Experimental Excitation Energies Research Articles

An ab initio diabatic study of rovibronic spectra of CN.

An ab initio study of the rovibronic spectra for the cyano radical (CN) based on a diabatic representation is presented. This work considers 17 electronic states, 59 dipole moment curves, 88 spin-orbit coupling curves, and 30 electronic angular momentum coupling curves, which are obtained using the internally contracted multireference configuration interaction method including the Davidson correction (icMRCI + Q) with the aug-cc-pwCV5Z-DK basis set. The diabatic transformations are performed based on a property-based diabatization method to remove the avoided crossings for the D2Π-H2Π and b4Π-24Π pairs. Ab initio potential energy curves of the X2Σ+, B2Σ+, E2Σ+, A2Π, D2Π, H2Π, F2Δ and J2Δ electronic states are shifted to match the experimental electronic excitation energies and the equilibrium internuclear distances. The coupled nuclear motion Schrödinger equations are then solved to obtain the rovibronic spectra of CN for wavenumbers from 0 to 80 000 cm-1. At wavenumbers of 0-30 000 cm-1, our absorption cross sections agree well with available theoretical data. For wavenumbers above 30 000 cm-1, our cross sections are larger than previous data in view of the fact that the transitions involving high-lying electronic states are considered. This work provides an overall prediction of the rovibronic spectrum of CN. Our results are suitable for temperatures below 8000 K and could be useful for the investigations of planetary exploration.

Multinucleon Transfer Studies of the 70Zn (15 MeV/nucleon) + 64Ni System with Focus on Excitation Energy Distributions

Existing high-resolution experimental data collected with the MAGNEX spectrometer were analyzed to investigate peripheral collisions of medium-mass nuclei from the reaction 70Zn (15 MeV/nucleon) + 64Ni. The main focus of this work was to correlate the observed ejectiles with the excitation energy of their progenitors. Experimental excitation energy distributions were generated and compared with the Deep-Inelastic Transfer (DIT) model. This revealed a dominance of direct reaction mechanisms located at low excitation energies and more complex mechanisms at higher energies. Future efforts include further detailed studies of the excitation energy distributions to elucidate the multinucleon transfer mechanisms and to comprehend the resolution limits achievable with medium-mass nuclei such as 70Zn.

When do tripdoublet states fluoresce? A theoretical study of copper(II) porphyrin.

Open-shell molecules rarely fluoresce, due to their typically faster non-radiative relaxation rates compared to closed-shell ones. Even rarer is the fluorescence from states that have two more unpaired electrons than the open-shell ground state, since they involve excitations from closed-shell orbitals to vacant-shell orbitals, which are typically higher in energy compared to excitations from or out of open-shell orbitals. States that are dominated by the former type of excitations are known as tripdoublet states when they can be described as a triplet excitation antiferromagnetically coupled to a doublet state, and their description by unrestricted single-reference methods (e.g., U-TDDFT) is notoriously inaccurate due to large spin contamination. In this work, we applied our spin-adapted TDDFT method, X-TDDFT, and the efficient and accurate static-dynamic-static second order perturbation theory (SDSPT2), to the study of the excited states as well as their relaxation pathways of copper(II) porphyrin; previous experimental works suggested that the photoluminescence of some substituted copper(II) porphyrins originate from a tripdoublet state, formed by a triplet ligand π → π* excitation antiferromagnetically coupled with the unpaired d electron. Our results demonstrated favorable agreement between the X-TDDFT, SDSPT2 and experimental excitation energies, and revealed noticeable improvements of X-TDDFT compared to U-TDDFT, not only for vertical excitation energies but also for adiabatic energy differences. These suggest that X-TDDFT is a reliable tool for the study of tripdoublet state fluorescence. Intriguingly, we showed that the aforementioned tripdoublet state is only slightly above the lowest doublet excited state and lies only slightly higher than the lowest quartet state, which suggests that the tripdoublet of copper(II) porphyrin is long-lived enough to fluoresce due to a lack of efficient non-radiative relaxation pathways; an explanation for this unusual state ordering is given. Indeed, thermal vibration correlation function (TVCF)-based calculations of internal conversion, intersystem crossing, and radiative transition rates confirm that copper(II) porphyrin emits thermally activated delayed fluorescence (TADF) and a small amount of phosphorescence at low temperature (83K), in accordance with experiment. The present contribution is concluded by a few possible approaches of designing new molecules that fluoresce from tripdoublet states.

Structures and Spectroscopic Properties of Polysulfide Radical Anions: A Theoretical Perspective.

The potential involvement of polysulfide radical anions Sn•- is a recurring theme in discussions of the basic and applied chemistry of elemental sulfur. However, while the spectroscopic features for n = 2 and 3 are well-established, information on the structures and optical characteristics of the larger congeners (n = 4-8) is sparse. To aid identification of these ephemeral species we have performed PCM-corrected DFT calculations to establish the preferred geometries for Sn•- (n = 4-8) in the polar media in which they are typically generated. TD-DFT calculations were then used to determine the number, nature and energies of the electronic excitations possible for these species. Numerical reliability of the approach was tested by comparison of the predicted and experimental excitation energies found for S2•- and S3•-. The low-energy (near-IR) transitions found for the two acyclic isomers of S4•- (C2h and C2v symmetry) and for S5•- (Cs symmetry) can be understood by extension of the simple HMO π-only chain model that serves for S2•- and S3•-. By contrast, the excitations predicted for the quasi-cyclic structures Sn•- (n = 6-8) are better described in terms of σ → σ* processes within a localized 2c-3e manifold.

Progress on the magnetic rotation in the nuclei of <italic>A</italic>~60 and <italic>A</italic>~80 mass regions

<p indent="0mm">Nuclear collective rotation, which involves coherent contributions from many nucleons, has been well known for a long time. It is ascribed as a consequence of deformation and gives rise to regular rotational bands, which are characterized by strong electric quadrupole (<italic>E</italic>2) transitions. Studies of the rotational bands in nuclei have been in the forefront of nuclear structure physics and have led to many interesting phenomena including the backbending, superdeformed bands, and chiral doublet bands. In 1990s, a new type of rotational-like sequences, which have strong <italic>M</italic>1 transitions and weak or vanishing <italic>E</italic>2 transitions, have been discovered in weakly deformed or near-spherical nuclei and attracted a lot of interests. This new type of rotational structure cannot be understood in terms of conventional rotation of deformed nuclei but has been successfully interpreted in terms of the shears mechanism. In this interpretation, nuclear orientation is specified by the current distribution rather than the deformation. The magnetic dipole vector arises from proton particles (holes) and neutron holes (particles) in high-<italic>j</italic> orbitals, and rotates around the total angular momentum vector. In the subsequent experimental studies, the magnetic rotation phenomenon were found in the <italic>A</italic>~60, <italic>A</italic>~80, <italic>A</italic>~110, <italic>A</italic>~140, and <italic>A</italic>~190 mass regions. Here, we report the studies of magnetic rotation in the <italic>A</italic>~80 and <italic>A</italic>~60 mass regions. The high-spin structures of⁷⁵As, ⁷⁹Se and ⁶²Cu were respectively populated via ⁷⁰Zn(⁹Be, 1p3n)⁷⁵As, ⁸²Se(α, α3n)⁷⁹Se and ⁵⁴Cr(¹²C, 1p3n)⁶²Cu heavy ion fusion–evaporation reactions. The dipole bands were established for the first time in these three nuclei. The properties of these dipole bands are investigated in terms of the self-consistent tilted axis cranking covariant density functional theory. In the calculation for ⁷⁵As, ⁷⁹Se and ⁶²Cu, the valence nucleon configurations of π[(1g_9/2)¹(1f_5/2)⁻²]<x content-type="symbol">Ä</x>υ[(1g_9/2)⁵(fp)⁻³], <sc>π[(1g_9/2)¹(fp)⁵]</sc><x content-type="symbol">Ä</x>υ[(1g_9/2)⁵] and π[(f_7/2)⁻¹(p_3/2f_5/2)²]<x content-type="symbol">Ä</x>υ[(g_9/2)¹(p_3/2f_5/2)⁴] are used, respectively. The calculated energy spectra reasonably reproduce the experimental excitation energies of ⁷⁵As, ⁷⁹Se, and ⁶²Cu. The evolutions of deformation parameters <italic>β</italic> and <italic>γ</italic> of these dipole bands driven by increasing rotational frequency are discussed. In contrast to the relatively large triaxial deformation of the dipole bands in ⁷⁵As and ⁶²Cu, the dipole band of ⁷⁹Se has a relatively axially symmetric and small prolate deformation. With the increase of rotational frequency, the <italic>β </italic>deformations for ⁷⁵As, ⁷⁹Se and⁶²Cu behave in a similar way, i.e., a smooth decrease in <italic>β</italic>. Meanwhile, both <italic>γ</italic> values of ⁷⁵As and ⁶²Cu show a smoothly increasing tendency. Based on the examination of the composition of the proton and neutron angular momentum vectors <italic>J</italic>_π and <italic>J</italic>_υ as well as the total angular momentum <italic>J</italic>_tot=<italic>J</italic>_π+<italic>J</italic>_υ at both the bandhead and the maximum rotational frequency, the dipole bands in ⁷⁵As and ⁷⁹Se can be interpreted as novel stapler bands, where the valence nucleons in (1g_9/2) orbital rather than the collective core are responsible for the closing of the stapler of angular momentum. Although not firmly confirmed in experiments, the dipole structure in ⁶²Cu may be a candidate of magnetic rotational bands. To unambiguously confirm this, further experimental investigations are strongly desirable.

Fission dynamics, dissipation, and clustering at finite temperature

The saddle-to-scission dynamics of the induced fission process is explored using a microscopic finite-temperature model based on time-dependent nuclear density functional theory (TDDFT), that allows to follow the evolution of local temperature along fission trajectories. Starting from a temperature that corresponds to the experimental excitation energy of the compound system, the model propagates the nucleons along isentropic paths toward scission. For the four illustrative cases of induced fission of $^{240}$Pu, $^{234}$U, $^{244}$Cm, and $^{250}$Cf, characteristic fission trajectories are considered, and the partition of the total energy into various kinetic and potential energy contributions at scission is analyzed, with special emphasis on the energy dissipated along the fission path and the prescission kinetic energy. The model is also applied to the dynamics of neck formation and rupture, characterized by the formation of few-nucleon clusters in the low-density region between the nascent fragments.

Accurate Vertical Excitation Energies of BODIPY/Aza-BODIPY Derivatives from Excited-State Mean-Field Calculations.

We report a benchmark study of vertical excitation energies and oscillator strengths for the HOMO → LUMO transitions of 17 boron–dipyrromethene (BODIPY) structures, showing a large variety of ring sizes and substituents. Results obtained at the time-dependent density functional theory (TDDFT) and at the delta-self-consistent-field (ΔSCF) by using 13 different exchange correlation kernels (within LDA, GGA, hybrid, and range-separated approximations) are benchmarked against the experimental excitation energies when available. It is found that the time-independent ΔSCF DFT method, when used in combination with hybrid PBE0 and B3LYP functionals, largely outperforms TDDFT and can be quite competitive, in terms of accuracy, with computationally more costly wave function based methods such as CC2 and CASPT2.

Excited states of chlorophyll a and b in solution by time-dependent density functional theory.

The ground state and excited state electronic properties of chlorophyll (Chl) a and Chl b in diethyl ether, acetone, and ethanol solutions are investigated using quantum mechanical and molecular mechanical calculations with density functional theory (DFT) and time-dependent DFT (TDDFT). Although the DFT/TDDFT methods are widely used, the electronic structures of molecules, especially large molecules, calculated with these methods are known to be strongly dependent on the functionals and the parameters used in the functionals. Here, we optimize the range-separated parameter, μ, of the CAM-B3LYP functional of Chl a and Chl b to reproduce the experimental excitation energy differences of these Chl molecules in solution. The optimal values of μ for Chl a and Chl b are smaller than the default value of μ and that for bacteriochlorophyll a, indicating the change in the electronic distribution, i.e., an increase in electron delocalization, within the molecule. We find that the electronic distribution of Chl b with an extra formyl group is different from that of Chl a. We also find that the polarity of the solution and hydrogen bond cause the decrease in the excitation energies and the increase in the widths of excitation energy distributions of Chl a and Chl b. The present results are expected to be useful for understanding the electronic properties of each pigment molecule in a local heterogeneous environment, which will play an important role in the excitation energy transfer in light-harvesting complex II.

Accurate ab initio calculations of RaF electronic structure appeal to more laser-spectroscopical measurements.

Recently, a breakthrough has been achieved in laser-spectroscopic studies of short-lived radioactive compounds with the first measurements of the radium monofluoride molecule (RaF) UV/vis spectra. We report results from high-accuracy ab initio calculations of the RaF electronic structure for ground and low-lying excited electronic states. Two different methods agree excellently with experimental excitation energies from the electronic ground state to the 2Π1/2 and 2Π3/2 states, but lead consistently and unambiguously to deviations from experimental-based adiabatic transition energy estimates for the 2Σ1/2 excited electronic state, and show that more measurements are needed to clarify spectroscopic assignment of the 2Δ state.

Accurate core excitation and ionization energies from a state-specific coupled-cluster singles and doubles approach.

We investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without the use of response theory or equation-of-motion (EOM) formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the methods studied, an effort is made to provide reasonable basis set limit estimates for the transition energies. Overall, we find that the two best-performing schemes studied here for ΔCCSD are capable of predicting excitation and ionization energies with errors comparable to experimental accuracies. The proposed ΔCCSD schemes reduces statistical errors against experimental excitation energies by more than a factor of two when compared to the frozen-core core-valence separated (FC-CVS) EOM-CCSD approach - a successful variant of EOM-CCSD tailored towards core excitations.

Active Learning Configuration Interaction for Excited-State Calculations of Polycyclic Aromatic Hydrocarbons.

We present the active learning configuration interaction (ALCI) method for multiconfigurational calculations based on large active spaces. ALCI leverages the use of an active learning procedure to find important electronic configurations among the full configurational space generated within an active space. We tested it for the calculation of singlet–singlet excited states of acenes and pyrene using different machine learning algorithms. The ALCI method yields excitation energies within 0.2–0.3 eV from those obtained by traditional complete active-space configuration interaction (CASCI) calculations (affordable for active spaces up to 16 electrons in 16 orbitals) by including only a small fraction of the CASCI configuration space in the calculations. For larger active spaces (we tested up to 26 electrons in 26 orbitals), not affordable with traditional CI methods, ALCI captures the trends of experimental excitation energies. Overall, ALCI provides satisfactory approximations to large active-space wave functions with up to 10 orders of magnitude fewer determinants for the systems presented here. These ALCI wave functions are promising and affordable starting points for the subsequent second-order perturbation theory or pair-density functional theory calculations.

Quadrupole phonon excitations and transition probabilities for low-lying states of neutron-rich Cd isotopes

In this paper we study the low-lying states of neutron-rich $^{122,124,126,128}\mathrm{Cd}$ and $^{130,132,134,136,138}\mathrm{Cd}$ within the nucleon-pair approximation of the shell model. We adopt the phenomenological Hamiltonian for $^{122,124,126,128}\mathrm{Cd}$, and the shell-model effective interaction $jj46$ for $^{130,132,134,136,138}\mathrm{Cd}$. The available experimental excitation energies and quadrupole transition probabilities are well reproduced by our calculation, and we also make predictions for very neutron-rich Cd nuclei. Based on our calculation, the $B(E2;{0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ values exhibit an asymmetric feature with respect to the $N=82$ shell closure, which mainly comes from the contributions of the proton transition matrix elements. We also investigate for the eight open-shell Cd nuclei, whether two low-lying yrast states with spins differing by 2 can be connected by a quadrupole-phonon excitation, and here we take the proton and neutron quadrupole operators multiplied by $1/{r}_{0}^{2}$ as our quadrupole phonon operators. We calculate explicit overlaps between the low-lying yrast states and the constructed quadrupole-phonon states based on the low-lying yrast states with lower spins, and the results indicate that, for all eight open-shell Cd nuclei, $|{2}_{1}^{+}\ensuremath{\rangle}$ and $|{4}_{1}^{+}\ensuremath{\rangle}$ can be well described to be the states constructed by coupling the proton or neutron phonon to $|{0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rangle}$ and $|{2}_{1}^{+}\ensuremath{\rangle}$, respectively. Very interestingly, for $^{126,124,122}\mathrm{Cd}$ and $^{136,138}\mathrm{Cd}$, the ${2}_{1}^{+}$ state can be well described to be both the proton phonon state and the neutron phonon state, which indicates a nonorthogonal feature of these two phonon states. We further present an analytic relation for the overlap between these two phonon states, which implies that the proton and neutron phonon states constructed using the quadrupole operators and the ${0}_{\mathrm{g}.\mathrm{s}.}^{+}$ state in an open-shell nucleus are almost impossibly orthogonal.

One-pot synthesis of sodium alginate-grafted-terpolymer hydrogel for As(III) and V(V) removal: In situ anchored comonomer and DFT studies on structures

In this work, an optimum sodium alginate (NaAlg)-grafted-[sodium 2-methylenesuccinate-co-sodium 2-((2-(isobutyryloxy)ethoxy)methyl)succinate-co-ethylene glycol methacrylate, i.e., SMS-co-SIBEMS-co-EGMA, i.e., P1], i.e., P2, was selected among twelve hydrogels synthesized by employing variable amounts of synthesis parameters through a facile polymerization of SMS and EGMA monomers. In P1 and P2, SIBEMS third comonomer was strategically anchored in situ. The formation of terpolymer, i.e., P1, rather than generally expected copolymer, i.e., SMS-co-EGMA/ CoP1, was explored via closeness of experimental and simulated excitation energies of P1 and CoP1, measured by using density functional theory (DFT). The grafting of NaAlg into synthetic P1 elevated swelling, crosslink density (CD), network stability, reusability, and adsorption capacity (AC) of semisynthetic hydrogel, i.e., P2. The reusable P2 presenting optimum result among swelling, CD, and mean molar mass was chosen selectively for removals of As(III) and V(V). The structures of P1, P2, and adsorbed P2, i.e., As(III)-P2 and V(V)-P2; NaAlg-grafting; in situ anchored SIBEMS comonomer; reusability; thermostability; and surface properties were explored through XPS-NMR-FTIR-UV-vis, DFT, TG, DLS, XRD, SEM, pHPZC, and network and thermodynamic energies. The ACs of 0.025 g P2 for As(III) and V(V) were 112.24 and 88.89 mg g−1, respectively, at 308 K and within 5–100 mg L−1. The ACs reduced to 67.26, 75.49, 71.42, and 98.25 mg g−1 for As(III) and 40.25, 50.49, 45.37, and 67.88 mg g−1 for V(V) in the presence of Mn(II), Cu(II), Ni(II), and Zn(II), respectively.

Possible ‘stapler’ band in 109Ag nucleus

High-spin states of 109Ag have been studied using the 7Li + 110Pd reaction at a beam energy of 46 MeV. A negative-parity band decaying to the ground-state band by several new linking transitions is established. Meanwhile, seven new E2 crossover transitions of this band are observed, thereby confirming the spin-parity assignment and ordering of the dipole transitions above the Iπ = 19/2− level. A low energy γ-ray transition of 88 keV is found and placed at the bottom of the negative-parity band, and thus the Iπ = 17/2− level is tentatively assigned as the lowest observed state of this band. Experimental excitation energies and total angular momenta of the negative-parity band are compared with the predictions of self-consistent titled axis cranking relativistic mean-field theory with a three-quasiparticle configuration of . Based on the theoretical description and the analyses of the angular momentum coupling, this negative-parity dipole band is suggested as a ‘stapler’ band. By investigating the angular momentum components, it is found that the valence nucleons in the low-j orbitals play an active role in the ‘stapler’ mechanism.

High-K multi-particle bands and pairing reduction in 254No * * Supported by the National Natural Science Foundation of China (11775112, 11535004, 11875027, 11761161001) and the Priority Academic Program Development of Jiangsu Higher Education Institutions

The multi-particle states and rotational properties of the two-particle bands in are investigated by the cranked shell model with pairing correlations treated by the particle number conserving method. The rotational bands on top of the two-particle and states and the pairing reduction are studied theoretically in for the first time. The experimental excitation energies and moments of inertia of the multi-particle states are reproduced well by the calculations. Better agreement with the data is achieved by including the high-order deformation , which leads to enlarged and deformed shell gaps. An increase of in these two-particle bands compared with the ground state band is attributed to the pairing reduction due to the Pauli blocking effect.

Structure of odd-odd Cs isotopes within the interacting boson-fermion-fermion model based on the Gogny-D1M energy density functional

The spectroscopic properties of the odd-odd isotopes $^{124-132}$Cs have been studied within the interacting boson-fermion-fermion model based on the Gogny-D1M energy density functional framework. Major ingredients to build the interacting boson-fermion-fermion Hamiltonian, such as the ($\beta,\gamma$)-deformation energy surfaces for the even-even core nuclei $^{124-132}$Xe as well as single-particle energies and occupation probabilities of the odd nucleons, have been computed microscopically with the constrained Hartree-Fock-Bogoliubov method. A few coupling constants of the boson-fermion and residual neutron-proton interactions are fitted to reproduce with a reasonable accuracy the experimental excitation energy of the low-lying levels of the odd-mass and odd-odd nuclei. The method is applied to describe the low-energy low-spin spectra of the odd-odd Cs nuclei and the band structures of higher-spin higher-energy states, mainly based on the $(\nu h_{11/2})^{-1}\otimes\pi h_{11/2}$ configuration. Many of those odd-odd Cs nuclei have been identified as candidates for exhibiting chiral doublet bands.

Synthesis and Characterization of Pyrano[3,2-C]Chromene Derivatives: Exploring Their Optoelectronic and Charge Transport Properties By First-Principles Approach

With the aim to enhance the charge transport, optoelectronic and semiconducting properties various multifunctional pyrano[3,2-c]chromene derivatives were synthesized and characterized. To shed light on the various properties of interests, the ground state geometries were optimized by Density Functional Theory (DFT). The effect of different substituents, e.g., thiophen-2-yl, 5-bromothiophen-2-yl, 1H-indol-3-yl, pyridin-3-yl, and benzo[d][1,3]dioxol-5-yl was studied on the structural stability, electronic properties, and absorption wavelengths by DFT and Time-Domain DFT (TDDFT). The experimental excitation energies were successfully reproduced at TD-PBE/6-31G** level in DMSO. The electron injection barrier, ionization potential, electron affinity and reorganization energies for hole and electron were calculated and compared systematically. The smaller electron reorganization energies of pyrano[3,2-c]chromene derivatives except indole substituted one are illuminating that these materials would be efficient to be used in n-type semiconductor devices.

Are Fully Conjugated Expanded Indenofluorenes Analogues and Diindeno[n]thiophene Derivatives Diradicals? A Simplified (Spin-Flip) Time-Dependent Density Functional Theory [(SF-)sTD-DFT] Study.

Polycyclic hydrocarbons are often used to understand the electronic structure of nanographene systems. Among them, indeno[1,2b]fluorene and indeno[1,2c]fluorene isomers present a central p-quinodimethane unit leading to unique optical properties. In this work, we characterized the absorption spectra of indeno[1,2b]fluorene and [2,1-c]diindeno[n]thiophene derivatives with (spin-flip) simplified time-dependent density functional theory [(SF-)sTD-DFT] methods. Note that the SF-sTD-DFT level of theory allows a computationally efficient treatment for large diradicals. To interpret spectra, we implemented natural transition orbitals (NTOs) at both SF-sTD-DFT and sTD-DFT levels. This compact and method-independent representation of the electronic excitation provides a simple interpretation for the low-lying excited states of this set of molecules in terms of three different types of NTOs: "quinoid", "aromatic", and "π-bonded". When comparing with experiment, we found that only one molecule of this set is actually a high-spin triplet diradical. Others are almost closed-shell molecules with a very small contribution from a doubly excited configuration that only the spin-flip method could capture. The small amount of static correlation recovered by the spin-flip active space provides a linear relation between the first visible theoretical and experimental excitation energies among this set.

Erratum: Explicitly correlated wave functions of the ground state and the lowest quintuplet state of the carbon atom [Phys. Rev. A 99 , 052512 (2019)

Variational, nonrelativisitic energies have been calculated for the ground state ($^3P_g$) and the lowest quintuplet state ($^5S_u$) of the carbon atom, with wavefunctions expressed in the basis of symmetry-projected, explicitly correlated Gaussian (ECG) lobe functions. New exact limits of these energies have been estimated, amounting to $-37.844906(4)$ and $-37.691751(2)$ hartree. With finite nuclear masses and leading, scalar relativistic corrections included, respective experimental excitation energy of $^{12}C$ has been reproduced with accuracy of about 7 cm$^{-1}$.

Prediction of Excited-State Properties of Oligoacene Crystals Using Fragment-Based Quantum Mechanical Method.

A fundamental understanding of the excited-state properties of molecular crystals is of central importance for their optoelectronics applications. In this study, we developed the electrostatically embedded generalized molecular fractionation (EE-GMF) method for the quantitative characterization of the excited-state properties of locally excited molecular clusters. The accuracy of the EE-GMF method is systematically assessed for oligoacene crystals. Our result demonstrates that the EE-GMF method is capable of providing the lowest vertical singlet (S1) and triplet excitation energies (T1), in excellent agreement with the full-system quantum mechanical calculations. Using this method, we also investigated the performance of different density functionals in predicting the excited-state properties of the oligoacene crystals. Among the 13 tested functionals, B3LYP and MN15 give the two lowest overall mean unsigned errors with reference to the experimental S1 and T1 excitation energies. The EE-GMF approach can be readily utilized for studying the excited-state properties of large-scale organic solids at diverse ab initio levels.