical distribution of CCSD amplitudes for n‐pentane. The perturbative electric field is oriented along the carbon backbone. The blue curve (t = 0) corresponds to the canonical CCSD ground‐state wave function, subjected to orbital localization; time‐propagation (t = 2.5 fs) of the coupled‐cluster amplitudes yields the green curve; the red curve represents the perturbed wave function from the linear response approach
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