Second-order Perturbation Theory Methods Research Articles

Study of Photoselectivity in Linear Conjugated Chromophores Using the XMS-CASPT2 Method.

Photoisomerization, the structural alteration of molecules upon absorption of light, is crucial for the function of biological chromophores such as retinal in opsins, proteins vital for vision and other light-sensitive processes. The intrinsic selectivity of this isomerization process (i.e., which double bond in the chromophore is isomerized) is governed by both the inherent properties of the chromophore and its surrounding environment. In this study, we employ the extended multistate complete active space second-order perturbation theory (XMS-CASPT2) method to investigate photoisomerization selectivity in linear conjugated chromophores, focusing on two simple molecular models resembling retinal. By analyzing electronic energies, intramolecular charge separation, and conical intersection topographies in the gas phase, we show that the photoproduct formed by rotation around the double bond near the Schiff base is energetically favored. The topographic differences at the conical intersections leading to different photoproducts reveal differences in photodynamics. In multiphoton excitation, the primary photoproduct typically reverts to the initial configuration rather than rotating around a different double bond. Our study offers new insights into the photodynamics of photoisomerizing double bonds in π-conjugated chromophores. We anticipate that our findings will provide valuable perspectives for advancing the understanding of biological chromophores and for designing efficient photochemical switches with applications in molecular electronics and phototherapy.

Equation-of-motion regularized orbital-optimized second-order perturbation theory with the density-fitting approximation.

The density-fitted equation-of-motion (EOM) orbital-optimized second-order perturbation theory (DF-EOM-OMP2) method is presented for the first time. In addition, κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods are implemented with the addition of κ-regularization. The accuracy of the DF-EOM-OMP2, κ-DF-EOM-MP2, and κ-DF-EOM-OMP2 methods are compared to the density-fitted EOM-MP2 (DF-EOM-MP2), EOM coupled-cluster (CC) singles and doubles (DF-EOM-CCSD), and EOM-CCSD with the triples excitation correction model [EOM-CCSD(fT)] for excitation energies of many closed- and open-shell chemical systems. The excitation energies computed using different test cases and methods were compared to the EOM-CCSD(fT) method and mean absolute errors (MAEs) are presented. The MAE values of closed- and open-shell cases (closed-shell organic chromophores set, open-shell set, peptide radicals set, and radical set) according to the EOM-CCSD(fT) method show that the κ-regularization technique yields highly accurate results for the first excited states. Our results indicate that the κ-DF-EOM-MP2 and κ-DF-EOM-OMP2 methods perform noticeably better than the DF-EOM-MP2 and DF-EOM-OMP2 methods. They approach the EOM-CCSD quality, at a significantly reduced cost, for the computation of excitation energies. Especially, the κ-DF-EOM-MP2 method provides outstanding results for most test cases considered. Overall, we conclude that the κ-versions of DF-EOM-MP2 and DF-EOM-OMP2 emerge as a useful computational tool for the study of excited-state molecular properties.

Ultrafast Photoinduced Dynamics in 1,3-Cyclohexadiene: A Comparison of Trajectory Surface Hopping Schemes†.

Photoinduced nonadiabatic processes play a crucial role in a wide range of disciplines, from fundamental steps in biology to modern applications in advanced materials science. A theoretical understanding of these processes is highly desirable, and trajectory surface hopping (TSH) has proven to be a well-suited framework for a wide range of systems. In this work, we present a comprehensive comparison between two TSH algorithms, the conventional Tully's fewest switches surface hopping (FSSH) scheme and the Landau-Zener surface hopping (LZSH), to study the photoinduced ring-opening of 1,3-cyclohexadiene (CHD) to 1,3,5-hexatriene at the spin-flip time-dependent density functional theory (SF-TDDFT) level of theory. Additionally, we compare our results with a literature study at the extended multistate complete active space second-order perturbation theory method (XMS-CASPT2) level of theory. Our results show that the average population and lifetimes estimated with LZSH using SF-TDDFT are closer to the literature (using multireference methods) than those estimated with FSSH using SF-TDDFT. The latter speaks in favor of applying LZSH in combination with the SF-TDDFT method to study larger and more complex systems such as molecular photoswitches where the CHD molecule acts as a backbone. In addition, we present an implementation of Tully's FSSH algorithm as an extension to the PySurf software package.

Ab Initio Calculation of UV-vis Absorption of Parent Mg, Fe, Co, Ni, Cu, and Zn Metalloporphyrins.

Relativistic restricted active space (RAS) second-order multireference perturbation theory (MRPT2) methods, incorporating spin-orbit (SO) coupling perturbatively via state interaction (SO-MRPT2/RASSCF), were used to reproduce the absorption spectra of parent metalloporphyrins containing the Mg2+, Zn2+, Co2+, Ni2+, Cu2+, or FeCl2+ ions in the 12,500-40,000 cm-1 region. Particular attention was paid to the interaction between the porphyrin ring and the metal 3d electrons in states of different multiplicities (we used metal 3d and double d-shell or 3d' orbitals). For this class of compounds, the N-electron valence state perturbation theory (NEVPT2) method is superior to the complete active space perturbation theory (CASPT2) and successfully reproduces the energies of all four characteristic transitions (Q, B, N, and L) of closed-shell metalloporphyrins. Inclusion of SO coupling was found to have very little effect on excitation energies and oscillator strengths. For FeCl2+ porphyrin, we treated ligand-to-metal charge-transfer (LMCT; π,d), metal ligand field (d,d), and metal-to-ligand charge-transfer (MLCT; d,π*) transitions within the same framework. The broad and intense spectral features associated with its B (Soret) band are attributed to multiconfigurational LMCT (d,π*) bands involving strong metal-ligand orbital mixing.

Theoretical insights into the photophysics of an unnatural base Z: A MS-CASPT2 investigation.

We have employed the highly accurate multistate complete active space second-order perturbation theory (MS-CASPT2) method to investigate the photoinduced excited state relaxation properties of one unnatural base, namely Z. Upon excitation to the S2 state of Z, the internal conversion to the S1 state would be dominant. From the S1 state, two intersystem crossing paths leading to the T2 and T1 states and one internal conversion path to the S0 state are possible. However, considering the large barrier to access the S1 /S0 conical intersection and the strong spin-orbit coupling between S1 and T2 states (>40 cm-1 ), the intersystem crossing to the triplet manifolds is predicted to be more preferred. Arriving at the T2 state, the internal conversion to the T1 state and the intersystem crossing back to the S1 state are both possible considering the S1 /T2 /T1 three-state intersection near the T2 minimum. Upon arrival at the T1 state, the deactivation to S0 can be efficient after overcoming a small barrier to access T1 /S0 crossing point, where the spin-orbit coupling (SOC) is as large as 39.7 cm-1 . Our present work not only provides in-depth insights into the photoinduced process of unnatural base Z, but can also help the future design of novel unnatural bases with better photostability.

Interpreting the Cu-O2 Antibonding Nature in Two Cu-O2 Complexes from Cu L-Edge X-ray Absorption Spectra.

Cu-O2 structures play important roles in bioinorganic chemistry and enzyme catalysis, where the bonding between the Cu and O2 parts serves as a fundamental research concern. Here, we performed a multiconfigurational study on the copper L2,3-edge X-ray absorption spectra (XAS) of two copper enzyme model complexes to gain a better understanding of the antibonding nature from the clearly interpreted structure-spectroscopy relation. We obtained spectra in good agreement with the experiments by using the restricted active space second-order perturbation theory (RASPT2) method, which facilitated reliable chemical analysis. Spectral feature interpretations were supported by computing the spin-orbit natural transition orbitals. All major features were assigned to be mainly from Cu 2p to antibonding orbitals between Cu 3d and O2 π*, Cu 3d-πO-O* (type A), and a few also to mixed antibonding/bonding orbitals between Cu 3d and O2 π, Cu 3d ± πO-O (type M). Our calculations provided a clear illustration of the interactions between Cu 3d and O2 π*/π orbitals that are carried in the metal L-edge XAS.

Photophysics of tz Adenine and tz Guanine fluorescent nucleobases embedded into DNA and RNA.

UV-VIS photoinduced events of tz A and tz G embedded into DNA and RNA are described by combining the Extended Multi-State Second-Order Perturbation Theory (XMS-CASPT2) and electrostatic embedding molecular mechanics methods (QM/MM). Our results point out that the S1 1 (ππ* La ) state is the bright state in both environments. After the photoexcitation to the S1 1 (ππ* La ) state, the electronic population evolves barrierless towards its minimum, from where the excess of energy can be dissipated by fluorescence. As the minimum energy crossing point structure between the ground and first bright states lies in a high-energy region, the direct internal conversion to the ground state is an unviable mechanism. Other spectroscopic properties (for instance, absorption and Stokes shifts) and comparisons with photochemical properties of canonical nucleobases are also provided.

Molecular properties of TCNQ and anions

The purpose of the work is to calculate accurate values of molecular properties of tetracyanoquinodimethane (TCNQ) and anions using the complete active space self-consistent field and complete active space second-order perturbation theory methods. The accuracy has been evaluated using several basis sets and active spaces. The calculated properties have, in many cases, been confirmed by experimental data (within parentheses), e.g., 9.54 eV (9.61 eV) and 3.36 eV (3.38 eV) for the ionization potential and electron affinity, respectively, of TCNQ; 3.12 eV (3.01 eV) and 3.54 eV (3.42 or 3.60 eV) for transition energies to the two lowest-lying excited singlet states of TCNQ; − 0.03, 0.46 and 1.44 eV (0, 0.5 and 1.4 eV) for electronic energies in electron attachment of TCNQ forming hbox {TCNQ}^-; and 3.88 eV (3.71 eV) for the transition energy to the second lowest-lying excited singlet state of hbox {TCNQ}^{2-}. Further, the calculations have brought insight into some experimental observations, e.g., the shape of the fluorescence spectrum of TCNQ at 3–4 eV.

Tuning functionalized hexagonal boron nitride quantum dots for full visible-light fluorescence emission.

Tunable photoluminescence has been observed in hexagonal boron nitride quantum dots (BNQDs), but the underlying luminescence mechanism remains elusive. In this study, we examine excited-state properties of several functionalized BNQDs models using density functional theory (DFT), time-dependent DFT, and multistate complete active space second-order perturbation theory (MS-CASPT2) methods. Unlike reported graphene quantum dots, photoluminescence of BNQDs is not affected by their sizes (<2.5 nm). Instead, the embedded single sp3 carbon atom connecting different functional groups can tune emission colors of BNQDs, whose emission wavelength cover full range of visible light and even extend toward near-infrared region. Further analysis reveals that both exciton self-trapping and electron-hole separation decrease HOMO-LUMO energy gaps, leading to large Stokes shifts. Moreover, uneven and even hybridizations induce blue- and red-shifted emission spectra. These findings provide novel insights into full-spectrum emission of BNQDs modified with functional groups.

Photodissociation dynamics and UV absorption spectrum of acetone oxide (CH3)2COO.

The photodynamics and B1A' ← X1A' absorption spectrum of acetone oxide, (CH3)2COO, are studied theoretically from first principles. The underlying adiabatic potential energy curves (and surfaces) are computed by a second-order multireference perturbation theory method and diabatized using a diabatization by ansatz scheme. To confirm the results, for selected geometries EOM-CCSD and XMS-RS2C calculations were also performed. The dynamical calculation rests on the multi-configuration time-dependent Hartree wavepacket propagation method. The experimental absorption spectrum is reproduced satisfactorily. This result serves to validate the Hamiltonian model built within the quasi-diabatic representation. Contrary to the smallest Criegee intermediate, CH2OO, it is found that the vibronic coupling between the B and C states of (CH3)2COO plays an essential role in reproducing the experimental absorption spectrum. Time-dependent electronic populations reveal a faster decay than for the smaller system CH2OO. This is interpreted in terms of the stronger coupling between the B and C states in the larger system leading to a shorter lifetime for the B state than in CH2OO.

Thermally activated delayed fluorescence of a Ir(III) complex: absorption and emission properties, nonradiative rates, and mechanism.

One recent experimental study reported a Ir(III) complex with thermally activated delayed fluorescence (TADF) phenomenon in solution, but its luminescent mechanism is elusive. In this work, we combined density functional theory (DFT), time-dependent DFT (TDDFT) and multi-state complete active space second-order perturbation theory (MS-CASPT2) methods to investigate excited-state properties, photophysics, and emission mechanism of this Ir(III) complex. Two main absorption bands observed in experiments can be attributed to the electronic transition from the S0 state to the S1 and S2 states; while, the fluorescence and phosphorescence are generated from the S1 and T1 states, respectively. Both the S1 and T1 states have clear metal-to-ligand charge transfer (MLCT) character. The present computational results reveal a three-state model including the S0, S1 and T1 states to rationalize the TADF behavior. The small energy gap between the S1 and T1 states benefits the forward and reverse intersystem crossing (ISC and rISC) processes. At 300 K, the rISC rate is five orders of magnitude larger than the phosphorescence rate therefore enabling TADF. At 77 K, the rISC rate is sharply decreased but remains close to the phosphorescence rate; therefore, in addition to the phosphorescence, the delayed fluorescence could also contribute to the experimental emission. The estimated TADF lifetime agrees well with experiments, 9.80 vs. 6.67 μs, which further verifies this three-state model.

Excited-State Properties and Relaxation Pathways of Selenium-Substituted Guanine Nucleobase in Aqueous Solution and DNA Duplex.

The excited-state properties and relaxation mechanisms after light irradiation of 6-selenoguanine (6SeG) in water and in DNA have been investigated using a quantum mechanics/molecular mechanics (QM/MM) approach with the multistate complete active space second-order perturbation theory (MS-CASPT2) method. In both environments, the S11(nSeπ5*) and S21(πSeπ5*) states are predicted to be the spectroscopically dark and bright states, respectively. Two triplet states, T13(πSeπ5*) and T23(nSeπ5*), are found energetically below the S2 state. Extending the QM region to include the 6SeG-Cyt base pair slightly stabilizes the S2 state and destabilizes the S1, due to hydrogen-bonding interactions, but it does not affect the order of the states. The optimized minima, conical intersections, and singlet–triplet crossings are very similar in water and in DNA, so that the same general mechanism is found. Additionally, for each excited state geometry optimization in DNA, three kind of structures (“up”, “down”, and “central”) are optimized which differ from each other by the orientation of the C=Se group with respect to the surrounding guanine and thymine nucleobases. After irradiation to the S2 state, 6SeG evolves to the S2 minimum, near to a S2/S1 conical intersection that allows for internal conversion to the S1 state. Linear interpolation in internal coordinates indicate that the “central” orientation is less favorable since extra energy is needed to surmount the high barrier in order to reach the S2/S1 conical intersection. From the S1 state, 6SeG can further decay to the T13(πSeπ5*) state via intersystem crossing, where it will be trapped due to the existence of a sizable energy barrier between the T1 minimum and the T1/S0 crossing point. Although this general S2 → T1 mechanism takes place in both media, the presence of DNA induces a steeper S2 potential energy surface, that it is expected to accelerate the S2 → S1 internal conversion.

Halogen Bond of Halonium Ions: Benchmarking DFT Methods for the Description of NMR Chemical Shifts.

Because of their anisotropic electron distribution and electron deficiency, halonium ions are unusually strong halogen-bond donors that form strong and directional three-center, four-electron halogen bonds. These halogen bonds have received considerable attention owing to their applicability in supramolecular and synthetic chemistry and have been intensely studied using spectroscopic and crystallographic techniques over the past decade. Their computational treatment faces different challenges to those of conventional weak and neutral halogen bonds. Literature studies have used a variety of wave functions and DFT functionals for prediction of their geometries and NMR chemical shifts, however, without any systematic evaluation of the accuracy of these methods being available. In order to provide guidance for future studies, we present the assessment of the accuracy of 12 common DFT functionals along with the Hartree–Fock (HF) and the second-order Møller–Plesset perturbation theory (MP2) methods, selected from an initial set of 36 prescreened functionals, for the prediction of 1H, 13C, and 15N NMR chemical shifts of [N–X–N]+ halogen-bond complexes, where X = F, Cl, Br, and I. Using a benchmark set of 14 complexes, providing 170 high-quality experimental chemical shifts, we show that the choice of the DFT functional is more important than that of the basis set. The M06 functional in combination with the aug-cc-pVTZ basis set is demonstrated to provide the overall most accurate NMR chemical shifts, whereas LC-ωPBE, ωB97X-D, LC-TPSS, CAM-B3LYP, and B3LYP to show acceptable performance. Our results are expected to provide a guideline to facilitate future developments and applications of the [N–X–N]+ halogen bond.

Assessment of the Density-Fitted Second-Order Quasidegenerate Perturbation Theory for Transition Energies: Accurate Computations of Singlet-Triplet Gaps for Charge-Transfer Compounds.

Organic light-emitting diodes (OLEDs) have been of significant interest because of their superior performance and low cost of production. Thermally activated delayed fluorescence (TADF) has attracted significant interest in the OLED technology because it improves the efficiency of OLEDs by harvesting triplet excitons. Therefore, the accurate computation of singlet-triplet transition energies (ΔES1-T1) of charge-transfer molecules is very important. However, the accurate computation of the ΔES1-T1 values is a challenging problem for single-reference methods because of the multireference character of excited states. In this research, an assessment of density-fitted second-order quasidegenerate perturbation theory (DF-QDPT2) [Bozkaya, U.; J. Chem. Theory Comput. 2019, 15, 4415-4429] for singlet-triplet transition energies (ΔES1-T1) of charge-transfer compounds is presented. The performance of the DF-QDPT2 method has been compared with those of several density-functional theory functionals, such as B3LYP, PBE0, M06-2X, ωB97X-D, and MN15; density-fitted state-averaged CASSCF (DF-SA-CASSCF); and single-state single-reference second-order perturbation theory (SS-SR-CASPT2) methods. For the TADF molecules considered, the DF-QDPT2 method provides a mean absolute error (MAE) of 0.13 eV, while the MAE values of DF-SA-CASSCF and SS-SR-CASPT2 are 0.65 and 0.74 eV, respectively. The performances of B3LYP and PBE0 are slightly better than that of DF-QDPT2, while M06-2X and ωB97X-D provide noticeably higher errors compared with DF-QDPT2. Furthermore, the standard CASSCF without state-averaging yields dramatic errors with an MAE value of 3.0 eV. Our results demonstrate that eigenvalues of the DF-QDPT2-effective Hamiltonian can be reliably used for the prediction of singlet-triplet transition energies, while eigenvalues of DF-CASSCF/DF-SA-CASSCF fail to provide accurate predictions. Overall, we conclude that the DF-QDPT2 method emerges as a very useful tool for the computation of excited-state properties.

The Structure of the "Vibration Hole" around an Isotopic Substitution-Implications for the Calculation of Nuclear Magnetic Resonance (NMR) Isotopic Shifts.

Calculations of nuclear magnetic resonance (NMR) isotopic shifts often rest on the unverified assumption that the “vibration hole”, that is, the change of the vibration motif upon an isotopic substitution, is strongly localized around the substitution site. Using our recently developed difference-dedicated (DD) second-order vibrational perturbation theory (VPT2) method, we test this assumption for a variety of molecules. The vibration hole turns out to be well localized in many cases but not in the interesting case where the H/D substitution site is involved in an intra-molecular hydrogen bond. For a series of salicylaldehyde derivatives recently studied by Hansen and co-workers (Molecules 2019, 24, 4533), the vibrational hole was found to stretch over the whole hydrogen-bond moiety, including the bonds to the neighbouring C atoms, and to be sensitive to substituent effects. We discuss consequences of this finding for the accurate calculation of NMR isotopic shifts and point out directions for the further improvement of our DD-VPT2 method.

Performance of density functional theory and orbital-optimised second-order perturbation theory methods for geometries and singlet–triplet state splittings of aryl-carbenes

Carbenes are challenging molecular species for quantum chemistry because of the energetic proximity of their singlet and triplet spin states and the sensitive dependence of spin-state energetics on the geometry of the carbene site. Here we use an extended set of aryl-carbenes to evaluate the performance of density functional theory (DFT) approximations as well as of wave function based perturbation theory approaches (orbital-optimised perturbation theory methods OO-MP2 and OO-SCS-MP2) against reference coupled cluster calculations with singles, doubles and perturbative triples conducted with the aid of the domain-based local pair natural orbitals approach, DLPNO-CCSD(T). In addition to the expected functional dependence, our results document a remarkable discordance in the performance of DFT methods in the sense that the functionals that yield the best geometries do not coincide with those that provide the best spin-state energetics. Analysis of the results allows us to propose a series of methods that are expected to perform reliably within certain confidence limits for the title systems. Additionally, methodological issues regarding the reference singlet–triplet gaps obtained by the DLPNO-CCSD(T) approach are discussed.

A study of H2CO•••HF Complex by Advanced Quantum Mechanical Methods

Our research is focused on the ab initio calculations of the equilibrium structures, binding energies, harmonic and anharmonic vibrational frequencies of a hydrogen-bonded complex, which is formed between formaldehyde H2CO and hydrogen fluoride HF, using the Gaussian 09 package of programs with full 6311++G(3df, 3pd) basis sets in the MP2 second-order perturbation theory and CCSD(T) methods. Harmonic and anharmonic vibrational frequencies and intensities of the H2CO···HF complex were calculated by the Gaussian 16 package programs within the same approximation. Geometric changes and frequency shifts at the complex formation were evaluated. The H2CO···HF complex formation energy and the dipole moment were calculated in the CCSD(T)6311++G(3df, 3pd) approximation to be equal, respectively, to 7.78 kcal/mol and 4.2 D. Changes of the geometric, spectral, and energetic parameters of the complex proved the existence of a stable hydrogen bond F–H···O=CH2 between the components.

Spectroscopic and theoretical studies of UN and UN.

The low-energy electronic states of UN and UN+ have been examined using high-level electronic structure calculations and two-color photoionization techniques. The experimental measurements provided an accurate ionization energy for UN (IE = 50 802 ± 5 cm-1). Spectra for UN+ yielded ro-vibrational constants and established that the ground state has the electronic angular momentum projection Ω = 4. Ab initio calculations were carried out using the spin-orbit state interacting approach with the complete active space second-order perturbation theory method. A series of correlation consistent basis sets were used in conjunction with small-core relativistic pseudopotentials on U to extrapolate to the complete basis set limits. The results for UN correctly obtained an Ω = 3.5 ground state and demonstrated a high density of configurationally related excited states with closely similar ro-vibrational constants. Similar results were obtained for UN+, with reduced complexity owing to the smaller number of outer-shell electrons. The calculated IE for UN was in excellent agreement with the measured value. Improved values for the dissociation energies of UN and UN+, as well as their heats of formation, were obtained using the Feller-Peterson-Dixon composite thermochemistry method, including corrections up through coupled cluster singles, doubles, triples and quadruples. An analysis of the ab initio results from the perspective of the ligand field theory shows that the patterns of electronic states for both UN and UN+ can be understood in terms of the underlying energy level structure of the atomic metal ion.

Extensive and accurate energy levels, transition rates, lifetimes, hyperfine structures and isotope shifts for the Rb XXXVI spectrum of plasma interest

We present relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) spectrum calculations for Rb XXXVI with correlations within the n = 8 complex. An extensive and accurate set of energy levels, wavelengths, line strengths, weighted oscillator strengths, lifetimes, isotope shifts, hyperfine structure and Landé gJ factors has been calculated for lower 127 odd- and even-parity states arising from the 1s2 and 1snl(n=1−8,0≤l≤n−1) configurations in He-like-Rb. Transition rates for electric-multipole (dipole (E1), quadrupole (E2), and octupole (E3)) and magnetic-multipole (dipole (M1), quadrupole (M2), and octupole (M3)) have been also calculated. For the accuracy of our results, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the Second-Order Many-Body Perturbation Theory (MBPT) method. Additionally, Breit interaction and leading quantum electrodynamic effects (QED) have been included as perturbations in extensive relativistic configuration interaction (RCI) calculations. The results arising in the two sets of calculations MCDHF and MBPT are quite close. Our results are compared with other available theory reported in the literature as well as the experimental data listed in the Atomic Spectra Database (ASD) of the National Institute of Standards and Technology (NIST) online database. Good agreement between them has been found. The present complete and consistent results can be used in line identification, plasma modeling and diagnostics of astrophysical plasma.

Extended Dynamically Weighted CASPT2: The Best of Two Worlds.

We introduce a new variant of the complete active space second-order perturbation theory (CASPT2) method that performs similarly to multistate CASPT2 (MS-CASPT2) in regions of the potential energy surface where the electronic states are energetically well separated and is akin to extended MS-CASPT2 (XMS-CASPT2) in case the underlying zeroth-order references are near-degenerate. Our approach follows a recipe analogous to that of XMS-CASPT2 to ensure approximate invariance under unitary transformations of the model states and a dynamic weighting scheme to smoothly interpolate the Fock operator between state-specific and state-average regimes. The resulting extended dynamically weighted CASPT2 (XDW-CASPT2) methodology possesses the most desirable features of both MS-CASPT2 and XMS-CASPT2, that is, the ability to provide accurate transition energies and correctly describe avoided crossings and conical intersections. The reliability of XDW-CASPT2 is assessed on a number of molecular systems. First, we consider the dissociation of lithium fluoride, highlighting the distinctive characteristics of the new approach. Second, the invariance of the theory is investigated by studying the conical intersection of the distorted allene molecule. Finally, the relative accuracy in the calculation of vertical excitation energies is benchmarked on a set of 26 organic compounds. We found that XDW-CASPT2, albeit being only approximately invariant, produces smooth potential energy surfaces around conical intersections and avoided crossings, performing equally well to the strictly invariant XMS-CASPT2 method. The accuracy of vertical transition energies is almost identical to MS-CASPT2, with a mean absolute deviation of 0.01–0.02 eV, in contrast to 0.12 eV for XMS-CASPT2.