The cis—trans thermal and photochemical interconversion mechanism in the dimide N-oxide. A comparison of the results obtainable with different ab initio calculation techniques

Two possible pathways have been investigated for the cis—trans conversion in diimide N-oxide, viz. a rotation around the NN bond and an in-plane inversion. Calculations have been performed for the ground and lowest excited states by means of a Cl treatment including the configurations found to be the most important in large Cl calculations performed in a few points. It is shown that the rotational mechanism is favoured in the excited states and is probable also in the thermal reaction. Such investigation has been repeated in parallel by using other techniques of lower accuracy: (1) Cl limited to single excitations (EHP method); (2) rigid excitation to virtual orbitals; (3) the half electron methods. Deficiencies of such methods have been brought out and analyzed. In particular methods (2) and (3) lead to an erroneus interpretation of the actual mechanism of the photochemical conversion by rotation.     

Variable metric optimization of molecular geometry in electronically excited states

The variable metric (VM) method is used to optimize molecular geometry in electronically excited states. A general expression for the first derivative of energy in the particular excited state is derived, considering configuration interaction of all singly excited configurations. A special expression for the excited states energy derivative is given for calculations with semiempirical methods of CNDO type. The geometry optimizations of a set of molecules in various excited states have been carried out by the CNDO/2 method. The results of computations have been discussed and compared with the available experimental data. A good agreement of the calculated geometries with the experimental ones has been shown in the first excited states and a relatively good agreement in the higher states, with some exceptions. Some special features of the proposed method are discussed.     

Linear-scaling quantum mechanical methods for excited states

The poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and have been applied widely to investigate the dynamics of complex molecular systems.     

Ab initio study of the electronic spectrum of peroxyacetyl nitrate

A theoretical study of the ground and excited states of peroxyacetyl nitrate (PAN), CH3C(O)OONO2, has been carried out using high level ab initio molecular orbital methods. The ground state geometry and vibrational frequencies are calculated using the coupled-cluster method. The vertical excitation energies for the lowest three excited states are calculated using the complete active space self-consistent field method along with the multireference internally contracted configuration interaction method. These results are compared with vertical excitation energies calculated with the coupled cluster equation of motion method. The calculation provides relevant insight into the origin of PAN absorption in the UV wavelength region from 200 to 300 nm. The nature of the electron transitions for these excited states is discussed.     

Deflation techniques in quantum chemistry: Excited states from ground states

Applications of deflation techniques to the study of excited states of quantum systems are analyzed. It is demonstrated how these methods allow us to transform the excited state problem of one Hamiltonian, into the ground state problem of an auxiliary one. As an example, potential application in the density functional treatment of excited states is discussed. The inclusion of approximations in this scheme, such as the solution of the proposed model within a finite basis set is discussed. An extension of the Hartree–Fock (HF) method to excited states is presented. This new treatment includes previous self consistent field extensions to excited states and provides us with a way to obtain the HF extension to excited states of any ground state method. These results make the excited states of a system accessible through all ground state theoretical techniques. © 2013 Wiley Periodicals, Inc.     

Potential--energy surfaces for excited states in extended systems

With a simple and physically intuitive method, first-principles calculations of potential-energy surfaces are performed for excited states in a number of illustrative systems, including dimers (H(2) and NaCl) and gas-surface systems [Cl-Na(100) and Cl(2)-Na(100)]. It is based on density-functional theory and is a generalization of the Delta self-consistent field (DeltaSCF) method, where electron-hole pairs are introduced in order to model excited states, corresponding to internal electron transfers in the considered system. The desired excitations are identified by analysis of calculated electron orbitals, local densities of states, and charge densities. For extended systems, where reliable first-principles methods to account for electronically excited states have so far been scarce, our method is very promising. Calculated results, such as the chemiluminescence of halogen molecules impinging on a alkali-metal surface, and the vertical (5 sigma-->2 pi(*)) excitation within the adsorbed CO molecule on the Pd(111) surface, are in working agreement with those of other studies and experiments.     

叶绿素a激发态电子结构的量子化学计算

采用密度泛函理论DFT(B3LYP/6-31G)对氢取代后叶绿素的几何构型进行优化,并用不同的量子化学方法包含TDDFT、SAC/SAC-CI等计算激发态能量和Qy 态跃迁偶极矩的三维夹角等性质,寻找和检验适合于计算色素大分子体系精确较高且易实现的理论化学方法.CAM-B3LYP是最好计算叶绿素a的激发态前四个激发态特征的泛函形式.     

Open-shell localized Hartree-Fock method based on the generalized adiabatic connection Kohn-Sham formalism for a self-consistent treatment of excited states

An effective exact-exchange Kohn-Sham approach for the treatment of excited electronic states, the generalized adiabatic connection open-shell localized Hartree-Fock (GAC-OSLHF) method is presented. The GAC-OSLHF method is based on the generalized adiabatic connection Kohn-Sham formalism and therefore capable of treating excited electronic states, which are not the energetically lowest of their symmetry. The method is self-interaction free and allows for a fully self-consistent computation of excited valence as well as Rydberg states. Results for atoms and small- and medium-size molecules are presented and compared to restricted open-shell Hartree-Fock (ROHF) and time-dependent density-functional results as well as to experimental data. While GAC-OSLHF and ROHF results are quite close to each other, the GAC-OSLHF method shows a much better convergence behavior. Moreover, the GAC-OSLHF method as a Kohn-Sham method, in contrast to the ROHF approach, represents a framework which allows also for a treatment of correlation besides an exchange by appropriate functionals. In contrast to the common time-dependent density-functional methods, the GAC-OSLHF approach is capable of treating doubly or multiply excited states and can be easily applied to molecules with an open-shell ground state. On the nodal planes of the energetically highest occupied orbital, the local multiplicative GAC-OSLHF exchange potential asymptotically approaches a different, i.e., nonzero, value than in other regions, an asymptotic behavior which is known from exact Kohn-Sham exchange potentials of ground states of molecules.     

Electronic excited-state energies from a linear response theory based on the ground-state two-electron reduced density matrix

Ground-state two-particle reduced density matrices (2-RDMs) are used to calculate excited-state energy spectra. Solving the Schrodinger equation for excited states dominated by single excitations from the ground-state wavefunction requires the ground-state 2- and 3-RDMs. The excited states, however, can be obtained without a knowledge of the ground-state 3-RDM by two methods: (i) cumulant expansion methods which build the 3-RDM from the 2-RDM, and (ii) double commutator methods which eliminate the 3-RDM. Previous work [Mazziotti, Phys. Rev. A 68, 052501 (2003)] examined the accuracy of excited states extracted from ground-state 2-RDMs, which were calculated by full configuration interaction or the variational 2-RDM method. In this work we employ (i) advances in semidefinite programming to treat the excited states of water and hydrogen fluoride and chains of hydrogen atoms, and (ii) the addition of partial three-particle N-representability conditions to compute more accurate ground-state 2-RDMs. With the hydrogen chains we examine the metal-to-insulator transition as measured by the band gap (the difference between the ground-state and the first excited-state energies), which is difficult for excited-state methods to capture.     

Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules

Time-dependent density functional theory (TDDFT) is now well established as an efficient method for molecular excited state treatments. In this work, we introduce the resolution of the identity approximation for the Coulomb energy (RI-J) to excited state gradient calculations. In combination with nonhybrid functionals, the RI-J approximation leads to speed ups in total timings of an order of magnitude compared to the conventional method; this is demonstrated for oligothiophenes with up to 40 monomeric units and adamantane clusters. We assess the accuracy of the computed adiabatic excitation energies, excited state structures, and vibrational frequencies on a set of 36 excited states. The error introduced by the RI-J approximation is found to be negligible compared to deficiencies of standard basis sets and functionals. Auxiliary basis sets optimized for ground states are suitable for excited state calculations with small modifications. In conclusion, the RI-J approximation significantly extends the scope of applications of analytical TDDFT derivative methods in photophysics and photochemistry.     

Full configuration interaction potential energy curves for the X (1)Sigma(g) (+), B (1)Delta(g), and B(') (1)Sigma(g) (+) states of C(2): a challenge for approximate methods

The C(2) molecule exhibits unusual bonding and several low-lying excited electronic states, making the prediction of its potential energy curves a challenging test for quantum chemical methods. We report full configuration interaction results for the X (1)Sigma(g) (+), B (1)Delta(g), and B(') (1)Sigma(g) (+) states of C(2), which exactly solve the electronic Schrodinger equation within the space spanned by a 6-31G( *) basis set. Within the D(2h) subgroup used by most electronic structure programs, these states all have the same symmetry ((1)A(g)), and all three states become energetically close for interatomic distances beyond 1.5 A. The quality of several single-reference ab initio methods is assessed by comparison to the benchmark results. Unfortunately, even coupled-cluster theory through perturbative triples using an unrestricted Hartree-Fock reference exhibits large nonparallelity errors (>20 kcal mol(-1)) for the ground state. The excited states are not accurately modeled by any commonly used single-reference method, nor by configuration interaction including full quadruple substitutions. The present benchmarks will be helpful in assessing theoretical methods designed to break bonds in ground and excited electronic states.     

The ground and excited states of polyenyl radicals C2n-1H2n + 1 (n = 2-13): a valence bond study.

The semiempirical valence bond (VB) method, VBDFT(s), is applied to the ground states and the covalent excited states of polyenyl radicals C2n - 1H2n + 1 (n = 2-13). The method uses a single scalable parameter with a value that carries over from the study of the covalent excited states of polyenes (W. Wu, D. Danovich, A. Shurki, S. Shaik, J. Phys. Chem. A, 2000, 104, 8744). Whenever comparison is possible, the VB excitation energies are found to be in good accord with sophisticated molecular orbital (MO)-based methods like CASPT2. The symmetry-adapted Rumer structures are used to discuss the state-symmetry and VB constitution of the ground and excited states, and the expansion to VB determinants is used to gain insight on spin density patterns. The theory helps to understand in a coherent and lucid manner the properties of polyenyl radicals, such as the makeup of the various states, their geometries and energies, and the distribution of the unpaired electrons (the neutral solitons).     

Conical intersections in thymine

The mechanisms which are responsible for the radiationless deactivation of the npi* and pipi* excited singlet states of thymine have been investigated with multireference ab initio methods (the complete-active-space self-consistent-field (CASSCF) method and second-order perturbation theory with respect to the CASSCF reference (CASPT2)) as well as with the CC2 (approximated singles and doubles coupled-cluster) method. The vertical excitation energies, the equilibrium geometries of the 1npi*and 1pipi* states, as well as their adiabatic excitation energies have been determined. Three conical intersections of the S1 and S0 energy surfaces have been located. The energy profiles of the excited states and the ground state have been calculated with the CASSCF method along straight-line reaction paths leading from the ground-state equilibrium geometry to the conical intersections. All three conical intersections are characterized by strongly out-of-plane distorted geometries. The lowest-energy conical intersection (CI1) arises from a crossing of the lowest 1pipi* state with the electronic ground state. It is found to be accessible in a barrierless manner from the minimum of the 1pipi* state, providing a direct and fast pathway for the quenching of the population of the lowest optically allowed excited states of thymine. This result explains the complete diffuseness of the absorption spectrum of thymine in supersonic jets. The lowest vibronic levels of the optically nearly dark 1npi* state are predicted to lie below CI1, explaining the experimental observation of a long-lived population of dark excited states in gas-phase thymine.     

Electronic optical response of molecules in intense fields: comparison of TD-HF, TD-CIS, and TD-CIS(D) approaches

Time-dependent Hartree-Fock (TD-HF) and time-dependent configuration interaction (TD-CI) methods with Gaussian basis sets have been compared in modeling the response of hydrogen molecule, butadiene, and hexatriene exposed to very short, intense laser pulses (760 nm, 3 cycles). After the electric field of the pulse returns to zero, the molecular dipole continues to oscillate due to the coherent superposition of excited states resulting from the nonadiabatic excitation caused by the pulse. The Fourier transform of this residual dipole gives a measure of the nonadiabatic excitation. For low fields, only the lowest excited states are populated, and TD-CI simulations using singly excited states with and without perturbative corrections for double excitations [TD-CIS(D) and TD-CIS, respectively] are generally in good agreement with the TD-HF simulations. At higher field strengths, higher states are populated and the methods begin to differ significantly if the coefficients of the excited states become larger than approximately 0.1. The response of individual excited states does not grow linearly with intensity because of excited state to excited state transitions. Beyond a threshold in the field strength, there is a rapid increase in the population of many higher excited states, possibly signaling an approach to ionization. However, without continuum functions, the present TD-HF and TD-CI calculations cannot model ionization directly. The TD-HF and TD-CIS simulations are in good accord because the excitation energies obtained by linear response TD-HF [also known as random phase approximation (RPA)] agree very well with those obtained from singly excited configuration interaction (CIS) calculations. Because CIS excitation energies with the perturbative doubles corrections [CIS(D)] are on average lower than the CIS excitation energies, the TD-CIS(D) response is generally stronger than TD-CIS.     

Internally contracted multiconfiguration-reference configuration interaction calculations for excited states

Summary The calculation of electronically excited states with the internally contracted multiconfiguration-reference configuration interaction (CMRCI) method is discussed. A straightforward method, in which contracted functions for all states are included in the basis, is shown to be very accurate and stable even in cases of narrow avoided crossings. However, the expense strongly increases with the number of states. A new method is proposed, which employs different contracted basis sets for each state, and in which eigensolutions of the Hamiltonian are found using an approximate projection operator technique. The computational effort for this method scales only linearly with the number of states. The two methods are compared for various applications.Dedicated in honor of Prof. Klaus Ruedenberg     

Theoretical study of the vertical excited states of benzene, pyrimidine, and pyrazine by the symmetry adapted cluster--configuration interaction method

The ground state and the excited states of benzene, pyrimidine, and pyrazine have been examined by using the symmetry adapted cluster-configuration interaction (SAC-CI) method. Detailed characterizations and the structures of the absorption peaks in the vacuum ultraviolet (VUV), low energy electron impact (LEEI), and electron energy loss (EEL) spectra were theoretically clarified by calculating the excitation energy and the oscillator strength for each excited state. We show that SAC-CI has the power to well reproduce the electronic excitation spectra (VUV, LEEI, and EEL) simultaneously to an accuracy for both the singlet and the triplet excited states originated from the low-lying pi --> pi*, n --> pi*, pi --> sigma* and n --> sigma* excited states of the titled compounds. The present results are compared with those of the previous theoretical studies by methods, such as EOM-CCSD(T), STEOM-CCSD, CASPT2 and TD-B3LYP, etc.     

Intermediate state representation approach to physical properties of electronically excited molecules

Propagator methods provide a direct approach to energies and transition moments for (generalized) electronic excitations from the ground state, but they do not usually allow one to determine excited state wave functions and properties. Using a specific intermediate state representation (ISR) concept, we here show how this restriction can be overcome in the case of the algebraic-diagrammatic construction (ADC) propagator approach. In the ISR reformulation of the theory the basic ADC secular matrix is written as a representation of the Hamiltonian (or the shifted Hamiltonian) in terms of explicitly constructable states, referred to as intermediate (or ADC) states. Similar intermediate state representations can be derived for operators other than the Hamiltonian. Together with the ADC eigenvectors, the intermediate states give rise to an explicit formulation of the excited wave functions and allow one to calculate physical properties of excited states as well as transition moments for transitions between different excited states. As for the ground-state excitation energies and transition moments, the ADC excited state properties are size consistent so that the theory is suitable for applications to large systems. The established hierarchy of higher-order [ADC(n)] approximations, corresponding to systematic truncations of the IS configuration space and the perturbation-theoretical expansions of the ISR matrix elements, can readily be extended to the excited state properties. Explicit ISR matrix elements for arbitrary one-particle operators have been derived and coded at the second-order [ADC(2)] level of theory. As a first computational test of the method we have carried out ADC(2) calculations for singlet and triplet excited state dipole moments in H(2)O and HF, where comparison to full CI results can be made. The potential of the ADC(2) method is further demonstrated in an exploratory study of the excitation energies and dipole moments of the low-lying excited states of paranitroaniline. We find that four triplet states, T1-T4, and two singlet states, S1 and S2, lie (vertically) below the prominent charge transfer (CT) excitation, S3. The dipole moment of the S3 state (17.0D) is distinctly larger than that of the corresponding T3 triplet state (11.7D).