Calculations of non-adiabatic couplings within equation-of-motion coupled-cluster framework: Theory, implementation, and validation against multi-reference methods

Abstract

We report an implementation of non-adiabatic coupling (NAC) forces within the equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD) framework via the summed-state approach. Using illustrative examples, we compare NAC forces computed with EOM-CCSD and multi-reference (MR) wave functions (for selected cases, we also consider configuration interaction singles). In addition to the magnitude of the NAC vectors, we analyze their direction, which is important for the calculations of the rate of non-adiabatic transitions. Our benchmark set comprises three doublet radical-cations (hexatriene, cyclohexadiene, and uracil), neutral uracil, and sodium-doped ammonia clusters. When the characters of the states agree among different methods, we observe good agreement between the respective NAC vectors, both in the Franck-Condon region and away. In the cases of large discrepancies between the methods, the disagreement can be attributed to the difference in the states' character, which, in some cases, is very sensitive to electron correlation, both within single-reference and multi-reference frameworks. The numeric results confirm that the accuracy of NAC vectors depends critically on the quality of the underlying wave functions. Within their domain of applicability, EOM-CC methods provide a viable alternative to MR approaches.

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

“…In contrast to multi-reference approaches, EOM-CC does not involve systemspecific parameterization (e.g., active-space selection), thus satisfying Pople's requirements of theoretical model chemistry 40 that can be used for systematic studies and comparisons between different systems. The EOM-CC framework yields reliable lowerorder properties such as solvatochromic shifts 41 , transition dipole moments 35 , spin-orbit [42][43][44][45] and non-adiabatic couplings [46][47][48] , as well as higher-order properties 49 such as two-photon absorption cross sections [50][51][52][53][54][55] , static and dynamical polarizabilities [56][57][58][59] . Whereas the bulk of prior developments and applications of the EOM-CC methods as well as of the closely related coupled-cluster response theory [60][61][62] were in the VUV regime, these methods are now being extended to the X-ray regime and their performance is being explored for computing, for example, XAS [15][16][17]19,[63][64][65] , XES 24,66 , and RIXS 24,66 spectra.…”

Coupled-cluster techniques for computational chemistry: The CFOUR program package

“…It is important to note that these are not "non-adiabatic couplings" (which are off-diagonal terms in the kinetic energy in the adiabatic basis rather than off-diagonal terms in the potential energy in the quasidiabatic basis), but are intimately related to them, as is discussed in Refs. 51,335,336 . In any event, once the quasidiabatic couplings are calculated, the force constants of the coupling modes appearing in the diagonal blocks of the potential are "diabatized" via…”

General framework for calculating spin–orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions

“…We can consider the transformation properties of the arithmetic average, Although weighted arithmetic average is more theoretically justified, 81 a simple arithmetic average is often numerically close to the weighted average. 82…”