The Low‐Lying Excited States of 2,2′‐Bithiophene: A Theoretical Analysis

The low‐energy regions of the singlet→singlet, singlet→triplet, and triplet→triplet electronic spectra of 2,2′‐bithiophene are studied using multiconfigurational second‐order perturbation theory (CASPT2) and extended atomic natural orbitals (ANO) basis sets. The computed vertical, adiabatic, and emission transition energies are in agreement with the available experimental data. The two lowest singlet excited states, 1¹B_u and 2¹B_u, are computed to be degenerate, a novel feature of the system to be borne in mind during the rationalization of its photophysics. As regards the observed high triplet quantum yield of the molecule, it is concluded that the triplet states 2³A_g and 2³B_u, separated about 0.4 eV from the two lowest singlet excited states, can be populated by intersystem crossing from nonplanar singlet states.     

Scanning‐Tunneling‐Spectroscopy‐Directed Design of Tailored Deep‐Blue Emitters

Frontier molecular orbitals can be visualized and selectively set to achieve blue phosphorescent metal complexes. For this purpose, the HOMOs and LUMOs of tridentate Pt^II complexes were measured using scanning tunneling microscopy and spectroscopy. The introduction of electron‐accepting or ‐donating moieties enables independent tuning of the frontier orbital energies, and the measured HOMO–LUMO gaps are reproduced by DFT calculations. The energy gaps correlate with the measured and the calculated energies of the emissive triplet states and the experimental luminescence wavelengths. This synergetic interplay between synthesis, microscopy, and spectroscopy enabled the design and realization of a deep‐blue triplet emitter. Finding and tuning the electronic “set screws” at molecular level constitutes a useful experimental method towards an in‐depth understanding and rational design of optoelectronic materials with tailored excited state energies and defined frontier‐orbital properties.     

New Fluorescence Domain “Excited Multimer” Formed upon Photoexcitation of Continuously Stacked Diaroylmethanatoboron Difluoride Molecules with Fused π‐Orbitals in Crystals

The crystal‐packing structures of seven derivatives of diaroylmethanatoboron difluoride ( 1 a – gBF₂ ) are characterized by no overlap of the π‐conjugated main units of two adjacent molecules (type I), overlap of the benzene ring π‐orbitals of two adjacent molecules (type II), and overlap of the benzene and dihydrodioxaborinine rings π‐orbitals of adjacent molecules (type III). The crystal‐packing structures govern the fluorescence (FL) properties in the crystalline states. The FL domain that is present in type I crystals, in which intermolecular orbital interactions are absent, leads to excited monomer‐like FL properties. In the case of the type II crystals, the presence of intermolecular overlap of the benzene rings π‐orbitals generates new FL domains, referred to as “excited multimers”, which possess allowed S₀–S₁ electronic transitions and, as a result, similar FL lifetimes at longer wavelengths than the FL of the type I crystals. Finally, intermolecular overlap of the benzene and dihydrodioxaborinine ring π‐orbitals in the type III crystals leads to “excited multimer” domains with forbidden S₀–S₁ electronic transitions and longer FL lifetimes at similar wavelengths as that in type I crystals.     

Analysis of chemical bonding in electronic excited states using parity function

The parity function (Schmider, J Chem Phys 1996, 105, 11134) is a projection of the spin‐traced one‐particle density matrix, which is strongly influenced by chemical bonding and its type. In this article, we apply the Parity Function to analyze chemical bonding in the electronic excited states of some small molecules, computed with the time‐dependent density functional theory. The calculations were carried out within the standard linear combination of atomic orbitals framework. We found that the changes in the parity function upon the excitation can be interpreted in terms of chemically relevant concepts such as bond breaking. We hope that the parity function will become a useful tool for understanding electronic excited states. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Theoretical analysis of the electronic spectrum of GeH4 from ab initio CI calculations

Ab initio CI calculations using pseudopotentials to describe germanium inner electrons are carried out on the low-lying excited singlet states (T₂) of GeH₄. A theoretical analysis of these states in terms of Mulliken population of Rydberg orbitals for each state and oscillator strengths allow us to reinterpret its experimental Vacuum UV electronic spectrum.     

A DFT/TDDFT Investigation of Excited State Dynamical Mechanism of (E)‐1‐((2,2‐Diphenylhydrazono)methyl)naphthalen‐2‐ol

The excited‐state intramolecular proton transfer (ESIPT) mechanism of a new compound (E )‐1‐((2,2‐diphenylhydrazono)methyl)naphthalen‐2‐ol ( EDMN ) sensor, reported and synthesized by Mukherjee et al . [Sensors Actuat. B‐Chem . 2014, 202 , 1190], is investigated in detail theoretically. The calculations on primary bond lengths, bond angles, and the corresponding infrared (IR) vibrational spectra and hydrogen‐bond energy involved in intramolecular hydrogen bond between the S₀ and S₁ states confirm that the intramolecular hydrogen bond is strengthened in the S₁ state, which reveals the tendency of ESIPT reaction. The fact that the experimental absorption and emission spectra are well reproduced demonstrates the rationality and effectiveness of the time‐dependent density functional theory (TDDFT) level of theory we adopt here. Furthermore, intramolecular charge transfer based on the frontier molecular orbitals (MOs) gives indication of the ESIPT reaction. The constructed potential energy curves of both the S₀ and S₁ states while keeping the O─H distance of EDMN fixed at a series of values are used to illustrate the ESIPT process. The lower barrier of ~3.934 kcal/mol in the S₁ state potential energy curve (lower than the 8.254 kcal/mol in the S₀ state) provides the transfer mechanism.     

Theoretical calculation about the valence and Rydberg excited states of hydrogen cyanide

The singlet and triplet excited states of hydrogen cyanide have been computed by using the complete active space self-consistent field and completed active space second order perturbation methods with the atomic natural orbital (ANO-L) basis set. Through calculations of vertical excitation energies, we have probed the transitions from ground state to valence excited states, and further extensions to the Rydberg states are achieved by adding 1s1p1d Rydberg orbitals into the ANO-L basis set. Four singlet and nine triplet excited states have been optimized. The computed adiabatic energies and the vertical transition energies agree well with the available experimental data and the inconsistencies with the available theoretical reports are discussed in detail.     

OClO里德堡态激发能的准确预测及其阴离子低能激发态的从头算研究

采用全活化空间自洽场方法(CASSCF)研究了OClO阴离子7个低能电子态及其自由基的基态. 为了进一步考虑动态电子相关效应, 采用二级多组态微扰理论(CASPT2)获得更加可靠的能量值. 此外, 在ANO-L基组的基础上, 在OClO自由基的电荷中心增加了为研究里德堡态所建立的1s1p1d的波函数, 并应用多组态二级微扰理论(MS-CASPT2)方法获得了里德堡态的准确电子激发能.     

Properties of atoms in electronically excited molecules within the formalism of TDDFT

The topological analysis of the electron density for electronic excited states under the formalism of the quantum theory of atoms in molecules using time‐dependent density functional theory (TDDFT) is presented. Relaxed electron densities for electronic excited states are computed by solving a Z‐vector equation which is obtained by means of the Sternheimer interchange method. This is in contrast to previous work in which the electron density for excited states is obtained using DFT instead of TDDFT, that is, through the imposition of molecular occupancies in accordance with the electron configuration of the excited state under consideration. Once the electron density of the excited state is computed, its topological characterization and the properties of the atoms in molecules are obtained in the same manner that for the ground state. The analysis of the low‐lying singlet and triplet vertical excitations of CO and C₆H₆ are used as representative examples of the application of this methodology. Altogether, it is shown how this procedure provides insights on the changes of the electron density following photoexcitation and it is our hope that it will be useful in the study of different photophysical and photochemical processes. © 2014 Wiley Periodicals, Inc.     

Application of the virial theorem to the study of molecular electronic wave functions

With aid of the virial theorem formulated for the energy differences of two electronic states some theorems on the wave functions of diatomic molecules have been proven. It is shown how proper Rydberg states can be distinguished from other electronic states with a diffuse outer orbital by virtue of the virial theorem and that a singlet-triplet pair of excited states cannot have the same equilibrium geometry and identical orbitals simultaneously. Furthermore if the two states have the same dissociation limit a theorem on the differences of the kinetic and the potential energy can be derived which allows an understanding of the shape of the electronic wave functions. As an application the wave functions and the ordering of the lowest states of H ₂ ⁺ and H₂ have been discussed.This work is part of the project Nr. SR 2.159.74 of the Schweizerischer Nationalfonds.     

Excited states of OsO4: A comprehensive time‐dependent relativistic density functional theory study

A large number of scalar as well as spinor excited states of OsO₄, in the experimentally accessible energy range of 3–11 eV, have been captured by time‐dependent relativistic density functional linear response theory based on an exact two‐component Hamiltonian resulting from the symmetrized elimination of the small component. The results are grossly in good agreement with those by the singles and doubles coupled‐cluster linear response theory in conjunction with relativistic effective core potentials. The simulated‐excitation spectrum is also in line with the available experiment. Furthermore, combined with detailed analysis of the excited states, the nature of the observed optical transitions is clearly elucidated. It is found that a few scalar states of ³T₁ and ³T₂ symmetries are split significantly by the spin‐orbit coupling. The possible source for the substantial spin‐orbit splittings of ligand molecular orbitals is carefully examined, leading to a new interpretation on the primary valence photoelectron ionization spectrum of OsO₄. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

State‐specific multireference perturbation theory with improved virtual orbitals: Taming the ground state of F2, Be2, and N2

Adaptation of improved virtual orbitals (IVOs) in state‐specific multireference perturbation theory using Møller–Plesset multipartitioning of the Hamiltonian (IVO‐SSMRPT) is examined in which the IVO‐complete active space configuration interaction (CASCI) is used as an inexpensive alternative to the more involved CAS‐self‐consistent field (CASSCF) orbitals. Unlike the CASSCF approach, IVO‐CASCI does not bear tedious and costly iterations beyond those in the initial SCF calculation. The IVO‐SSMRPT is intruder‐free, and explicitly size‐extensive. In the present preliminary study, the IVO‐SSMRPT method which relies on a small reference space is applied to study potential energy surfaces (PES) of the ground state of challenging, multiconfigurational F₂, Be₂, and N₂ molecules. These systems provide a serious challenge to any ab initio methodology due to the presence of an intricate interplay of nondynamical and dynamical correlations to the entire PES. The quality of the computed PES has been judged by extracting spectroscopic parameters and vibrational levels. The reported results illustrate that the IVO‐SSMRPT method has a potential to yield accuracies as good as the CASSCF‐SSMRPT one with reduced computational labor. Even with small reference spaces, our estimates demonstrate a good agreement with the available experimental values, and some benchmark computations. The blend of accuracy and low computational cost of IVO‐SSMRPT should deserve future attention for the accurate treatment of electronic states of small to large molecular systems for which the wavefunction is characterized by various configurations. © 2015 Wiley Periodicals, Inc.     

Application of the Stabilized Koopmans’ Theorem to the Temporary Anion States of Chlorosilanes in Long‐Range Corrected Density Functional Theory

The stabilized Koopmans’ theorem (SKT) is very successful in predicting relative vertical electron attachment energies in the Hartree‐Fock theory. It is mainly accomplished by systematically scaling the most diffuse functions in the basis set. Recently, the SKT has been extended to the temporary anion states (TASs) of polyatomic molecules in the long‐range corrected density functional theory. In this paper, this method will be further applied to chlorosilanes for their importance in the chemical processes of the semiconductor industry. Their resonance energies and lifetimes are determined by computing the density of resonance states via SKT. The detailed characteristics of resonance orbitals are then analyzed. It turns out that the lowest unfilled orbitals of chlorosilanes are essentially σ*_Si‐Cl in character. Moreover, several TASs with strong Si/Cl “d” character have been identified. These results, definitely, will help us in understanding the peculiar bonding and chemical properties of chlorosilanes.     

A comparison of the effect of nanotube chirality and electronic properties on the π–π interaction of single‐wall carbon nanotubes with pyrazinamide antitubercular drug

Theoretical investigation on local electronic structure and stability of the π–π stacking interaction of pyrazinamide (PZA) with armchair (5,5) and zigzag (9,0) single‐walled carbon nanotubes (SWCNTs) is performed using density functional theory (DFT). PZA is physisorbed onto nanotube sidewall through interaction of π orbitals of PZA and SWCNT and the enhanced structural stability of PZA/SWCNT systems is due to weak side‐on rather than the head‐on π‐interactions. The physisorption of PZA onto SWCNT sidewall is thermodynamically favored; as a consequence, it modulates the electronic properties of pristine nanotube in the vicinity of Fermi region and π–π stacked interactions is stronger in (9,0) SWCNT compared to (5,5) SWCNT. The density of states (DOS) analysis show that PZA contributes toward the enhancement of electronic states. Projected DOS and frontier orbital analysis in the vicinity of Fermi level region suggest the electronic states to be contributed from SWCNT rather than PZA. In addition, hybrid DFT calculation which includes the dispersion correction is employed to explain the non‐covalent π–π stacking interaction between PZA and SWCNT. The local density approximation and GGA results are compared with DFT‐D to explain near about accurately the weak nonbonded van der Waals interactions between PZA and SWCNTs. © 2012 Wiley Periodicals, Inc.     

Coherent Motion Reveals Non‐Ergodic Nature of Internal Conversion between Excited States

We found that specific nuclear motion along low‐frequency modes is effective in coupling electronic states and that this motion prevail in some small molecules. Thus, in direct contradiction to what is expected based on the standard models, the internal conversion process can proceed faster for smaller molecules. Specifically, we focus on the S₂→S₁ internal conversion in cyclobutanone, cyclopentanone, and cyclohexanone. By means of time‐resolved mass spectrometry and photoelectron spectroscopy the relative rate of this transition is determined to be 13:2:1. Remarkably, we observe coherent nuclear motion on the S₂ surface in a ring‐puckering mode and motion along this mode in combination with symmetry considerations allow for a consistent explanation of the observed relative time‐scales not afforded by only considering the density of vibrational states or other aspects of the standard models.     

Rydberg character of the higher excited states of free-base porphin

 The Rydberg character of the excited states of free-base porphin (FBP) has been investigated by the ab initio configuration interaction singles (CIS) method and the state-averaged complete-active-space self-consistent-field method. Double-zeta basis sets augmented with s, p, and d Rydberg functions and d polarization functions have been employed. Two types of molecular orbitals sets, the restricted Hartree–Fock molecular orbitals obtained for the ground state (¹A _g ) and for the cation state (²A _u ), have been used in the CIS calculations. All the calculations show that Rydberg-type excitations play important roles especially in the N bands. In this article we propose applying the model of a perturbed Rydberg series to interpret the excited states of FBP. By using this model, we have succeeded in analyzing the characteristics of the excited states as well as the experimental oscillator strengths, which have considerable magnitude even in the higher excited states. Received: 27 November 2000 / Accepted: 11 April 2001 / Published online: 27 June 2001     

Time‐dependent density functional theory study on the electronic excited‐state geometric structure,infrared spectra,and hydrogen bonding of a doubly hydrogen‐bonded complex

The geometric structures and infrared (IR) spectra in the electronically excited state of a novel doubly hydrogen‐bonded complex formed by fluorenone and alcohols, which has been observed by IR spectra in experimental study, are investigated by the time‐dependent density functional theory (TDDFT) method. The geometric structures and IR spectra in both ground state and the S₁ state of this doubly hydrogen‐bonded FN‐2MeOH complex are calculated using the DFT and TDDFT methods, respectively. Two intermolecular hydrogen bonds are formed between FN and methanol molecules in the doubly hydrogen‐bonded FN‐2MeOH complex. Moreover, the formation of the second intermolecular hydrogen bond can make the first intermolecular hydrogen bond become slightly weak. Furthermore, it is confirmed that the spectral shoulder at around 1700 cm^?1 observed in the IR spectra should be assigned as the doubly hydrogen‐bonded FN‐2MeOH complex from our calculated results. The electronic excited‐state hydrogen bonding dynamics is also studied by monitoring some vibraitonal modes related to the formation of hydrogen bonds in different electronic states. As a result, both the two intermolecular hydrogen bonds are significantly strengthened in the S₁ state of the doubly hydrogen‐bonded FN‐2MeOH complex. The hydrogen bond strengthening in the electronically excited state is similar to the previous study on the singly hydrogen‐bonded FN‐MeOH complex and play important role on the photophysics of fluorenone in solutions. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

Electronic spectrum of F<Subscript>2</Subscript>CO: theoretical calculations of vertical excitation energies and intensities

In this work, the linear response formalism with a triples-corrected CCSD reference wave function, LR-CCSDR(3), is applied to the calculation of vertical excitation energies of singlet states of the F₂CO molecule. A basis set of atomic natural orbitals augmented with a series of Rydberg functions has been used in the calculations. A large number of electronically excited states were calculated, and the valence, Rydberg, or mixed character of the states were investigated. In addition, the molecular quantum defect orbital (MQDO) method has been used to determine transition intensities involving Rydberg states. Excitation energies and transition intensities for Rydberg states with n > 3 are reported for the first time.     

Analysis of pseudo jahn–teller distortion based on natural bond orbital theory: Case study for silicene

Ground state (GS) instability of nondegenerate molecules in high symmetric structures is understood through Pseudo Jahn–Teller mixing of the electronic states through the vibronic coupling. The general approach involves setting up of a Pseudo Jahn–Teller (PJT) problem wherein one or more symmetry allowed excited states couple to the GS to create vibrational instability along a normal mode. This faces two major complications namely (1) estimating the adiabatic potential energy surfaces for the excited states which are often difficult to describe in case the excited states have charge-transfer or multi-excitonic (ME) character and (2) finding out how many such excited states (all satisfying the symmetry requirements for vibronic coupling) of increasing energies need to be coupled with the GS for a particular PJT problem. An analogous alternative approach presented here for the well-known case of symmetry breaking of planar (D_6h) hexasilabenzene (Si₆H₆) to the buckled (D_3d) structure involves identifying the second-order donor–acceptor, hyperconjugative interactions (E²_{i → j}) that stabilize the distorted structure. Following the recent work of Nori-Shargh and Weinhold, one observes that the orbitals involved in the vibronic coupling between the S₀/S_n states and those for the donor (filled)–acceptor (empty) interactions are identical. In fact, deletion of any particular pair of E²_{i → j} interaction creates vibrational instability in the buckled structure and as a corollary, deleting it for the planar structure removes its instability. The one-to-one correlation between the natural bond orbital theory and PJT theory assists in an intuitive identification of the relevant (few) excited states from a manifold of computed ones that cause symmetry breaking by vibronic coupling. © 2019 Wiley Periodicals, Inc.     

Characterization of the excited states of ethylene by MRCI

The excited states of ethylene are systematically analyzed and characterized according to the natural orbitals (NOs) resulting from multireference configuration interaction singles and doubles (MRCISD) calculations. By comparing the shapes and nodal structures of the NOs with those of hydrogen atomic orbitals, the Rydberg series can be classified. Two or three different types of Rydberg series appear within five excited states for each symmetry of D_2h. For example, in the ¹A_g symmetry there are three series having np and two nf hydrogen‐like atomic orbitals. Electronic correlation effects for the (π→π*) V state are also discussed on the basis of a complete active space self‐consistent field (CASSCF) calculation, showing that electron correlation effects merely within the valence space cannot explain contraction of the V state. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005