Inverting the external-potential-to-electron density map in systems of electrons by minimization of a least-squares fit functional for analytic potentials

In a system of electrons, there is a map connecting any external potential v with its electron density ρ _v. In this work, we describe a procedure for inverting this potential-to-density map, so that potentials (if any) corresponding to a target density ρ_t can be obtained. We give the trial external potential v _α , an analytic expression depending on a number of parameters α = (α₁, …) and then minimize the least-squares integral ∫(ρ _α − ρ_t)² d r by the conjugate gradient method, where ρ _α is the density corresponding to v _α . The implementation takes advantage of the analytic nature of v _α . The procedure can be applied to any system and quantum chemistry model, and works both for ground and excited states, as well as for ensembles of states. The method is tested with some excited states of the particle-in-a-box model, confirming the lack of a Hohenberg–Kohn theorem for excited states. It is also applied to the first singlet excited state of the helium atom, where, apart from the nucleus–electron attraction potential, some generalized external potentials are found.     

Small nickel clusters: Two low-lying Ni<Subscript>3</Subscript> states

Matrix isolation IR spectroscopy and quantum-chemical calculations were jointly used to identify the system of bands related to Ni₃ clusters. The positions of two low-lying electronic states were determined, and vibrational frequencies and geometry in the ground and excited states were estimated. In all the calculated states, Ni₃ had the structure of an isosceles triangle. In the X ³ B ₂ ground and a ³ B ₁ lower excited states, this was an acute-angled triangle. In the b ³ B ₂ and c ³ B ₁ excited states, the triangle was obtuse-angled.     

基态PuOH分子的多体展式分析势能函数

Using the density functional method B3LYP with relativistic effective core potential(RECP)for Pu atom,thelow-lying excited states(~4Σ~ ,~6Σ~ ,~8Σ~ )for three structures of PuOH molecule were optimized.The results showthat the ground state is X~6Σ~ of the linear Pu-O-H(C_(∞v)),its corresponding equilibrium geometry and dissociationenergy are R_(Pu-O)=0.20595 nm,R_(O-H)=0.09581 nm and —8.68 eV,respectively.At the same time,two other me-tastable structures [PuOH(C_s)and H-Pu-O(C_(∞v)] were found.The analytical potential energy function has alsobeen derived for whole range using the many-body expansion method.This potential energy function represents theconsiderable topographical features of PuOH molecule in detail,which is adequately accurate in the whole potentialsurface and can be used for the molecular reaction dynamics research.     

Multiple-State Emissions from Neat,Single-Component Molecular Solids: Suppression of Kasha's Rule

Three rigid and structurally simple heterocyclic stilbene derivatives, (E)-3H,3′H-[1,1′-biisobenzofuranylidene]-3,3′-dione, (E)-3-(3-oxobenzo[c] thiophen-1(3H)-ylidene)isobenzofuran-1(3H)-one, and (E)-3H,3′H-[1,1′-bibenzo[c] thiophenylidene]-3,3′-dione, are found to fluoresce in their neat solid phases, from upper (S₂) and lowest (S₁) singlet excited states, even at room temperature in air. Photophysical studies, single-crystal structures, and theoretical calculations indicate that large energy gaps between S₂ and S₁ states (T₂ and T₁ states) as well as an abundance of intra and intermolecular hydrogen bonds suppress internal conversions of the upper excited states in the solids and make possible the fluorescence from S₂ excited states (phosphorescence from T₂ excited states). These results, including unprecedented fluorescence quantum yields (2.3–9.6 %) from the S₂ states in the neat solids, establish a unique molecular skeleton for achieving multi-colored emissions from upper excited states by “suppressing” Kasha's rule.     

Multiple‐State Emissions from Neat,Single‐Component Molecular Solids: Suppression of Kasha's Rule

Three rigid and structurally simple heterocyclic stilbene derivatives, (E)‐3H,3′H‐[1,1′‐biisobenzofuranylidene]‐3,3′‐dione, (E)‐3‐(3‐oxobenzo[c] thiophen‐1(3H)‐ylidene)isobenzofuran‐1(3H)‐one, and (E)‐3H,3′H‐[1,1′‐bibenzo[c] thiophenylidene]‐3,3′‐dione, are found to fluoresce in their neat solid phases, from upper (S₂) and lowest (S₁) singlet excited states, even at room temperature in air. Photophysical studies, single‐crystal structures, and theoretical calculations indicate that large energy gaps between S₂ and S₁ states (T₂ and T₁ states) as well as an abundance of intra and intermolecular hydrogen bonds suppress internal conversions of the upper excited states in the solids and make possible the fluorescence from S₂ excited states (phosphorescence from T₂ excited states). These results, including unprecedented fluorescence quantum yields (2.3–9.6 %) from the S₂ states in the neat solids, establish a unique molecular skeleton for achieving multi‐colored emissions from upper excited states by “suppressing” Kasha's rule.     

Low‐lying singlet excited states of isocyanogen

Recent photofragment fluorescence excitation (PHOFEX) spectroscopy experiments have observed the ùA″ singlet excited state of isocyanogen (CNCN) for the first time. The observed spectrum is not completely assigned and significant questions remain about the excited states of this system. To provide insight into the energetically accessible excited states of CNCN, optimized geometries, harmonic vibrational frequencies, and excitation energies for the first three singlet excited states are determined using equation‐of‐motion coupled‐cluster theory with singles and doubles (EOM‐CCSD) and correlation‐consistent basis sets. Additionally, excited state coupled‐cluster methods which approximate the contributions from triples (CC3) are utilized to estimate the effect of higher‐order correlation on the energy of each excited state. For the ùA″ state, our best estimate for T₀ is about 42,200 cm^?1, in agreement with the experimentally estimated upper limit for the zero‐point level of 42,523 cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

A multi-configuration LCAO–MO study for complex unsaturated molecules. I. General theory and its application to the benzene anion

A multi-configuration LCAO –MO approach using a π-bond order–bond length linear relation is introduced to predict the geometrical structures for the electronic ground and excited states of unsaturated hydrocarbons. The procedure is designed to include configuration interaction in each iterative computation where the π-electron approximation is employed under the Pariser–Parr type semi-empirical treatment. The π-bond order–bond length relation is determined as r_pq = 1.523 – 0.193P_pq, when the bond lengths of ethylene, benzene and naphthalene are used and the groundstate functions including the singly and doubly excited configurations are taken into account to obtain the bond orders P_pq. The iterative calculation is applied to the ground state and the two lowest excited states of the benzene anion in both D_6h and D_2h molecular geometries. The geometrical structures and the π-electron energies are computed for the ground and excited states of the anion; for the latter, two types of configuration species are used. It is found that the first lowest excited state is not subjected to the Jahn–Teller effect and the calculated excited state energies do not agree with the observed values (c. 1.0 ～ 2.5 eV higher than the observed values). The latter point is discussed in detail. It is also found that the resultant ground state energy depression due to configuration mixing is not very large and the two types of configuration species used give different CI effects on the energy levels of the two lowest excited states of the anion. Finally, the stabilization energy due to the Jahn–Teller distortion is estimated for the ground state of the anion.     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

Quantum-Chemical Analysis of Electronic Excitation and Reactivity of Olefins and Dienes

Results obtained in studying the structure of olefin and diene molecules, and complexes of these, in the ground and lower excited states by RHF, ROHF, GVB/DN, and 6-31G^* quantum-chemical methods are presented. Attention is paid to the identity of the main structural and electronic parameters of triplet T ₁ and singlet S ₁ states forming a reactive fourfold spin-degenerate diradical equilibrium excited state (S·T)₁ having the lowest energy. A new mechanism of cyclodimerization of ethylene and tetrafluoroethylene and anionic polymerization of dienes, involving the (S·T)₁ states, is suggested.     

Doublet instability and the molecular structure of AlO2

The possible C_s, C_2v, and C_∞v structures of AlO₂ corresponding to the two lowest electronic states which dissociate into the neutral Al(²P) and O₂(³Σ_g^?) fragments have been investigated at the ab initio self-consistent field (SCF) and CI levels using nonempirical pseudopotentials. The most stable structure corresponds to a C_2v symmetry in the ²A₂ electronic state. However, this structure presents the three-center three-electron Hartree-Fock instability and CASSCF calculations were necessary to unequivocally characterize it as true minimum. Moreover, only another stable structure, of C_2v geometry, was found to be a minimum, corresponding to a low-lying excited state of ²A₁ symmetry. The optimized C_∞v structures were not minima on the corresponding potential energy surfaces and no evidence of any stable C_s structure was found. Calculating values are compared with the different experimental data obtained from the reaction of Al and O₂ in frozen gas inert matrices.     

One-Electron Pseudo-Potential Determination of Stable Isomers of the Li*Ar n Excited Clusters: Absorption Spectra

We present pseudo-potential calculations of geometrical structures of stable isomers of LiAr _n clusters with both an electronic ground state and excited states of the lithium atom. The Li atom is perturbed by argon atoms in LiAr _n clusters. Its electronic structure obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Li⁺Ar _n core, the Li⁺ and Ar atoms are replaced by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for the polarization and correlation of the inert core with the valence Lithium electron [J Chem Phys 116, 1839 1]. The geometry optimization of the ground and excited states of LiAr _n (n = 1–12) clusters is carried out via the Basin-Hopping method of Wales et al. [J Phys Chem 101, 5111 2; J Chem Phys 285, 1368 3]. The geometries of the ground and ionic states of LiAr _n clusters were used to determine the energy of the high excited states of the neutral LiAr _n clusters. The variation of the excited state energies of LiAr _n clusters as a function of the number of argon atoms shows an approximate Rydberg character, corresponding to the picture of an excited electron surrounding an ionic cluster core, is already reached for the 3s state. The result of optical transitions calculations shows that the absorption spectral features are sensitive to isomer structure. It is clearly the case for transitions close to the 2p levels of Li which are distorted by the cluster environment.     

Molecular electric properties in electronic excited states: multipole moments and polarizabilities of H2O in the lowest1 B 1 and3 B 1 excited states

Summary The dipole and quadrupole moments and the dipole polarizability tensor components are calculated for the¹ B ₁ and³ B ₁ excited states of the water molecule by using the complete active space (CAS) SCF method and an extended basis set of atomic natural orbitals. The dipole moment in the lowest¹ B ₁ (0.640 a.u.) and³ B ₁ (0.416 a.u.) states is found to be antiparallel to that in the ground electronic state of H₂O. The shape of the quadrupole moment ellipsoid is significantly modified by the electronic excitation to both states investigated in this paper. All components of the excited state dipole polarizability tensor increase by about an order of magnitude compared to their values in the ground electronic state. The present results are used to discuss some aspects of intermolecular interactions involving molecules in their excited electronic states.     

Change of molecular structure in the excited states: A (CNDO/2) hole-potential study on phosphine

Molecular structure of phosphine in a number of excited electronic states is studied using the method of hole-potential within the basic framework of CNDO/2 theory. Effects of including 3d-functions of phosphorus in the basis set on computed molecular geometries, transition energies and inversion barriers in the excited states have been investigated. An attempt is made to rationalise qualitatively the structural changes in the excitedstate in terms of Walsh-type correlation diagram constructed with the eigenvalues of the Fock operator in theV _N-1 potential model. A simple orbital model for predicting the nature of structural changes in the excited states is proposed.     

Temperature-dependent a factor in thermal unimolecular reactions II. Exponential dependence

It is assumed that A_∞ in the limiting high-pressure unimolecular rate constant expression k_∞ = A_∞ exp(?E_a∞/kT) is given by A_∞ = A″_∞e^BkT. The test case is the decomposition butane → 2 ethyl, where a negative B reproduces the temperature dependence of A_∞ about as well as the previously considered power law A_∞ = A′_∞(kT)ⁿ. It is shown that the term e^BkT modifies significantly the high-temperature falloff of the general-pressure rate constant k_uni and its various derivatives, and admits of a fairly simple interpretation in terms of Benson's restricted rotor theory. On physical grounds, the exponential law appears more reasonable than the power law.     

Theoretical description of nuclear quadrupole coupling in light diatomic molecules

A practical procedure for calculation of nuclear quadrupole coupling constants for light diatomic molecules is discussed. The procedure is based on a molecular wave function that explicitly describes nuclear motion. The approach is capable of yielding quadrupole coupling constants for excited rovibrational levels of diatomic molecules in their ground and excited electronic states. An application of the procedure to the X¹Σ⁺_g and B¹Σ⁺_u states of HD and D₂ is presented.     

A comparison of ground- and excited-state properties of [Ru(bz)2]2+ and bis(η6-benzene)ruthenium(II) p-toluenesulfonate using the density functional theory

The ground- and excited-state properties of both [Ru(bz)₂]²⁺ and crystalline bis(η⁶-benzene)ruthenium(II) p-toluenesulfonate are investigated using the density functional theory. A symmetry-based technique is employed to calculate the energies of the multiplet structure splitting of the singly excited triplet states. For the crystalline system, a Buckingham potential is introduced to describe the intermolecular interactions between the [Ru(bz)₂]²⁺ system and its first shell of neighbor molecules. The overall agreement between experimental and calculated ground- and excited-state properties is good, as far as the absolute transition energies, the Stokes shift, and the geometry of the excited states are concerned. The calculated d-d excitation energies of the isolated cluster are typically 1000–2000 cm⁻¹ too low. An energy lowering is obtained in a_1g→e_1g(³E_1g) excited state when the geometry of [Ru(bz)₂]²⁺ is bent along the e_1u Renner–Teller active coordinate. It vanishes as the crystal packing is taken into account. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1343–1353, 1999     

Efficient Direct Reverse Intersystem Crossing between Charge Transfer-Type Singlet and Triplet States in a Purely Organic Molecule

In the field of organic light-emitting diodes, thermally activated delayed fluorescence (TADF) materials have achieved great performance. The key factor for this performance is the small energy gap (ΔE_ST) between the lowest triplet (T₁) and singlet excited (S₁) states, which can be realized in a well-separated donor-acceptor system. Such systems are likely to possess similar charge transfer (CT)-type T₁ and S₁ states. Recent investigations have suggested that the intervention of other type-states, such as locally excited triplet state(s), is necessary for efficient reverse intersystem crossing (RISC). Here, we theoretically and experimentally demonstrate that our blue TADF material exhibits efficient RISC even between singlet CT and triplet CT states without any additional states. The key factor is dynamic flexibility of the torsion angle between the donor and acceptor, which enhances spin-orbit coupling even between the charge transfer-type T₁ and S₁ states, without sacrificing the small ΔE_ST. This results in excellent photoluminescence and electroluminescence performances in all the host materials we investigate, with sky-blue to deep-blue emissions. Among the hosts investigated, the deepest blue emission with CIE coordinates of (0.15, 0.16) and the highest EQE_MAX of 23.9 % are achieved simultaneously.     

Anab initio investigation of the inner shell excited states of the molecule Cl2

Restricted Hartree-Fock calculations of the Cl₂ molecule have been carried out to investigate the X-ray excited states below Cl 2p-electron ionization potential. Some inner shell excited states are shown to have a valence or a valence-Rydberg nature that results in a considerable intensity of the appropriate transitions in the X-ray absorption spectrum. A significant interaction among some electron configurations with a 2p vacancy is predicted.