Effect of Oriented External Electric Fields on the Electronic Properties of Linear Acenes: A Thermally Assisted Occupation DFT Study.

Recently, oriented external electric fields (OEEFs) have earned much attention due to the possibility of tuning the properties of electronic systems. From a theoretical perspective, one can resort to electronic structure calculations to understand how the direction and strength of OEEFs affect the properties of electronic systems. However, for multi-reference (MR) systems, calculations employing the popular Kohn-Sham density functional theory with the traditional semilocal and hybrid exchange-correlation energy functionals can yield erroneous results. Owing to its decent compromise between accuracy and efficiency for MR systems at the nanoscale (i.e., MR nanosystems), in this study, thermally assisted occupation density functional theory (TAO-DFT) is adopted to explore the electronic properties of n-acenes (n = 2-10), containing n linearly fused benzene rings, in OEEFs, where the OEEFs of various electric field strengths are applied along the long axes of n-acenes. According to our TAO-DFT calculations, the ground states of n-acenes in OEEFs are singlets for all the cases examined. The effect of OEEFs is shown to be significant on the vertical ionization potentials and vertical electron affinities of ground-state n-acenes with odd-number fused benzene rings. Moreover, the MR character of ground-state n-acenes in OEEFs increases with the increase in the acene length and/or the electric field strength.

Electronic Properties of Graphene Nano-Parallelograms: A Thermally Assisted Occupation DFT Computational Study.

In this computational study, we investigate the electronic properties of zigzag graphene nano-parallelograms (GNPs), which are parallelogram-shaped graphene nanoribbons of various widths and lengths, using thermally assisted occupation density functional theory (TAO-DFT). Our calculations revealed a monotonic decrease in the singlet-triplet energy gap as the GNP length increased. The GNPs possessed singlet ground states for all the cases examined. With the increase of GNP length, the vertical ionization potential and fundamental gap decreased monotonically, while the vertical electron affinity increased monotonically. Some of the GNPs studied were found to possess fundamental gaps in the range of 1-3 eV, lying in the ideal region relevant to solar energy applications. Besides, as the GNP length increased, the symmetrized von Neumann entropy increased monotonically, denoting an increase in the degree of the multi-reference character associated with the ground state GNPs. The occupation numbers and real-space representation of active orbitals indicated that there was a transition from the nonradical nature of the shorter GNPs to the increasing polyradical nature of the longer GNPs. In addition, the edge/corner localization of the active orbitals was found for the wider and longer GNPs.

Reply to the Comments on Planar Tetracoordinate Hydrogen: Pushing the Limit of Multicentre Bonding.

Recently, Huo et al. has commented on our communication (Angew. Chem. Int. Ed. 2024, 63, e202317312, DOI: 10.1002/anie.202317312), regarding the multireference character (MRC) of our proposed cluster. Their argument is based on small HOMO-LUMO gap, fractional occupation density (FOD) and CASPT2(12,13) calculations. They also proposed that the singlet planar In4H+ cluster cannot be observed. We present our calculations which reveals that some of their arguments are based on wrong interpretation of data and inadequate use of methodology. While we certainly agree with the strong physical ground of FOD, CASSF and CASPT2 methodology, we believe that such analysis for clusters is not adequate.

Impact of the Protein Environment on Two-Photon Absorption Cross-Sections of the GFP Chromophore Anion Resolved at the XMCQDPT2 Level of Theory.

The search for fluorescent proteins with large two-photon absorption (TPA) cross-sections and improved brightness is required for their efficient use in bioimaging. Here, we explored the impact of a single-point mutation close to the anionic form of the GFP chromophore on its TPA activity. We considered the lowest-energy transition of EGFP and its modification EGFP T203I. We focused on a methodology for obtaining reliable TPA cross-sections for mutated proteins, based on conformational sampling using molecular dynamics simulations and a high-level XMCQDPT2-based QM/MM approach. We also studied the numerical convergence of the sum-over-states formalism and provide direct evidence for the applicability of the two-level model for calculating TPA cross-sections in EGFP. The calculated values were found to be very sensitive to changes in the permanent dipole moments between the ground and excited states and highly tunable by internal electric field of the protein environment. In the case of the GFP chromophore anion, even a single hydrogen bond was shown to be capable of drastically increasing the TPA cross-section. Such high tunability of the nonlinear photophysical properties of the chromophore anions can be used for the rational design of brighter fluorescent proteins for bioimaging using two-photon laser scanning microscopy.

Valence and Core Photoelectron Spectra of Aqueous I3- from Multi-Reference Quantum Chemistry.

The I3- molecule is known to undergo substantial structural reorganization upon solvation by a protic solvent, e.g., water. However, the details of this process are still controversially discussed in the literature. In the present study, we combined experimental and theoretical efforts to disentangle this controversy. The valence (5p), N4,5 (4d), and M4,5 (3d) edge photoelectron spectra were measured in an aqueous solution and computed using high-level multi-reference methods. Our previous publication mainly focused on obtaining reliable experimental evidence, whereas in the present article, we focused primarily on theoretical aspects. The complex electronic structure of I3- requires the inclusion of both static and dynamic correlation, e.g., via the multi-configurational perturbation theory treatment. However, the resulting photoelectron spectra appear to be very sensitive to problems with variational stability and intruder states. We attempted to obtain artifact-free spectra, allowing for a more reliable interpretation of experiments. Finally, we concluded that the 3d Photoelectron Spectrum (PES) is particularly informative, evidencing an almost linear structure with a smaller degree of bond asymmetry than previously reported.

Real-Time Extension of TAO-DFT.

Thermally assisted occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Moreover, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

Ab Initio Calculations on the Ground and Excited Electronic States of Thorium-Ammonia, Thorium-Aza-Crown, and Thorium-Crown Ether Complexes.

Positively charged metal-ammonia complexes are known to host peripheral, diffuse electrons around their molecular skeleton. The resulting neutral species form materials known as expanded or liquid metals. Alkali, alkaline earth, and transition metals have been investigated previously in experimental and theoretical studies of both the gas and condensed phase. This work is the first ab initio exploration of an f-block metal-ammonia complex. The ground and excited states are calculated for Th0-3+ complexes with ammonia, crown ethers, and aza-crown ethers. For Th3+ complexes, the one valence electron Th populates the metal's 6d or 7f orbitals. For Th0-2+, the additional electrons prefer occupation of the outer s- and p-type orbitals of the complex, except Th(NH3)10, which uniquely places all four electrons in outer orbitals of the complex. Although thorium coordinates up to ten ammonia ligands, octa-coordinated complexes are more stable. Crown ether complexes have a similar electronic spectrum to ammonia complexes, but excitations of electrons in the outer orbitals of the complex are higher in energy. Aza-crown ethers disfavor the orbitals perpendicular to the crowns, attributed to the N-H bonds pointing along the plane of the crowns.

Spectroscopic Signature of Dynamical Instability of the Aqueous Complex in the Brown-Ring Nitrate Test.

The chemistry of the brown-ring test has been investigated for nearly a century. Though recent studies have focused on solid state structure determination and measurement of spectra, mechanistic details and kinetics, the aspects of solution structure and dynamics remain unknown. We have studied structural fluctuations of the brown-ring complex in aqueous solution with ab-initio molecular dynamics simulations, from which we identified that the classically established pseudo-octahedral [Fe(H2 O)5 (NO)]2+ complex is present along with a square-pyramidal [Fe(H2 O)4 (NO)]2+ complex. Based on the inability in multi-reference calculations to reproduce the experimental UV-vis spectra in aqueous solution by inclusion of thermal fluctuations of the [Fe(H2 O)5 (NO)]2+ complex alone, we propose the existence of an equilibrium between pseudo-octahedral and square-pyramidal complexes. Despite challenges in constructing models reproducing the solid-state UV-vis spectrum, the advanced spectrum simulation tool motivates us to challenge the established picture of a sole pseudo-octahedral complex in solution.

The Adsorption of Small Molecules on the Copper Paddle-Wheel: Influence of the Multi-Reference Ground State.

We report a theoretical study of the adsorption of a set of small molecules (C2H2, CO, CO2, O2, H2O, CH3OH, C2H5OH) on the metal centers of the "copper paddle-wheel"-a key structural motif of many MOFs. A systematic comparison between DFT of different rungs, single-reference post-HF methods (MP2, SOS-MP2, MP3, DLPNO-CCSD(T)), and multi-reference approaches (CASSCF, DCD-CAS(2), NEVPT2) is performed in order to find a methodology that correctly describes the complicated electronic structure of paddle-wheel structure together with a reasonable description of non-covalent interactions. Apart from comparison with literature data (experimental values wherever possible), benchmark calculations with DLPNO-MR-CCSD were also performed. Despite tested methods show qualitative agreement in the majority of cases, we showed and discussed reasons for quantitative differences as well as more fundamental problems of specific cases.

MUREN: a robust and multi-reference approach of RNA-seq transcript normalization.

BACKGROUND: Normalization of RNA-seq data aims at identifying biological expression differentiation between samples by removing the effects of unwanted confounding factors. Explicitly or implicitly, the justification of normalization requires a set of housekeeping genes. However, the existence of housekeeping genes common for a very large collection of samples, especially under a wide range of conditions, is questionable. RESULTS: We propose to carry out pairwise normalization with respect to multiple references, selected from representative samples. Then the pairwise intermediates are integrated based on a linear model that adjusts the reference effects. Motivated by the notion of housekeeping genes and their statistical counterparts, we adopt the robust least trimmed squares regression in pairwise normalization. The proposed method (MUREN) is compared with other existing tools on some standard data sets. The goodness of normalization emphasizes on preserving possible asymmetric differentiation, whose biological significance is exemplified by a single cell data of cell cycle. MUREN is implemented as an R package. The code under license GPL-3 is available on the github platform: github.com/hippo-yf/MUREN and on the conda platform: anaconda.org/hippo-yf/r-muren. CONCLUSIONS: MUREN performs the RNA-seq normalization using a two-step statistical regression induced from a general principle. We propose that the densities of pairwise differentiations are used to evaluate the goodness of normalization. MUREN adjusts the mode of differentiation toward zero while preserving the skewness due to biological asymmetric differentiation. Moreover, by robustly integrating pre-normalized counts with respect to multiple references, MUREN is immune to individual outlier samples.

Controlling Light-Induced Proton Transfer from the GFP Chromophore.

Green Fluorescent Protein (GFP) is known to undergo excited-state proton transfer (ESPT). Formation of a short H-bond favors ultrafast ESPT in GFP-like proteins, such as the GFP S65T/H148D mutant, but the detailed mechanism and its quantum nature remain to be resolved. Here we study in vacuo, light-induced proton transfer from the GFP chromophore in hydrogen-bonded complexes with two anionic proton acceptors, I- and deprotonated trichloroacetic acid (TCA- ). We address the role of the strong H-bond and the quantum mechanical proton-density distribution in the excited state, which determines the proton-transfer probability. Our study shows that chemical modifications to the molecular network drastically change the proton-transfer probability and it can become strongly wavelength dependent. The proton-transfer branching ratio is found to be 60 % for the TCA complex and 10 % for the iodide complex, being highly dependent on the photon energy in the latter case. Using high-level ab initio calculations, we show that light-induced proton transfer takes place in S1 , revealing intrinsic photoacid properties of the isolated GFP chromophore in strongly bound H-bonded complexes. ESPT is found to be very sensitive to the topography of the highly anharmonic potential in S1 , depending on the quantum-density distribution upon vibrational excitation. We also show that the S1 potential-energy surface, and hence excited-state proton transfer, can be controlled by altering the chromophore microenvironment.

Three-Body Excitations in Fock-Space Coupled-Cluster: Fourth Order Perturbation Correction to Electron Affinity and Its Relation to Bondonic Formalism.

In this paper, we present a formulation of highly correlated Fock-space multi-reference coupled-cluster (FSMRCC) methods, including approximate triples on top of the FSMRCC with singles and doubles, which correct the electron affinities by at least at third and up to the fourth order in perturbation. We discuss various partial fourth-order schemes, which are reliable and yet computationally more efficient than the full fourth-order triples scheme. The third-order scheme is called MRCCSD+T*(3). We present two approximate fourth-order schemes, MRCCSD+T*-a(4) and MRCCSD+T*(4). The results that are presented allow one to choose an appropriate fourth-order scheme, which is less expensive and right for the problem. All these schemes are based on the effective Hamiltonian scheme, and provide a direct calculation of the vertical electron affinities. We apply these schemes to a prototype Li2 molecule, using four different basis sets, as well as BeO and CH+. We have calculated the vertical electron affinities of Li2 at the geometry of the neutral Li2 molecule. We also present the vertical ionization potentials of the Li2 anion at the geometry of the anion ground state. We have also shown how to calculate adiabatic electron affinity, though in that case we lose the advantages of direct calculation. BeO has been examined in two basis sets. For CH+, four different basis sets have been used. We have presented the partial fourth-order schemes to the EA in all the basis sets. The results are analyzed to illustrate the importance of triples, as well as highlight computationally efficient partial fourth-order schemes. The choice of the basis set on the electron affinity calculation is also emphasized. Comparisons with available experimental and theoretical results are presented. The general fourth-order schemes, which are conceptually equivalent with the Fock-space multi-reference coupled-cluster singles, doubles, and triplets (MRCCSD+T) methods, based on bondonic formalism, are also presented here in a composed way, for quantum electronic affinity.

Designing Red-Shifted Molecular Emitters Based on the Annulated Locked GFP Chromophore Derivatives.

Bioimaging techniques require development of a wide variety of fluorescent probes that absorb and emit red light. One way to shift absorption and emission of a chromophore to longer wavelengths is to modify its chemical structure by adding polycyclic aromatic hydrocarbon (PAH) fragments, thus increasing the conjugation length of a molecule while maintaining its rigidity. Here, we consider four novel classes of conformationally locked Green Fluorescent Protein (GFP) chromophore derivatives obtained by extending their aromatic systems in different directions. Using high-level ab initio quantum chemistry calculations, we show that the alteration of their electronic structure upon annulation may unexpectedly result in a drastic change of their fluorescent properties. A flip of optically bright and dark electronic states is most prominent in the symmetric fluorene-based derivative. The presence of a completely dark lowest-lying excited state is supported by the experimentally measured extremely low fluorescence quantum yield of the newly synthesized compound. Importantly, one of the asymmetric modes of annulation provides a very promising strategy for developing red-shifted molecular emitters with an absorption wavelength of ∼600 nm, having no significant impact on the character of the bright S-S1 transition.

Ab Initio Analysis of Metal-Ligand Bonding in An(COT)2 with An=Th, U in Their Ground- and Core-Excited States.

Relativistic multireference ab initio wave function calculations with the restricted active space second-order perturbation theory (RASPT2) were performed on thorocene and uranocene to determine the actinide N4,5 -edge and carbon K-edge X-ray absorption near-edge structure (XANES) intensities and the metal-ligand orbital mixing in the ground state and core-excited states. Calculated spectral intensities show very good agreement with the experiments and therefore allow detailed and unambiguous assignment of the observed spectral features. φ-type covalent bonding or antibonding interactions are observed for thorocene in the core-excited states, though not in the ground state. This is because the molecular orbital of φ symmetry, which is the in-phase combination of the ligand Lφ and the Th 5fφ orbitals, can be populated with electrons in core-excited states, whereas it is essentially unoccupied in the ground state. For uranocene, the XANES spectra do not reveal much information beyond multiplet broadening, despite the presence of distinct peaks in the spectra. Every core-excited peak is best characterized by its own set of bond orbitals, as the excited state covalency is clearly different from the ground state covalency.

Photochemical activation of carbon dioxide in Mg+(CO2)(H2O)0,1.

We combine multi-reference ab initio calculations with UV-VIS action spectroscopy to study photochemical activation of CO2 on a singly charged magnesium ion, [MgCO2(H2O)0,1]+, as a model system for the metal/ligand interactions relevant in CO2 photochemistry. For the non-hydrated species, two separated Mg+ 3s-3p bands are observed within 5.0 eV. The low-energy band splits upon hydration with one water molecule. [Mg(CO2)]+ decomposes highly state-selectively, predominantly via multiphoton processes. Within the low-energy band, CO2 is exclusively lost within the excited state manifold. For the high-energy band, an additional pathway becomes accessible: the CO2 ligand is activated via a charge transfer, with photochemistry taking place on the CO2 - moiety eventually leading to a loss of CO after absorption of a second photon. Upon hydration, already excitation into the first and second excited state leads to CO2 activation in the excited state minimum; however, CO2 predominantly evaporates upon fluorescence or absorption of another photon.

Fock-Space Coupled Cluster Theory: Systematic Study of Partial Fourth Order Triples Schemes for Ionization Potential and Comparison with Bondonic Formalism.

In this paper, we have made a systematic study of partial fourth order perturbative schemes due to triples to compute the ionization potential within Fock-space multi-reference coupled-cluster theory. In particular, we have obtained computationally less expensive correlation schemes due to fourth order triples. Prototype examples have been considered to explore the efficacy of the approximate methods mentioned, while the bondonic formalism supporting the bonding phenomenology is also respectively for the first time here advanced.

Diradicalar Character and Ring Stability of Mesoionic Heterocyclic Oxazoles and Thiazoles by Ab Initio Mono and Multi-Reference Methods.

Mesoionics are neutral compounds that cannot be represented by a fully covalent or purely ionic structure. Among the possible mesomeric structures of these compounds are the diradical electronic configurations. Theoretical and experimental studies indicate that some mesoionic rings are unstable, which may be related to a significant diradical character, that until then is not quantified. In this work, we investigated the diradical character of four heterocycles: 1,3-oxazol-5-one, 1,3-oxazol-5-thione, 1,3-thiazole-5-one, and 1,3-thiazole-5-thione. The oxazoles are known to be significatively less stable than thiazoles. DFT and ab initio single (B3LYP, MP2, CCSD, and QCISD) and ab initio multi-reference (MR-CISD) methods with three basis sets (6-311+G(d), aug-cc-pVDZ, and aug-cc-pVTZ) were employed to assess the diradical character of the investigated systems, in gas phase and DMSO solvent, from three criteria: (i) HOMO-LUMO energy gap, (ii) determination of energy difference between singlet and triplet wave functions, and (iii) quantification of the most significant diradical character (y0, determined in the unrestricted formalism). All of the results showed that the diradical character of the investigated systems is very small. However, the calculated electronic structures made it possible to identify the possible origin of the oxazoles instability, which can help the design of mesoionic systems with the desired properties.

Extending spin-symmetry projected coupled-cluster to large model spaces using an iterative null-space projection technique.

Recently, we introduced an orbital-invariant approximate coupled-cluster (CC) method in the spin-projection manifold. The multi-determinantal property of spin-projection means that the parametrization in the spin-extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi-reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin-projected Hartree-Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null-space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F2 and transition metal complexes such as NiO, Mn2 , and [Cu2 O2 ]2+ , which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin-projected Hartree-Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.

Dipole moments of molecules with multi-reference character from optimally tuned range-separated density functional theory.

Dipole moment is the first nonzero moment of the charge density of neutral systems. If a density functional theory (DFT) method is able to yield accurate dipole moments, it should first provide an accurate geometry and then predict a reliable charge distribution for that geometry. In this respect, recent literatures have revealed that most DFT approximations work considerably better for single-reference molecules with respect to multi-reference ones, as may be expected from this fact that DFT utilizes a single configuration state function as reference function to represent the density. Putting together, it seems that as compared to the single-reference systems, situation is slightly more involved in the case of dipole moment calculations of multi-reference molecules. Effort to address this latter issue constitutes the cornerstone of the present investigation. To this end, we rely on a different approach where the new optimally (nonempirically) tuned range-separated hybrid density functionals (OT-RSHs) without invoking any empirical fitting are proposed for predicting the dipole moments of multi-reference molecules containing both main-group elements and transition metals. We have scanned the controlling factors of OT-RSHs like short- and long-range exchange contributions and range-separation parameter with the aim of deriving the best performing models for the purpose. The obtained results unveil that, as compared to the standard range-separated density functionals, our newly developed OT-RSHs not only give an improved description on the dipole moments of the molecules with multi-reference character but also the quality of their predictions is better than other conventional and recently proposed DFT approximations. © 2018 Wiley Periodicals, Inc.

Full-Dimensional Ab Initio Potential Energy Surface and Vibrational Energy Levels of Li2H.

We built a full-dimensional analytical potential energy surface of the ground electronic state of Li2H from ca. 20,000 ab initio multi-reference configuration interaction calculations, including core⁻valence correlation effects. The surface is flexible enough to accurately describe the three dissociation channels: Li (2s ²S) + LiH (¹Σ⁺), Li2 (¹Σg⁺) + H (1s ²S) and 2Li (2s ²S) + H (1s ²S). Using a local fit of this surface, we calculated pure (J = 0) vibrational states of Li2H up to the barrier to linearity (ca. 3400 cm-1 above the global minimum) using a vibrational self-consistent field/virtual state configuration interaction method. We found 18 vibrational states below this barrier, with a maximum of 6 quanta in the bending mode, which indicates that Li2H could be spectroscopically observable. Moreover, we show that some of these vibrational states are highly correlated already ca. 1000 cm-1 below the height of the barrier. We hope these calculations can help the assignment of experimental spectra. In addition, the first low-lying excited states of each B1, B2 and A2 symmetry of Li2H were characterized.