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It is well-known that photolysis of pyrimidine nucleobases, such as uracil, in an aqueous environment results in the formation of hydrate as one of the main products. Although several hypotheses regarding photohydration have been proposed in the past, e.g., the zwitterionic and “hot” ground-state mechanisms, its detailed mechanism remains elusive. Here, theoretical nonadiabatic simulations of the uracil photodynamics reveal the formation of a highly energetic but kinetically stable intermediate that features a half-chair puckered pyrimidine ring and a strongly twisted intracyclic double bond. The existence and the kinetic stability of the intermediate are confirmed by a variety of computational chemistry methods. According to the simulations, the unusual intermediate is mainly formed almost immediately (∼50–200 fs) upon photoabsorption and survives long enough to engage in a hydration reaction with a neighboring water. A plausible mechanism of uracil photohydration is proposed on the basis of the modeling of nucleophilic insertion of water into the twisted double bond of the intermediate.

The molecular orbital (MO) concept is a useful tool, which relates the molecular ground-state energy with the energies (and occupations) of the individual orbitals. However, analysis of the excited states from linear response computations is performed in terms of the initial state MOs or some other forms of orbitals, e.g., natural or natural transition orbitals. Because these orbitals lack the respective energies, they do not allow developing a consistent orbital picture of the excited states. Herein, we argue that Dyson’s orbitals enable description of the response states compatible with the concepts of molecular orbital theory. The Dyson orbitals and their energies obtained by mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) for the response ground state are remarkably similar to the canonical MOs obtained by the usual DFT calculation. For excited states, the Dyson orbitals provide a chemically sensible picture of the electronic transitions, thus bridging the chasm between orbital theory and response computations.

Internal conversion (IC) between the two lowest singlet excited states, 11Bu+ and 21Ag-, of s-trans-butadiene and s-trans-hexatriene is investigated using a series of single- and multi- reference wave function and density functional theory (DFT) methodologies. Three independent types of the equation-of-motion coupled-cluster (EOMCC) theory capable of providing an accurate and balanced description of one- as well as two-electron transitions, abbreviated as δ-CR-EOMCC(2,3), DIP-EOMCC(4h2p){No}, and DEA-EOMCC(4p2h){Nu} or DEA-EOMCC(3p1h,4p2h){Nu}, consistently predict that the 11Bu+/21Ag- crossing in both molecules occurs along the bond length alternation coordinate. However, the analogous 11Bu+ and 21Ag- potentials obtained with some multireference approaches, such as CASSCF and MRCIS(D), as well as with the linear-response formulation of time-dependent DFT (TDDFT), do not cross. Hence, caution needs to be exercised when studying the low-lying singlet excited states of polyenes with conventional multiconfigurational methods and TDDFT. The multistate many-body perturbation theory methods, such as XMCQDPT2, do correctly reproduce the curve crossing. Among the simplest and least expensive computational methodologies, the DFT approaches that incorporate the contributions of doubly excited configurations, abbreviated as MRSF (mixed reference spin-flip) TDDFT and SSR(4,4), accurately reproduce our best EOMCC results. This is highly promising for nonadiabatic molecular dynamics simulations in larger systems.

Computation of the ionization energies and of the respective Dyson orbitals based on the use of the extended Koopmans theorem (EKT) is implemented in connection with an ensemble density functional theory (eDFT) method, the state-interaction state-averaged spin-restricted ensemble-referenced Kohn–Sham (SI-SA-REKS or SSR) method. The new methodology enables fast computation of the ionization energies and evaluation of the respective Dyson orbitals, the square norms of which are related with the ionization probabilities, in the ground and excited electronic states of molecules. As the application of EKT recycles the intermediate quantities from the SSR analytical energy gradient, evaluation of the ionization energies and probabilities can be carried out on-the-fly during the nonadiabatic molecular dynamics simulations. This opens up a perspective for fast theoretical simulation of the time-resolved photoelectron spectroscopy observations. In the present work, the new methodology is tested in the computation of the ionization energies and Dyson orbitals of several molecules in the ground and excited electronic states, including strongly correlated species, such as the ozone molecule, dissociating chemical bonds, and conical intersections.

The analytic derivative algorithm for the effective contact densities obtained by the exact two-component (X2C) relativistic Hamiltonian is extended to the local approximations to X2C to achieve a higher computational efficiency without losing accuracy. The new algorithm has been implemented in a standalone program, which can utilize the molecular orbitals from state-of-the-art ab initio or density functional theory (DFT) calculations by other quantum chemistry programs in connection with various relativistic Hamiltonians. With the help of the utility program, the effective contact densities as well as the related Mössbauer isomer shifts can be studied by various advanced single-reference and multi-reference ab initio methods as long as the canonical or natural orbitals are available. Using the developed algorithm, the effective contact densities and the Mössbauer isomer shifts in a series of iron compounds and in HgFn (n = 1, 2, 4, and 6) molecules were studied. The obtained results show that (1) adequate account of the static electron correlation significantly improves the agreement of the theoretical 57Fe effective contact densities with the experimental isomer shifts, and (2) the non-monotonous changes of the effective contact density in a series of HgFn compounds are caused by the increasing screening effect due to shrinking of the Hg 5d orbitals.

Time-resolved photoelectron spectra during the photochemical ring-opening reaction of 1,3-cyclohexadiene (CHD) are modeled by an ensemble density functional theory (eDFT) method. The computational methodology employed in this work is capable of correctly describing the multi-reference effects arising in the ground and excited electronic states of molecules, which is important for the correct description of the ring-opening reaction of CHD. The geometries of molecular species along the non-adiabatic molecular dynamics (NAMD) trajectories reported in a previous study of the CHD photochemical ring-opening were used in this work to calculate the ionization energies and the respective Dyson orbitals for all possible ionization channels. The obtained theoretical time-resolved spectra display decay characteristics in a reasonable agreement with the experimental observations; i.e., the decay (and rise) of the most mechanistically significant signals occurs on the timescale of 100–150 fs. This is very different from the excited state population decay characteristics (τ _(S1) = 234 ± 8 fs) obtained in the previous NAMD study. The difference between the population decay and the decay of the photoelectron signal intensity is traced back to the geometric transformation that the molecule undergoes during the photoreaction. This demonstrates the importance of including the geometric information in interpretation of the experimental observations.

Internal conversion (IC) between the two lowest singlet excited states, 1

Sudden polarization (SP) is one of the manifestations of electron transfer in the electronically excited states of molecules. Proposed initially to explain the unusual reactivity of photoexcited olefins, SP often occurs in the excited states of molecules possessing strongly correlated diradical ground state. Theoretical description of SP involves mixing between the singly excited and the doubly excited zwitterionic states, which makes it inaccessible with the use of the popular linear-response time-dependent density functional theory methods. In this work, an extended variant of the state-interaction state-averaged spin-restricted ensemble-referenced Kohn–Sham (SI-SA-REKS, or SSR) method is applied to study SP in a number of organic diradical systems. To this end, the analytical derivative formalism is derived and implemented for the SSR(3,2) method (see the main text for explanation of the acronym), which enables the automatic geometry optimization and obtains the relaxed density matrices as well as the electron binding energies and respective Dyson’s orbitals. Application of the new method to SP in the lowest singlet excited state of ethylene agrees with the results obtained previously with the use of multireference methods of wavefunction theory. A number of interesting manifestations of SP are observed, such as the charge transfer in photoexcited tetramethyleneethene (TME) diradical mediated by the vibrational motion and conductivity switching in the excited state of a donor–acceptor dyad placed in an external electric field.

The mixed-reference spin-flip (MRSF) time-dependent density functional theory (TDDFT) method eliminates the notorious spin contamination of SF-TDDFT, thus enabling identification of states of proper spin-symmetry for automatic geometry optimization and molecular dynamics simulations. Here, we analyze and optimize the MRSF-TDDFT in the calculations of the vertical excitation energies (VEEs) and the singlet-triplet (ST) gaps. The dependence of the obtained VEEs and ST gaps on the intrinsic parameters of the MRSF-TDDFT method is investigated, and prescriptions for the proper use of the method are formulated. For VEEs, MRSF-TDDFT displays similar or better accuracy than SF-TDDFT (ca. 0.5 eV), while considerably outperforming the LR-TDDFT for the ST gaps. As a result, a new functional of STG1X (dubbed here), especially for ST gaps is suggested on the basis of splitting between the components of the atomic multiplets.

The mixed-reference spin-flip time-dependent density functional theory (MRSF-TD-DFT) method eliminates the erroneous spin contamination of the SF-TD-DFT methodology, while retaining the conceptual and practical simplicity of the latter. The availability of the analytic gradient of the energy of the MRSF-TD-DFT response states enables automatic geometry optimization of the targeted states. Here, we apply the new method to optimize the geometry of several S1/S0 conical intersections occurring in typical organic molecules. We demonstrate that MRSF-TD-DFT is capable of producing the correct double-cone topology of the intersections and describing the geometry of the lowest-energy conical intersections and their relative energies with accuracy matching that of the best multireference wavefunction ab initio methods. In this regard, MRSF-TD-DFT differs from many popular single-reference methods, such as, e.g., the linear response TD-DFT method, which fail to produce the correct topology of the intersections. As the new methodology completely eliminates the ambiguity with the identification of the response states as proper singlets or triplets, which is plaguing the SF-TD-DFT calculations, it can be used for automatic geometry optimization and molecular dynamic simulations not requiring constant human intervention.

The spin-restricted ensemble-referenced Kohn-Sham (REKS) method and its state-interaction state-averaged variant (SI-SA-REKS, or SSR) provide computational platform for seamless inclusion of multireference effects into the density functional calculations. The SSR method enables an accurate calculation of the vertical excitation energies for the molecules with multireference ground states and describes conical intersections between the ground and excited states with the accuracy matching the most sophisticated ab initio multireference wave function methods. In this work, the SSR method is formulated and implemented in the context of the long-range corrected density functional tight binding (LC-DFTB) approach. The new LC-DFTB/SSR method enables calculation of the excited electronic states and the S1/S0 conical intersections of very large molecules. The LC-DFTB/SSR method is benchmarked against vertical excitation energies and conical intersection energies and geometries of several organic molecules with π/π* and n/π* transitions. It is demonstrated that the LC-DFTB/SSR method describes these molecules with reasonable accuracy, which can be considerably improved by a slight modification of the LC-DFTB spin polarization parameters.

The factors underlying two possible pathways for the Dihydrocostunolide (DHCL) photochemical ring-opening reaction were investigated; the first pathway returned to the ring-closed conformation of the reactant and the second pathway progressed to the ring-opened product. High-level multi-reference DFT methods were used to optimize the two pathways and the density was analyzed using QTAIM and the stress tensor. Oscillations in the chemical character of the fissile bond were found for the first pathway before and after the conical intersection that steered the reaction back to reactant. Conversely, this behavior was absent for the second pathway that led forward to the product.

A new family of light driven molecular rotary motors, which can be synthesized from easily available precursor compounds and which are capable of completing a full 360° revolution by two photoisomerization steps only, is proposed. The non-adiabatic molecular dynamic simulations show that the photoisomerization steps of the motor's working cycle occur on an ultrafast time scale (ca. 200-300 fs), have a very high quantum yield of isomerization (0.91-0.97), and display high selectivity of torsion in the same direction. It is expected that the new motor should remain operational at lower temperatures than the currently existing motors.

Photodecomposition of cyclopropanone is investigated by static quantum chemical calculations and non-adiabatic molecular dynamics (NAMD) simulations. The quantum chemical calculations are carried out by an ensemble density functional theory (eDFT) method capable of delivering high quality results for the ground and excited electronic states of molecules with dissociating bonds. In the NAMD simulations, this method is combined with a novel trajectory surface hopping (TSH) methodology derived from the exact factorization of the electronic-nuclear wavefunction. An ultrafast biexponential decay of the S1 state of cyclopropanone is predicted, where the short (ca. 30 fs) decay time is due to the trajectories reaching the conical intersection (CI) seam on the first approach and the long (ca. 120 fs) decay time is due to recrossing of the CI seam. The experimentally observed dependence of the dissociation (C3H4O* → C2H4 + CO) quantum yield on the excitation wavelength is correctly reproduced by the NAMD simulations. The dependence is explained by the necessity to excite certain vibrational normal modes (e.g., a ring stretching mode with the frequency of 769 cm-1) to break a lateral C-C bond remaining intact at the geometries of the CI seam.

We present a fast and accurate numerical algorithm for computing the first-order nonadiabatic coupling matrix element (NACME). The algorithm employs the truncated Leibniz formula (TLF) approximation within the finite-difference method, which makes it easily applicable in connection with any wave function-based methodology. In this work, we used the algorithm in connection with the recently developed mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT, MRSF for brevity). The accuracy is assessed for NACME between the singlet electronic states of a dissociating hydrogen molecule. It is demonstrated that an intermediate approximation, TLF(1), affords a negligible numeric error on the order of ∼10⁻¹⁰ a.u. while enabling a fast computation of NACME. As the MRSF method yields the correct description of the dissociation curves of H₂ for all the electronic states involved, the numeric TLF(1)/MRSF NACME values are in excellent agreement with the reference analytical values obtained by the full configuration interaction. For polyatomic molecules, the MRSF NAC vectors agree very closely with the MRCISD NAC vectors. Hence, the proposed protocol is a promising tool for the evaluation of NACMEs.

Non-radiative relaxation of the photoexcited thymine in the gas phase shows an unusually long excited-state lifetime, and, over the years, a number of models, i.e., S1-trapping, S2-trapping, and S1&S2-trapping, have been put forward to explain its mechanism. Here, we investigate this mechanism using non-adiabatic molecular dynamics (NAMD) simulations in connection with the recently developed mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) method. We show that the previously predicted S2-trapping model was due to an artifact caused by an insufficient account of the dynamic electron correlation. The current work supports the S1-trapping mechanism with two lifetimes, τ1 = 30 ± 1 fs and τ2 = 6.1 ± 0.035 ps, quantitatively consistent with the recent time-resolved experiments. Upon excitation to the S2 (ππ*) state, thymine undergoes an ultrafast (ca. 30 fs) S2→S1 internal conversion and resides around the minimum on the S1 (nOπ*) surface, slowly decaying to the ground state (ca. 6.1 ps). While the S2→S1 internal conversion is mediated by fast bond length alternation distortion, the subsequent S1→S0 occurs through several conical intersections, involving a slow puckering motion.

The non-adiabatic dynamics of furan excited in the ππ* state (S2 in the Franck–Condon geometry) was studied using non-adiabatic molecular dynamics simulations in connection with an ensemble density functional method. The time-resolved photoelectron spectra were theoretically simulated in a wide range of electron binding energies that covered the valence as well as the core electrons. The dynamics of the decay (rise) of the photoelectron signal were compared with the excited-state population dynamics. It was observed that the photoelectron signal decay parameters at certain electron binding energies displayed a good correlation with the events occurring during the excited-state dynamics. Thus, the time profile of the photoelectron intensity of the K-shell electrons of oxygen (decay constant of 34 ± 3 fs) showed a reasonable correlation with the time of passage through conical intersections with the ground state (47 ± 2 fs). The ground-state recovery constant of the photoelectron signal (121 ± 30 fs) was in good agreement with the theoretically obtained excited-state lifetime (93 ± 9 fs), as well as with the experimentally estimated recovery time constant (ca. 110 fs). Hence, it is proposed to complement the traditional TRPES observations with the trXPS (or trNEXAFS) measurements to obtain more reliable estimates of the most mechanistically important events during the excited-state dynamics.

Conical intersections control excited state reactivity, and thus, elucidating and predicting their geometric and energetic characteristics are crucial for understanding photochemistry. Locating these intersections requires accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g., multireference perturbation theories such as XMS-CASPT2) are computationally challenging for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn-Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units. We demonstrate that our implementation gives the correct conical intersection topography and energetics for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient, with observed sub-quadratic scaling as a function of molecular size. This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems.

A new adaptive algorithm for penalty function optimization for minimum-energy three-states conical intersections (ME3CI) is suggested. The new algorithm differs from the original penalty function algorithm by (a) removing the redundancy in the target function, (b) using an adaptive increment for the penalty function weighting factor, and (c) using tighter convergence criteria for the energy gap. The latter was introduced to guarantee convergence to a true conical intersection rather than to a narrowly avoided crossing geometry. The new algorithm was tested in the optimization of the ME3CI geometries in butadiene and malonaldehyde, where all of the previously found true ME3CI geometries were recovered. The previously found butadiene's CI

In different branches of time-dependent density functional theory (TDDFT), the static and dynamic electron correlation enters in different ways. The standard spin-conserving linear response (LR-TDDFT) methodology includes explicitly the contributions of the singly-excited configurations; however, it relies on an implicit account of the electron correlation through an (approximate) exchange-correlation (XC) functional. In the mixed-reference spin-flip TDDFT (MRSF-TDDFT), a number of doubly-excited (DE) configurations are explicitly included in the description of their response states. Here, the importance of the explicit account of DE is investigated for the lowest four excited singlet states of all-trans-polyenes up to C₂₄H₂₆. For the optically bright 1B_u⁺ state, the DE contribution in MRSF-TDDFT approaches 10% with the increasing system size. For the optically dark 2Ag⁻ state, the DE contribution increases from ca. 13% (C₄H₆) to nearly 30% (C₂₄H₂₆). An even more considerable DE contribution (∼50%) is observed in the higher 1B_u⁻ states. As LR-TDDFT misses these contributions entirely, its ability to accurately describe the excited states is limited by the XC functional. The hybrid XC functionals with a small fraction of the exact exchange, e.g., B3LYP, may mimic certain effects of DE through the self-interaction error (SIE). However, the description of the 1B_u⁺ state by LR-TDDFT remains poor. On the other hand, MRSF-TDDFT can flexibly take an implicit (through the XC functional) and an explicit (through DE) account of the electron correlation, which enables a more balanced description of various types of the excited states regardless of their character, thus reducing the chances of failure.

Due to their multiconfigurational nature featuring strong electron correlation, accurate description of diradicals and diradicaloids is a challenge for quantum chemical methods. The recently developed mixed-reference spin-flip (MRSF)-TDDFT method is capable of describing the multiconfigurational electronic states of these systems while avoiding the spin-contamination pitfalls of SF-TDDFT. Here, we apply MRSF-TDDFT to study the adiabatic singlet-triplet (ST) gaps in a series of well-known diradicals and diradicaloids. On average, MRSF displays a very high prediction accuracy of the adiabatic ST gaps with the mean absolute error (MAE) amounting to 0.14 eV. In addition, MRSF is capable of accurately describing the effect of the Jahn-Teller distortion occurring in the trimethylenemethane diradical, the violation of the Hund rule in a series of the didehydrotoluene diradicals, and the potential energy surfaces of the didehydrobenzene (benzyne) diradicals. A convenient criterion for distinguishing diradicals and diradicaloids is suggested on the basis of the easily obtainable quantities. In all of these cases, which are difficult for the conventional methods of density functional theory (DFT), MRSF shows results consistent with the experiment and the high-level ab initio computations. Hence, the present study documents the reliability and accuracy of MRSF and lays out the guidelines for its application to strongly correlated molecular systems.

In different branches of time-dependent density functional theory (TDDFT), the static and dynamic electron correlation enters in different ways. The standard spin-conserving linear response (LR-TDDFT) methodology includes

The computation of electron attachment energies (electron affinities) was implemented in connection with an ensemble density functional theory method, the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method. With the use of the extended Koopmans' theorem, the electron affinities and the respective Dyson orbitals are obtained directly for the neutral molecule, thus avoiding the necessity to compute the ionized system. Together with the EKT-SSR (extended Koopmans' theorem-SSR) method for ionization potentials, which was developed earlier, EKT-SSR for electron affinities completes the implementation of the EKT-SSR formalism, which can now be used for obtaining electron detachment as well as the electron attachment energies of molecules in the ground and excited electronic states. The extended EKT-SSR method was tested in the calculation of several closed-shell molecules. For the molecules in the ground states, the EKT-SSR energies of Dyson's orbitals are virtually identical to the energies of the unoccupied orbitals in the usual single-reference spin-restricted Kohn-Sham calculations. For the molecules in the excited states, EKT-SSR predicts an increase of the most positive electron affinity by approximately the amount of the vertical excitation energy. The electron affinities of a number of diradicals were calculated with EKT-SSR and compared with the available experimental data. With the use of a standard density functional (BH&HLYP), the EKT-SSR electron affinities deviate on average by ca. 0.2 eV from the experimental data. It is expected that the agreement with the experiment can be improved by designing density functionals parametrized for ionization energies.

We present, for the ground and first excited states of fulvene, the complete 3-D bond-path framework set B = {(p0,p1), (q0,q1), (r0,r1)} from the quantum theory of atoms in molecules (QTAIM) and B σH = {(pσH0,pσH1), (qσH0,qσH1), (r0,r1)} and B σ = {(pσ0,pσ1), (qσ0,qσ1), (r0,r1)} from the stress tensor within the QTAIM partitioning. We find that both the QTAIM bond-path framework sets B = {(p0,p1), (q0,q1), (r0,r1)} and the stress tensor B σ = {(pσ0,pσ1), (qσ0,qσ1), (r0,r1)} provide a quantitative 3-D rendering of the bonding that is consistent with understanding of the bonding provided by using Lewis structures.

Utilizing the analytic derivative formalism for the Mossbauer isomer shift in connection with the Dirac-exact two-component Normalized Elimination of the Small Component (2c-NESC) method a new appr...

A new family of light-driven molecular rotary motors utilizing the fulgide motif is proposed and its prototype molecule is studied by quantum chemical calculations and nonadiabatic molecular dynamics simulations. The new motor performs pure unidirectional axial rotation of the rotor blade with high quantum efficiency (ϕ ∼ 0.55–0.68) and ultrafast dynamics (⟨t⟩S1 ∼ 200–300 fs) of its successive photoisomerization steps. The photocyclization reaction typical of fulgide compounds is blocked by the design of the new motor and never occurred in the molecular dynamics simulations. The new motors can be synthesized from easily available precursors. In view of its remarkable photoisomerization ability, the new motor represents a prospective class of compounds for the use in nanosized molecular devices.

In this work, a direct mixed quantum-classical dynamics approach is presented, which combines two new computational methodologies. The nuclear dynamics is solved by the decoherence-induced surface hopping based on the exact factorization (DISH-XF) method, which is derived from the exact factorization of the electronic-nuclear wave function and correctly describes quantum decoherence phenomena. The state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS, or SSR, for brevity) electronic structure method is based on ensemble density functional theory (eDFT) and provides correct description of real crossings between the ground and excited Born–Oppenheimer electronic states. The new combined approach has been applied to the excited-state nonadiabatic dynamics of the trans-penta-2,4-dieniminium cation (PSB3). The predicted S1 lifetime of trans-PSB3, τ = 99 ± 51 fs, and the quantum yield of the cis conformation, ϕ = 0.63, agree with the results obtained previously in nonadiabat...

A QTAIM investigation of the torsion in both the clockwise and counter-clockwise directions about the π bonds of the retinal protonated Schiff base chromophore in the lowest electronically excited state provided a detailed description of the changing bonding topology that was sensitive to both the torsion and the direction of torsion. Analysis of the separate torsion calculations demonstrated a clear order of preferred bonding torsion in terms of principles of maximizing bonding. Unusual behavior of the bond ellipticity in the S 1 state was found for the two less favorable bonds for torsion and explained in terms of the presence of weak bonding interactions.