OCT4 Expression in Gliomas Is Dependent on Cell Metabolism.

The OCT4 transcription factor is necessary to maintain cell stemness in the early stages of embryogenesis and is involved in the formation of induced pluripotent stem cells, but its role in oncogenesis is not yet entirely clear. In this work, OCT4 expression was investigated in malignant gliomas. Twenty glioma cell lines and a sample of normal adult brain tissue were used. OCT4 expression was found in all studied glioma cell lines but was not detected in normal adult brain tissue. For one of these lines, OCT4 knockdown caused tumor cell death. By varying the culture conditions of these cells, we unexpectedly found that OCT4 expression increased when cells were incubated in serum-free medium, and this effect was significantly enhanced in serum-free and L-glutamine-free medium. L-glutamine and the Krebs cycle, which is slowed down in serum-free medium according to our NMR data, are sources of α-KG. Thus, our data indicate that OCT4 expression in gliomas may be regulated by the α-KG-dependent metabolic reprogramming of cells.

Unraveling the effect of aromaticity for the dynamics of excited states of single benzene fluorophores.

The photophysical properties of a series of recently synthesized single benzene fluorophores were investigated using ensemble density functional theory calculations. The energetic stability of the ground and excited state species were counterposed against the aromaticity index derived from local vibrational modes. It was found that the large Stokes shift of the fluorophores (up to ca. 5800 cm - 1 ) originates from the effect of electron donating and electron withdrawing substituents rather than π -delocalization and related (anti-)aromaticity. On the basis of nonadiabatic molecular dynamics simulations, the absence of fluorescence from one of the regioisomers was explained by the occurrence of easily accessible S 1 /S 0 conical intersections below the vertical excitation energy level. It is demonstrated in the manuscript that the analysis of local mode force constants and the related aromaticity index represent a useful tool for the characterization of π -delocalization effects in π -conjugated compounds.

Calculation of electric field gradients with the exact two-component (X2C) quasi-relativistic method and its local approximations.

When calculating electric field gradients (EFGs), relativistic and electron correlation effects are crucial for obtaining accurate results, and the commonly used density functional methods produce unsatisfactory results, especially for heavy elements and/or strongly correlated systems. In this work, a stand-alone program is presented, which enables calculation of EFGs from the molecular orbitals supplied by an external high accuracy quantum chemical calculation and includes relativistic effects through the exact two-component (X2C) formalism and efficient local approximations to it. Application to BiN and BiP molecules shows that a high precision can be achieved in the calculation of nuclear quadrupole coupling constants of 209Bi by combining advanced ab initio methods with the X2C approach. For seventeen iron compounds, the Mössbauer nuclear quadrupole splittings (NQS) of 57Fe calculated using a double-hybrid functional method are in very good agreement with the experimental values. It is shown that, for strongly correlated molecules, the double-hybrid functionals are much more accurate than the commonly used hybrid functionals. The computer program developed in this study furnishes a useful utility for obtaining EFGs and related nuclear properties with high accuracy.

Formulation of transition dipole gradients for non-adiabatic dynamics with polaritonic states.

A general formulation of the strong coupling between photons confined in a cavity and molecular electronic states is developed for the state-interaction state-average spin-restricted ensemble-referenced Kohn-Sham method. The light-matter interaction is included in the Jaynes-Cummings model, which requires the derivation and implementation of the analytical derivatives of the transition dipole moments between the molecular electronic states. The developed formalism is tested in the simulations of the nonadiabatic dynamics in the polaritonic states resulting from the strong coupling between the cavity photon mode and the ground and excited states of the penta-2,4-dieniminium cation, also known as PSB3. Comparison with the field-free simulations of the excited-state decay dynamics in PSB3 reveals that the light-matter coupling can considerably alter the decay dynamics by increasing the excited state lifetime and hindering photochemically induced torsion about the C=C double bonds of PSB3. The necessity of obtaining analytical transition dipole gradients for the accurate propagation of the dynamics is underlined.

Ultrafast Excited State Aromatization in Dihydroazulene.

Excited-state aromatization dynamics in the photochemical ring opening of dihydroazulene (DHA) is investigated by nonadiabatic molecular dynamics simulations in connection with the mixed-reference spin-flip (MRSF)-TDDFT method. It is found that, in the main reaction channel, the ring opening occurs in the excited state in a sequence of steps with increasing aromaticity. The first stage lasting ca. 200 fs produces an 8π semiaromatic S1 minimum (S1, min) through an ultrafast damped bond length alternation (BLA) movement synchronized with a partial planarization of the cycloheptatriene ring. An additional ca. 200 fs are required to gain the vibrational energy needed to overcome a ring-opening transition state characterized by an enhanced Baird aromaticity. Unlike other BLA motions of ππ* state, it was shown that their damping is a characteristic feature of aromatic bond-equalization process. In addition, some minor channels of the reaction have also been discovered, where noticeably higher barriers of the S1 non/antiaromatic transition structures must be surmounted. These anti-Baird channels led to reformation of DHA or other closed-ring products. The observed competition between the Baird and anti-Baird channels suggests that the quantum yield of photochemical products can be controllable by tipping their balance. Hence, here we suggest including the concept of anti-Baird, which would expand the applicability of Baird rule to much broader situations.

Variations on the Bergman Cyclization Theme: Electrocyclizations of Ionic Penta-, Hepta-, and Octadiynes.

The Bergman cyclization of (Z)-hexa-3-ene-1,5-diyne to form the aromatic diradical p-benzyne has garnered attention as a potential antitumor agent due to its relatively low cyclization barrier and the stability of the resulting diradical. Here, we present a theoretical investigation of several ionic extensions of the fundamental Bergman cyclization: electrocyclizations of the penta-1,4-diyne anion, hepta-1,6-diyne cation, and octa-1,7-diyne dication, leveraging the spin-flip formulation of the equation-of-motion coupled cluster theory with single and double substitutions (EOM-SF-CCSD). Though the penta-1,4-diyne anion exhibits a large cyclization barrier of +66 kcal mol-1, cyclization of both the hepta-1,6-diyne cation and octa-1,7-diyne dication along a previously unreported triplet pathway requires relatively low energy. We also identified the presence of significant aromaticity in the triplet diradical products of these two cationic cyclizations.

Single-Benzene Dual-Emitters Harness Excited-State Antiaromaticity for White Light Generation and Fluorescence Imaging.

Molecular emitters simultaneously generating light at different wavelengths have wide applications. With a small molecule, however, it is challenging to realize two independent radiative pathways. We invented the first examples of dual-emissive single-benzene fluorophores (SBFs). Two emissive tautomers are generated by synthetic modulation of the hydrogen bond acidity, which opens up pathways for excited-state proton transfer. White light is produced by a delicate balance between the energy and intensity of the emission from each tautomer. We show that the excited-state antiaromaticity of the benzene core itself dictates the proton movements driving the tautomer equilibrium. Using this simple benzene platform, a fluorinated SBF was synthesized with a record high solubility in perfluorocarbon solvents. White light-emitting devices and multicolor imaging of perfluorocarbon nanodroplets in live cells demonstrate the practical utility of these molecules.

Optimization of Three State Conical Intersections by Adaptive Penalty Function Algorithm in Connection with the Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory Method (MRSF-TDDFT).

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 CI3/2/1 turned out to be a narrowly avoided crossing. For butadiene, seven new ME3CI geometries have been located. Because of the removal of the redundancy and the use of the adaptive weighting factor, the convergence rate of the new algorithm is noticeably improved as compared to that of the previously proposed penalty function algorithm. The application to malonaldehyde and butadiene demonstrates that the three-state conical intersections may be more abundant and hence more involved in the photochemistry than previously thought. The recently developed mixed-reference spin flip (MRSF)-TDDFT method yields ME3CI geometries and relative energies quantitatively consistent with the previously reported calculations at a much reduced computational cost.

Analytical derivatives of the individual state energies in ensemble density functional theory. II. Implementation on graphical processing units (GPUs).

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.

Signatures of Conical Intersection Dynamics in the Time-Resolved Photoelectron Spectrum of Furan: Theoretical Modeling with an Ensemble Density Functional Theory Method.

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.

Structural or population dynamics: what is revealed by the time-resolved photoelectron spectroscopy of 1,3-cyclohexadiene? A study with an ensemble density functional theory method.

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 (τS1 = 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.

Mössbauer isomer shifts and effective contact densities obtained by the exact two-component (X2C) relativistic method and its local variants.

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.

Computation of Molecular Electron Affinities Using an Ensemble Density Functional Theory Method.

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.

Theoretical modelling of the dynamics of primary photoprocess of cyclopropanone.

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.

Conical Intersections in Organic Molecules: Benchmarking Mixed-Reference Spin-Flip Time-Dependent DFT (MRSF-TD-DFT) vs Spin-Flip TD-DFT.

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.

Performance Analysis and Optimization of Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) for Vertical Excitation Energies and Singlet-Triplet Energy Gaps.

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.

Eliminating spin-contamination of spin-flip time dependent density functional theory within linear response formalism by the use of zeroth-order mixed-reference (MR) reduced density matrix.

The use of the mixed reference (MR) reduced density matrix, which combines reduced density matrices of the MS = +1 and -1 triplet-ground states, is proposed in the context of the collinear spin-flip-time-dependent density functional theory (SF-TDDFT) methodology. The time-dependent Kohn-Sham equation with the mixed state is solved by the use of spinor-like open-shell orbitals within the linear response formalism, which enables to generate additional configurations in the realm of TD-DFT. The resulting MR-SF-TDDFT computational scheme has several advantages before the conventional collinear SF-TDDFT. The spin-contamination of the response states of SF-TDDFT is nearly removed. This considerably simplifies the identification of the excited states, especially in the "black-box" type applications, such as the automatic geometry optimization, reaction path following, or molecular dynamics simulations. With the new methodology, the accuracy of the description of the excited states is improved as compared to the collinear SF-TDDFT. Several test examples, which include systems typified by strong non-dynamic correlation, orbital (near) degeneracy, and conical intersections, are given to illustrate the performance of the new method.

QTAIM and Stress Tensor Characterization of Intramolecular Interactions Along Dynamics Trajectories of a Light-Driven Rotary Molecular Motor.

A quantum theory of atoms in molecules (QTAIM) and stress tensor analysis was applied to analyze intramolecular interactions influencing the photoisomerization dynamics of a light-driven rotary molecular motor. For selected nonadiabatic molecular dynamics trajectories characterized by markedly different S1 state lifetimes, the electron densities were obtained using the ensemble density functional theory method. The analysis revealed that torsional motion of the molecular motor blades from the Franck-Condon point to the S1 energy minimum and the S1/S0 conical intersection is controlled by two factors: greater numbers of intramolecular bonds before the hop-time and unusually strongly coupled bonds between the atoms of the rotor and the stator blades. This results in the effective stalling of the progress along the torsional path for an extended period of time. This finding suggests a possibility of chemical tuning of the speed of photoisomerization of molecular motors and related molecular switches by reshaping their molecular backbones to decrease or increase the degree of coupling and numbers of intramolecular bond critical points as revealed by the QTAIM/stress tensor analysis of the electron density. Additionally, the stress tensor scalar and vector analysis was found to provide new methods to follow the trajectories, and from this, new insight was gained into the behavior of the S1 state in the vicinity of the conical intersection.

Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism.

The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. In this work, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirely in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. The implementation and benchmarking of the derived formalism will be described in a subsequent article of this series.

Description of ground and excited electronic states by ensemble density functional method with extended active space.

An extended variant of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, the REKS(4,4) method, designed to describe the ground electronic states of strongly multireference systems is modified to enable calculation of excited states within the time-independent variational formalism. The new method, the state-interaction state-averaged REKS(4,4), i.e., SI-SA-REKS(4,4), is capable of describing several excited states of a molecule involving double bond cleavage, polyradical character, or multiple chromophoric units. We demonstrate that the new method correctly describes the ground and the lowest singlet excited states of a molecule (ethylene) undergoing double bond cleavage. The applicability of the new method for excitonic states is illustrated with π stacked ethylene and tetracene dimers. We conclude that the new method can describe a wide range of multireference phenomena.