Reactions between the Criegee intermediate and HC(O)OH exhibit large rate coefficients, contributing significantly to secondary organic aerosol formation in the atmosphere. This study examines the reaction of methyl vinyl ketone oxide [MVKO, (CH)C(CH)OO], a Criegee intermediate generated via isoprene ozonolysis in the atmosphere, with HC(O)OH. Product analysis was performed using step-scan Fourier-transform infrared spectroscopy, capturing time-resolved infrared absorption spectra following irradiation at 248 nm of a flowing mixture of ()-(CHI)HC═C(CH)I/HC(O)OH and O at 298 K and 10-40 Torr. Ten absorption bands near 1726, 1425, 1378, 1310, 1247, 1215, 1170, 1068, 984, and 952 cm were assigned to 2-hydroperoxybut-3-en-2-yl formate [HPBF, CHC(CH)(OCHO)OOH], the hydrogen-transfer adduct of MVKO and HC(O)OH. Additional weak bands near 1675, 1600, 1432, 1387, 1330, and 1254 cm were tentatively attributed to 2-hydroperoxybuta-1,3-diene [HPBD, (CH)C(═CH)OOH], a hydrogen-transfer isomer of MVKO formed via HC(O)OH-catalyzed rearrangement. Two further bands near 1733 and 1200 cm were tentatively assigned to a complex of HPBD and HC(O)OH, with additional features overlapping those of HPBD. Spectral assignments were supported by B3LYP + D3/aug-cc-pVTZ calculations of vibrational wavenumbers and IR intensities. The identification of HPBF and HPBD is consistent with the reaction pathway scheme predicted by the CCSD(T)/aug-cc-pVTZ//B3LYP + D3/aug-cc-pVTZ method. In contrast to reactions of CHOO or CHCHOO with HC(O)OH, no dehydrated end product of the adduct was observed, which was attributed to the lack of an abstractable hydrogen atom in HPBF.

We investigate the origin dependence in the computation of vibrationally resolved electronic circular dichroism (ECD) and circularly polarized luminescence (CPL) spectral shapes with particular attention to non-Condon approximations. To that end, we adopt the length and velocity representations for the electric transition dipole moment (TDM), expressing both electric and magnetic TDMs as Taylor expansions in nuclear coordinates, including the constant (Franck-Condon, FC), non-Condon linear (Herzberg-Teller, HT) and, in some cases, second-order terms. Our analysis evidence that HT spectra, in the standard formulation, i.e., including the full first-order expansions of both TDMs, are not origin invariant, even in the velocity gauge. This inconsistency arises because the corresponding expression for the rotatory strength, which, unlike the individual TDMs, directly encodes the measurable chiroptical response, involves an incomplete second-order expansion. We show that origin invariance in the velocity gauge is restored when the product terms between the electric and magnetic TDM expansions are selected to yield a complete either first- or second-order expansion of the rotatory strength. In particular, excluding the cross-linear terms in the HT expression results in a consistent linear expansion, which delivers origin invariant rotatory strengths and ECD/CPL lineshapes. We refer to this formulation as the approach. Similarly, including the additional terms required for a complete second-order expansion, i.e., those combining constant and quadratic TDM terms, defines the approach, which also produces origin-invariant rotatory strengths. However, the ECD/CPL spectra lineshapes computed at this level still depend weakly on the gauge origin because the intensity of each single vibronic transition does. Nonetheless, the fact that the integrated ECD/CPL lineshapes remain origin invariant effectively mitigates origin-related variations in the spectra. Simulations of ECD and CPL lineshapes for three representative systems, spanning different non-Condon strengths and sensitivities to the gauge origin, confirm these predictions. All calculations are performed at the TDDFT level, using analytical first-order derivatives and numerical second-order derivatives of the TDMs with respect to nuclear coordinates. The analytical time-correlation functions necessary to run and vibronic computations, in a time-dependent framework, were derived in harmonic approximation, providing a general and robust route toward origin-independent vibronic simulations of chiroptical spectra.

Electron energy loss spectra (EELS) of benzisoxazole reveal signatures of anionic resonances in the vicinity of 1.2 and 2.2 eV incident electron energies. Another low-energy resonance is likely present just below 0.5 eV, but its contributions are difficult to discern definitively because of the overlap with intense near-threshold scattering and thermionic emission features. The observed resonances decay via two competing mechanisms: the excitation of specific vibrational modes and emission of low-energy electrons following statistical thermalization of resonance energy among unspecific vibrations. The thermionic pathway is likely mediated and amplified by vibronic couplings between the resonance states and the weakly bound dipole-bound anion supported by the 3.2 D dipole moment of benzisoxazole. The existence of the stable dipole-bound and metastable π* resonance states is confirmed by equation-of-motion coupled-cluster theory calculations. The non-Hermitian theory using a complex absorbing potential to stabilize the temporary-anion states predicts three such states in benzisoxazole below 3 eV. These states are assigned to the observed experimental features and described as π, π, and π scattering resonances. Additional structureless features in the 3-6 eV range observed in the EELS excitation curves for some vibrations are tentatively ascribed to several additional resonances predicted in that range. The existence of the dipole-bound anion state and its role in resonance decay dynamics set benzisoxazole sharply apart from its isomer benzoxazole.

Anion photoelectron (PE) spectra of lanthanide oxide clusters obtained previously have exhibited anomalous photoelectron angular distributions which were attributed to strong PE-valence electron (PEVE) interactions. To further explore this effect, we have obtained the PE spectra of GdO and GdO, two clusters that have similarly complex electronic structures but contrasting symmetries. The spectra exhibit manifolds of detachment transitions at similar binding energies in a 0.5 eV window of energy. The electron affinity of GdO is measured to be 1.29 ± 0.05 eV, and that of GdO is 1.31 ± 0.05 eV. As seen in previous studies on lanthanide oxide cluster anions in lower than conventional oxidation states, transitions in spectra obtained lower photon energies are more congested than those obtained with higher photon energy, a signature of strong PEVE interactions. While the detachment transitions have predominantly parallel photoelectron angular distributions (PAD), the PAD varies across the manifold of transitions in the PE spectrum of GdO in a way that suggests four different subgroups of transitions. Results of calculations on GdO suggest kite or V-shape structures with antiferromagnetic coupling between one of the 4f subshells with the two others. Calculations on GdO more definitively point to ring structures with a nearly isoenergetic ferromagnetically coupled high spin (24-tet) state and a dectet state in which one of the 4f subshells is antiferromagnetically coupled with the other two. Taking these results as qualitative, we propose that strong mixing between the unperturbed states predicted computationally leads to overlapping transitions with different PADs.

We present nonrelativistic finite nuclear mass corrections to the rovibrational energies of six isotopologues of HeH (HeH), calculated within the framework of nonadiabatic perturbation theory (NAPT) up to the second order in the electron-to-nucleus mass ratio. Corrections are expressed through adiabatic and nonadiabatic potentials, evaluated with high numerical precision using explicitly correlated Kołos-Wolniewicz basis functions, suitable for heteronuclear systems with unequal nuclear charges. The potentials were determined over a broad range of internuclear distances, with accuracy close to the MHz level in the nonrelativistic dissociation energies of low-lying rovibrational states. For the ground level, the results were independently verified by variational calculations with the nonadiabatic James-Coolidge wave functions. The reported results establish a robust foundation for the spectroscopic precision modeling of HeH, including an accurate treatment of relativistic and QED effects.

Magneto-chiral dichroism (MChD) is a fundamental but experimentally elusive chiroptical effect. Carbo[]helicenes, with their strong and systematically evolving chirality, represent ideal systems for its investigation. Here, we present the first theoretical predictions of the MChD spectra for a series of carbo[]helicenes, from [4]- to [8]helicene, calculated using time-dependent density functional theory (TD-DFT) within the damped response framework. To contextualize these predictions and enhance their reliability, we also computed the corresponding electronic circular dichroism (ECD) and magnetic circular dichroism (MCD) spectra, and report the first experimental MCD spectrum of [7]helicene. A systematic scaling procedure, calibrating the computed wavelengths against available experimental ECD and MCD data, was employed to provide reliable estimates for the yet-to-be-measured MChD signals. Our results predict that the MChD signals for larger helicenes, in particular [6]-, [7]-, and [8]helicene, are potentially within the sensitivity of modern experimental setups, with dissymmetry factors () of the order of 10. An increasing trend in the MChD signal is observed with increasing helicene size, suggesting a correlation with the number of benzene rings. These findings provide a robust theoretical benchmark and are intended to motivate new experimental investigations of this fundamental light-matter interaction.

By measuring a small circularly polarized component in the scattered light, we report the first observation of Rayleigh optical activity (RayOA) for isotropic samples of chiral molecules, namely the two enantiomers of α-pinene in neat liquid form. Our work validates fundamental theoretical predictions made over 50 years ago and expands the chiroptical toolkit.

The identification of individual molecular species in the interstellar medium (ISM) via radio astronomical observations relies on precise laboratory measurement of the species' rotational spectrum. Following the detections of benzonitrile and ethynylbenzene in the ISM, we perform a search for the disubstituted benzene derivatives that feature both a nitrile and an ethynyl substituent: the ortho (o), meta (m), and para (p) isomers of ethynylbenzonitrile (EBN). Having previously been measured in the millimeter-wave regime, we extend the rotational spectroscopy of the isomeric family down to the centimeter-wave regime where hyperfine splitting due to the electric quadrupole moment of the N atom can be resolved. Transitions of the singly substituted C and N isotopologues of the o- and p-EBN isomers are observed in their respective spectra, and the rotational constants of these isotopologues are also determined. Experimental ground state structural parameters are determined for o- and p-EBN with the rotational constants of the observed isotopologues, and their geometries are compared to that of benzene to determine how the substituents distort the aromatic ring. With the hyperfine splitting characterized, the rotational spectra are compared to the narrow emission lines observed toward the cold molecular cloud TMC-1. No individual transitions are identified in the observational data, and upper limits on the column densities of the three isomers are derived from the observations. Rate coefficients and product branching ratios are theoretically estimated for the formation of the EBN isomers from both benzonitrile and ethynylbenzene via CCH and CN addition, respectively. Based on these formation rates, and the observed column densities of other substituted aromatic species, the column densities of each of the EBN isomers are estimated to be less than an order of magnitude below their computed upper limits.

Hydroperoxymethyl acetate (HPMA, CHC(O)OCHOOH), formed from the reaction of carbonyl oxide (CHOO) with acetic acid (CHCOOH), is a multifunctional organic peroxide of atmospheric relevance. Despite its potential importance, the kinetics of HPMA remain poorly characterized. In this work, we present a comprehensive theoretical study of its bimolecular reactions with CHOO and hydroxyl radicals (OH). For the electronic structure calculations, we benchmark against GMM(Q).FNO//DF-CCSD(T)-F12b/jun-cc-pVDZ, a high-level method that closely approaches CCSDT(Q)/CBS accuracy for the reaction with CHOO, and CCSD(T)-F12a/cc-pVTZ-F12//M08-HX/MG3S for the reaction with OH. We computed rate constants using conventional transition state theory at the benchmark electronic structure level, combined with multistructural canonical variational transition state theory with small-curvature tunneling using a well-benchmarked density functional. The results show cycloaddition dominates the CHOO + HPMA, while OH predominantly abstracts the -OOH hydrogen to yield RO. We find that for the CHOO + HPMA reaction, vibrational anharmonicity increases the hydroperoxide addition rate constant by factors of 4-40 at 190 to 350 K. In the HPMA + OH system, tunneling increases the rate constant by over 100-fold for hydrogen abstraction from the -OOH and -CH groups at 190 K. Furthermore, our results indicate that under low-temperature or nighttime conditions, where OH concentrations are limited, the CHOO-initiated reaction becomes a dominant atmospheric sink for HPMA. The present work provides a valuable reference for kinetic evaluations of multifunctional organic peroxides in atmospheric oxidation.

We present the implementation of relativistic coupled cluster quadratic response theory (QR-CC), following our development of relativistic equation of motion coupled cluster quadratic response theory (QR-EOMCC) [X. Yuan et al., , 19, 9248-9259]. These codes, which can be used in combination with relativistic (2- and 4-component based) as well as nonrelativistic Hamiltonians, are capable of treating both static and dynamic perturbations for electric and magnetic operators. We have employed this new implementation to revisit the calculation of static and frequency-dependent first hyperpolarizabilities of hydrogen halides (HX, X = F-Ts) and the Verdet constant of heavy noble gas atoms (Xe, Rn, Og) and of selected hydrogen halides (HF to HI), in order to investigate the differences and similarities of QR-CC and the more approximate QR-EOMCC. Furthermore, we have determined the relative importance of scalar relativistic effects and spin-orbit coupling to these properties, through a comparison of different Hamiltonians, and extended our calculations to superheavy element species (HTs for hyperpolarizabilities, Og for the Verdet constant). Our results show that as one moves toward the bottom of the periodic table, QR-EOMCC can yield rather different results (hyperpolarizabilities) or perform rather similarly (Verdet constant) to QR-CC. These results underscore the importance of further characterizing the performance of QR-EOMCC for heavy element systems.

The reported "dissociation times" for the Br C (Π 1) state by various measurement methods differ widely across the literature (30 to 340 fs). We consider this issue by leveraging attosecond extreme ultraviolet (XUV) transient absorption spectroscopy at the Br M 3d edges (66 to 80 eV), tracking core-to-valence (3d → 4p) and core-to-Rydberg (3d → s, p, ≥ 5) transitions from the molecular to the atomic limit. The progress of dissociation can be ascertained by the buildup of the atomic absorption in time. Notably, the measured rise times of the 3d → 4p transitions depend on the probed core level final state, 38 ± 1 and 20 ± 5 fs for D and D at 64.31 and 65.34 eV, respectively. Simulations by the nuclear time-dependent Schrödinger equation reproduce the rise-time difference of the 3d → 4p transitions, and the theory suggests several important factors. One is the transition dipole moments of each probe transition have different molecular and atomic values for D versus D that depend on the bond length. The other is the merger of multiple molecular absorptions into the same atomic absorption, creating multiple time scales even for a single probe transition. On the other hand, the core-to-Rydberg absorptions did not allow accurate atomic Br buildup times to be extracted due to spectral overlaps with ground state bleaching, otherwise an even more comprehensive picture of the role of the probe state transition would be possible. This work shows that the measured XUV probe signals accurately contain the dissociative wavepacket dynamics but also reveal how the specific core-to-valence transition affects the apparent progress toward dissociation with bond length. These results highlight the potential probe-transition-dependent effects that need to be considered when interpreting measured signals and their time scales.

Mixtures of water and miscible organic compounds sometimes show physical/chemical anomalies, referred to as microheterogeneity. Reaction mechanisms in multicomponent aqueous mixtures such as atmospheric aerosols are expected to be different from those in single-solvent systems but remain to be fully elucidated. Here, by using electrospray mass spectrometry, we showed that the hydrolysis rates of C, C, and C α-hydroxyalkyl-hydroperoxides (α-HHs) derived from ozonolysis of nerolidol in water/acetonitrile solutions changed as a nonlinear function of water content. Notably, the mass spectral signals of C and C α-HHs at 10 vol % water persisted for at least a week, whereas they decayed to zero within a few hours at 20 vol %. Dynamic light scattering experiments indicated the presence of nanodroplets ( ≤ 100 nm) in these macroscopically homogeneous aqueous mixtures. The relative contribution of scattering intensity from small droplets (<10 nm) decreased as the water content increased from zero to 20 vol % water, whereas that of larger droplets (10-100 nm) increased. Based on these findings, we proposed a mechanism in which the α-HHs residing in the hydrophobic cores of the nanodroplets did not undergo hydrolysis because they were isolated from the water in the bulk phase.

To achieve accurate molecular properties, rigorous consideration of corrections to the Born-Oppenheimer approximation (BOA) is warranted. This work employs a finite difference method to calculate the Diagonal Born-Oppenheimer Correction (DBOC) at various levels of density functional theory (DFT). These calculations are systematically compared with the reference values obtained at CCSD/aug-cc-pVTZ level. DBOC values are calculated for H, HO, HO, HS, HCl, HCN, HF, HNC, NH, CH, OH, NH, and CH molecules. Systematic examinations are performed using six exchange-correlation functionals (SVWN, PBE, B3LYP, PBE0, ωB97XD, M06-2X) combined with six basis sets (6-31G(d,p), 6-31++G(d,p), 6-311G(d,p), 6-311++G(d,p), cc-pVTZ, aug-cc-pVTZ). Compared with those "reference values", our analysis reveals significant error cancellation phenomena for specific functional/basis set combinations. Notably, minimal basis sets such as 6-31G(d,p) prove sufficient for DBOC computation across all small molecules examined. The introduction of diffuse functions demonstrates negligible improvement in accuracy while substantially increasing computational expense and occasionally introducing numerical instability. Furthermore, our results indicate that meta-GGA functionals (e.g., M06-2X, ωB97XD) require increased integration grid density to ensure numerical precision. Based on comparative accuracy and computational efficiency, the B3LYP/6-311G(d,p) and PBE/6-311G(d,p) levels are recommended for DBOC calculations involving hydrogen atoms for these small molecule systems. The finite difference method employed in this study, relying on wave function calculations, demonstrates broad applicability. The implementation is also quite simple, i.e., requiring handling the wave function data and the overlap integral calculations, making it a highly simple and efficient method for calculating DBOC. While this methodology proves effective for the current molecular set, extension to more complex systems necessitate further investigation into functional and basis set dependencies.

Nucleotide fragmentation after photoexcitation in the ultraviolet is a potential cause for damage to DNA strands. Consequently, the fragmentation process needs to be explored to understand the stability of nucleotides on a molecular level. Here, we present wavelength-dependent relative photoabsorption cross section measurements of [dAMP-H] below the photodetachment threshold, which lead to fragmentation along several different channels. Several spectral features are observed in the broad absorption peak in the range of 240 to 270 nm, the resolution of which we attribute to the low temperature of 3 K achieved in our cryogenic 16-pole radiofrequency wire trap. These features likely originate from different Franck-Condon-active vibrational bands in only one or two different conformers. Quantum chemical calculations predict that the spectrum originates from a strong ππ* excitation located at the adenine moiety. Furthermore, the wavelength-dependent yield of the five observed photofragments was studied. This revealed no preferred single photofragment, but showed different trends for different fragments as a function of photon energy. Finally, an absolute photofragmentation cross section of [dAMP-H] was obtained by comparison with the photodetachment cross section of I.

Our understanding of the roles metal-bearing molecules play in interstellar chemistry is limited by the lack of rotational spectroscopic data crucial for astronomical identification/detection. Although calcium is the second most abundant alkaline earth metal in space (after magnesium), only two calcium-bearing molecules have been detected in space, both in the circumstellar envelope of the evolved carbon-rich star IRC+10216. In this work, we report the rotational, fine, and hyperfine structure of two linear calcium-bearing molecules, CaCN and CaCH, in their Σ ground electronic states. These findings both confirm the hypothesized ionic metal-ligand bonding characteristics of this class of molecules that make them potential candidates for optical cooling applications and point the way to detecting these and other calcium-bearing molecules in carbon-rich stars.

We assess the competing preference for hydrogen and chalcogen bonding in the aqueous heterodimers of the chalcogen hydrides HO-HX (X = S, Se, Te). We employ the CCSD(T) method near the complete basis set limit and include an explicit account of anharmonic zero-point energy corrections to establish accurate binding energies. We identify three bonding motifs in the HO-HX dimers, namely, HX (i) donating a hydrogen bond, (ii) accepting a hydrogen bond, and (iii) donating a chalcogen bond, and observe the emergence of chalcogen bonds to water for HSe and HTe. The hydrogen bond donated by a water molecule is consistently more stable than the hydrogen bond donated by the HX (X = S, Se, Te) molecule, with the strength of the former decreasing by a smaller margin than the latter down the chalcogen series. Conversely, the chalcogen bond becomes stronger progressing from HSe, in which it is weaker, to HTe, in which it is more stable than the two other bonding motifs. As a result, the global minimum for HO-HTe is chalcogen bonded. The analysis of the bonding using quasi-atomic orbitals (QUAOs) offers insights into the nature of the chalcogen- and hydrogen-bond accepting bonding motifs. Specifically, the water molecule prefers to accept hydrogen bonds from its mixed / hybrid lone pair and chalcogen bonds from its primarily -hybridized lone pair. In contrast, the heavier chalcogen hydrides prefer to accept hydrogen bonds from their primarily -hybridized lone pairs. A remarkable linear correlation exists between the QUAO-derived atomic charges localized on the donor and acceptor heavy atoms and the respective binding energies of the heterodimers.

Fluorescent 1,8-naphthalimide dyes are often used as chemosensors and imaging agents, but there is a need for modified molecular designs that exploit Förster resonance energy transfer (FRET) to produce red-shifted emission wavelengths. This study compared the capacity of multicomponent 1,8-naphthalimide-squaraine and 1,8-naphthalimide-squaraine rotaxane conjugates to act as FRET pairs and produce a very large pseudo-Stokes shift. Evidence for FRET from a 1,8-naphthalimide donor to a squaraine acceptor included diagnostic changes in the fluorescence emission profile and a shorter 1,8-naphthalimide excited-state lifetime. FRET was more efficient when the conjugate's squaraine component was encapsulated as a rotaxane. Notably, the FRET efficiency for a 1,8-naphthalimide-squaraine rotaxane pentad increased in more polar solvents. To demonstrate potential as a practically useful chemosensor, a boronate-based analogue was synthesized and used to detect the presence of hydrogen peroxide in living cells by producing a ratiometric change in deep-red fluorescence with a pseudo-Stokes shift of 254 nm.

In this work, accurate potential energy surfaces (PESs) of the neutral molecule SO(X̃A') and the anion SO(X̃A″) were constructed using high-level explicitly correlated CCSD(T)-F12 and MRCI-F12+Q methods with the cc-pCVQZ-F12 basis set, in which the PESs were represented by the neural network approach. Based on the PESs, we investigated the vibrational spectra of SO(X̃A') and SO(X̃A″), the photoelectron spectrum of the SO(X̃A″) anion with hot bands, and associated isotope effects involving S, S, S, S, O, and O via a rigorous quantum mechanical approach. It was found that the calculated isotope ratios of SO(X̃A')/SO(X̃A″) and the photoelectron spectrum for SO exhibit excellent agreement with experimental results. Associated isotope effects in the photoelectron spectrum are observed to be notably small, manifested by minor shifts in both peak positions and peak intensities. Vibrational wave function analysis reveals that the photoelectron spectrum of SO(X̃A″) is dominated by a strong vibrational progression, 3, corresponding to the S-S stretching vibrational mode. Relatively weaker progressions are assigned to coupled vibrational states involving (S-S stretching) and (S-O stretching) modes, namely, the 31 and 31 progressions. The mode specificity in the photoelectron spectrum of SO(X̃A″) is qualitatively consistent with the relative amplitudes of the normal coordinate displacement (Δ) for vibrational modes during the ionization process.

In this work, we address one of the most fundamental questions in cluster science─how do the structure and properties evolve from clusters to crystals? Using density functional theory (DFT), we focus our study on the evolution of structure and magnetism in iron-chloride systems, from clusters to monolayers. The choice of this system is motivated by the recent experimental confirmation of one of the author's earlier theoretical prediction that the FeCl cluster is magnetic with a spin magnetic moment of 4 μ localized at the Fe site, while its dimer, FeCl, is antiferromagnetic. Similarly, FeCl cluster is magnetic with a total spin magnetic moment of 5 μ, with 4 μ localized at the Fe site and 1 μ distributed over the Cl sites. The dimer clusters FeCl and FeCl have an antiferromagnetic ground state, and upon Li-functionalization, both can be magnetically transformed from antiferromagnetic to ferromagnetic states. In contrast, FeCl and FeCl monolayers exhibit different magnetic ground states in their periodic forms: FeCl is ferromagnetic (FM), but in FeCl, the antiferromagnetic (AFM) and FM states are energetically nearly degenerate. Such a difference arises due to the different chemical coordination of the Fe atoms with the Cl atoms, caused by their different oxidation states, which is +2 in FeCl and +3 in FeCl, respectively. Interestingly, Li-functionalization allows both FeCl and FeCl monolayers to be ferromagnetic. Our study highlights that several, but not all, electronic and magnetic characteristics of isolated clusters are preserved in the extended periodic structures. This systematic investigation of iron-halide clusters is expected to inspire further experimental and theoretical exploration into the magnetism of other transition metal halides.

We benchmark second-order perturbative corrections to the Restricted Active Space Configuration Interaction in the hole and particle approximation, RAS(,), for valence singlet and triplet excitations in a set of organic molecules. Two partitioning schemes, Epstein-Nesbet (EN) and Davidson-Kapuy (DK), were assessed against NEVPT2 and reference data from the literature. The lack of dynamic correlation in RAS(,) leads to a systematic overestimation of singlet excitation energies by ∼0.8 eV, with much smaller errors for triplets. EN perturbation provides only marginal improvement and increases statistical scatter, whereas DK yields a more consistent correction but tends to overcompensate. Introducing an energy level shift in the DK partition effectively removes this bias, producing excitation energies of comparable accuracy to NEVPT2. An optimal shift of ε ≈ 0.55 a.u. for singlets and slightly larger values for triplets was found to be broadly transferable across the data set, with ε in the range 0.4-0.6 a.u. offering a robust compromise. Analysis of second-order contributions shows that the dominant 11 terms act synergistically with the variational singles, resembling a state-specific orbital relaxation, while the more expensive 12 and 22 terms have a minor impact, suggesting a route to cheaper, targeted perturbative schemes. DK-based corrections exhibit weak basis-set dependence, enabling efficient composite strategies in which large-basis RAS(,) energies are combined with small-basis DK+shift corrections, achieving significant computational savings with minimal loss of accuracy.