The problem of orbital relaxation in computational core-hole spectroscopies, including x-ray absorption and x-ray photoionization, has long plagued linear response approaches, including equation-of-motion coupled cluster with singles and doubles (EOM-CCSD). Instead of addressing this problem by including additional electron correlation, we propose an explicit treatment of orbital relaxation via the use of “transition potential” reference orbitals, leading to a transition-potential coupled cluster (TP-CC) family of methods. One member of this family, in particular, TP-CCSD($\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ ), is found to essentially eliminate the orbital relaxation error and achieve the same level of accuracy for the core-hole spectra as is typically expected of EOM-CCSD in the valence region. These results show that very accurate x-ray absorption spectra for molecules with first-row atoms can be computed at a cost essentially the same as that for EOM-CCSD.

The issue of orbital relaxation in computational core-hole spectroscopy, specifically x-ray absorption, has been a major problem for methods such as equation-of-motion coupled cluster with singles and doubles (EOM-CCSD). The transition-potential coupled cluster (TP-CC) method is utilised to address this problem by including an explicit treatment of orbital relaxation via the use of reference orbitals with a fractional core occupation number. The value of the fractional occupation parameter λ was optimised for both TP-CCSD and XTP-CCSD methods in an element-specific manner due to the differences in atomic charge and energy scale. Additionally, TP-CCSD calculations using the optimised parameters were performed for the K-edge absorption spectra of gas-phase adenine and thymine. TP-CCSD reproduces the valence region well and requires smaller overall energy shifts in comparison to EOM-CCSD, while also improving on the relative position and intensities of several absorption peaks. GRAPHICAL ABSTRACT

We develop an information-theoretic, cost-first framework for discrete dynamics in which the primitive operation is ratio-based comparison. Given two quantities compared via their ratio $x=a/b$, we assign a cost $F\left(x\right)$ measuring deviation from equilibrium ($x=1$). Adopting a reciprocal d’Alembert composition law motivated by coherent chaining, together with quadratic calibration at unity, uniquely determines a reciprocal comparison cost $J\left(x\right)=\frac{1}{2}\left(x+x^{-1}\right)-1$. Taking J as input, we model recognition events as deterministic updates on directed graphs recorded in a minimal ledger. Minimality (no intra-tick ordering metadata) together with non-commutativity of events implies atomic ticks: at most one event per tick. With conservation, pairwise locality, and quantization in $\delta \mathbb{Z}$, each event is recorded as a balanced double-entry posting. For graphs with cycles, assuming time-aggregated cycle closure over a finite clearing horizon, we show that cleared cycle closure is equivalent to path-independence and that the cumulative flow admits a scalar potential on each connected component (unique up to additive constant) via a discrete Poincaré lemma. On hypercube graphs $Q_d$, atomic single-edge updates impose a $2^d$-tick minimal period for timestamp-unique coverage, realized by cyclic Gray codes (explicitly for $d=3$). The framework links ratio-based cost functions, conservative graph flows, and discrete potential theory through explicitly stated axioms and structural assumptions.