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.

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.

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.

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.

On the fluorescence enhancement of arch neuronal optogenetic reporters.

The lack of a theory capable of connecting the amino acid sequence of a light-absorbing protein with its fluorescence brightness is hampering the development of tools for understanding neuronal communications. Here we demonstrate that a theory can be established by constructing quantum chemical models of a set of Archaerhodopsin reporters in their electronically excited state. We found that the experimentally observed increase in fluorescence quantum yield is proportional to the computed decrease in energy difference between the fluorescent state and a nearby photoisomerization channel leading to an exotic diradical of the protein chromophore. This finding will ultimately support the development of technologies for searching novel fluorescent rhodopsin variants and unveil electrostatic changes that make light emission brighter and brighter.

Exploring Dyson's Orbitals and Their Electron Binding Energies for Conceptualizing Excited States from Response Methodology.

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 between Bright (11Bu+) and Dark (21Ag-) States in s-trans-Butadiene and s-trans-Hexatriene.

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.

Relief of excited-state antiaromaticity enables the smallest red emitter.

It is commonly accepted that a large π-conjugated system is necessary to realize low-energy electronic transitions. Contrary to this prevailing notion, we present a new class of light-emitters utilizing a simple benzene core. Among different isomeric forms of diacetylphenylenediamine (DAPA), o- and p-DAPA are fluorescent, whereas m-DAPA is not. Remarkably, p-DAPA is the lightest (FW = 192) molecule displaying red emission. A systematic modification of the DAPA system allows the construction of a library of emitters covering the entire visible color spectrum. Theoretical analysis shows that their large Stokes shifts originate from the relief of excited-state antiaromaticity, rather than the typically assumed intramolecular charge transfer or proton transfer. A delicate interplay of the excited-state antiaromaticity and hydrogen bonding defines the photophysics of this new class of single benzene fluorophores. The formulated molecular design rules suggest that an extended π-conjugation is no longer a prerequisite for a long-wavelength light emission.

Description of Sudden Polarization in the Excited Electronic States with an Ensemble Density Functional Theory Method.

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.

Fast and Accurate Computation of Nonadiabatic Coupling Matrix Elements Using the Truncated Leibniz Formula and Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory.

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.

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.

Impact of the Dynamic Electron Correlation on the Unusually Long Excited-State Lifetime of Thymine.

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.

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.

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.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) as a Simple yet Accurate Method for Diradicals and Diradicaloids.

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.

How Beneficial Is the Explicit Account of Doubly-Excited Configurations in Linear Response Theory?

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 1Bu+ 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 1Bu- 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 1Bu+ 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.

Biomechanical Properties of Blood Plasma Extracellular Vesicles Revealed by Atomic Force Microscopy.

While extracellular vesicles (EVs) are extensively studied by various practical applications in biomedicine, there is still little information on their biomechanical properties due to their nanoscale size. We identified isolated blood plasma vesicles that carried on biomarkers associated with exosomes and exomeres and applied atomic force microscopy (AFM) to study them at single particle level in air and in liquid. Air measurements of exosomes revealed a mechanically indented internal cavity in which highly adhesive sites were located. In contrast, the highly adhesive sites of exomeres were located at the periphery and the observed diameter of the particles was ~35 nm. In liquid, the reversible deformation of the internal cavity of exosomes was observed and a slightly deformed lipid bi-layer was identified. In contrast, exomeres were not deformed and their observed diameter was ~16 nm. The difference in diameters might be associated with a higher sorption of water film in air. The parameters we revealed correlated with the well-known structure and function for exosomes and were observed for exomeres for the first time. Our data provide a new insight into the biomechanical properties of nanoparticles and positioned AFM as an exclusive source of in situ information about their biophysical characteristics.