Description of core excitations by time-dependent density functional theory with local density approximation, generalized gradient approximation, meta-generalized gradient approximation, and hybrid functionals

Time-dependent density functional theory (TDDFT) is employed to investigate exchange-correlation-functional dependence of the vertical core-excitation energies of several molecules including H, C, N, O, and F atoms. For the local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, the calculated X1s-->pi* excitation energies (X = C, N, O, and F) are severely underestimated by more than 13 eV. On the other hand, time-dependent Hartree-Fock (TDHF) overestimates the excitation energies by more than 6 eV. The hybrid functionals perform better than pure TDDFT because HF exchange remedies the underestimation of pure TDDFT. Among these hybrid functionals, the Becke-Half-and-Half-Lee-Yang-Parr (BHHLYP) functional including 50% HF exchange provides the smallest error for core excitations. We have also discovered the systematic trend that the deviations of TDHF and TDDFT with the LDA, GGA, and meta-GGA functionals show a strong atom-dependence. Namely, their deviations become larger for heavier atoms, while the hybrid functionals are significantly less atom-dependent.     

Ab initio study of the mechanism for photoinduced Yl-oxygen exchange in uranyl(VI) in acidic aqueous solution

The mechanism for the photochemically induced isotope-exchange reaction U(17/18)O2(2+)(aq) + H2(16)O <==> U(16)O2(2+)(aq) + H2(17/18)O has been studied using quantum-chemical methods. There is a dense manifold of states between 22,000 and 54,000 cm(-1) that results from excitations from the sigma(u) and pi(u) bonding orbitals in the (1)Sigma(g)(+) ground state to the nonbonding f(delta) and f(phi) orbitals localized on uranium. On the basis of investigations of the reaction profile in the (1)Sigma(g)(+) ground state and the excited states (3)Delta(g) (the lowest triplet state) and (3)Gamma(g) (one of the several higher triplet states), the latter two of which have the electron configurations sigma(u)f(delta) and pi(u)f(phi), respectively, we suggest that the isotope exchange takes place in one of the higher triplet states, of which the (3)Gamma(g) state was used as a representative. The geometries of the luminescent (3)Delta(g) state, the lowest in the sigma(u)f(delta,phi) manifold (the "sigma" states), and the (1)Sigma(g)(+) ground state are very similar, except that the bond distances are slightly longer in the former. This is presumably a result of transfer of a bonding electron to a nonbonding f orbital, which makes the excited state in some respects similar to uranyl(V). As is the case for all of the states of the pi(u)f(delta,phi) manifold (the "pi" states), the geometry of the (3)Gamma(g) state is very different from that of the (3)Delta(g) "sigma" state and has nonequivalent U-O(yl) distances of 1.982 and 1.763 A; in the (3)Gamma(g) state, the yl-exchange takes place by transfer of a proton or hydrogen from water to the more distant yl-oxygen. The activation barriers for proton/hydrogen transfer in the ground state and the (3)Delta(g) and (3)Gamma(g) states are 186, 219, and 84 kJ/mol, respectively. The relaxation energy for the (3)Gamma(g) state in the solvent after photoexcitation is -86 kJ/mol, indicating that the energy barrier can be overcome; the "pi" states are therefore the most probable route for proton/hydrogen transfer. They can be populated after UV irradiation but are too high in energy (approximately 36,000-40,000 cm(-1)) to be reached by a single-photon absorption at 436 nm (22,900 cm(-1)), where experimental data have demonstrated that exchange can take place. Okuyama et al. [Bull. Res. Lab. Nucl. React. (Tokyo Inst. Technol.) 1978, 3, 39-50] have demonstrated that an intermediate is formed when an acidic solution of UO2(2+)(aq) is flash-photolyzed in the UV range. The absorption spectrum of this short-lived intermediate (which has a maximum at 560 nm) indicates that this species arises from 436 nm excitation of the luminescent (3)Delta(g) state (which has a lifetime of approximately 2 x 10(-6) s); this is sufficient to reach the reactive "pi" states. It has been speculated that the primary reaction in acidic solutions of UO2(2+)(aq) is the formation of a uranyl(V) species; our results indicate that the structure in the luminescent state has some similarity to that of UO2(+) but that the reactive species in the "pi" states is a cation radical with a distinctly different structure.     

Spectroscopic investigation of Al2N and its anion via negative ion photoelectron spectroscopy

Negative ion photoelectron spectroscopy was used to elucidate the electronic and geometric structure of the gaseous Al2N/Al2N- molecules, using photodetachment wavelengths of 416 nm (2.977 eV), 355 nm (3.493 eV), and 266 nm (4.661 eV). Three electronic bands are observed and assigned to the X2Sigma(u)+ <-- X1Sigma(g)+, A2Pi(u) <-- X1Sigma(g)+, and B2Sigma(g)+ <-- X1Sigma(g)+ electronic transitions, with the caveat that one or both excited states may be slightly bent. With the aid of density functional theory calculations and Franck-Condon spectral simulations, we determine the adiabatic electron affinity of Al2N, 2.571 +/- 0.008 eV, along with geometry changes upon photodetachment, vibrational frequencies, and excited-state term energies. Observation of excitation of the odd vibrational levels of the antisymmetric stretch (nu3) suggests a breakdown of the Franck-Condon approximation, caused by the vibronic coupling between the X2Sigma(u)+ and B2Sigma(g)+ electronic states through the nu3 mode.     

Time-dependent density functional theory based on a noncollinear formulation of the exchange-correlation potential

In this study we have introduced a formulation of time-dependent density functional theory (TDDFT) based on a noncollinear exchange-correlation potential. This formulation is a generalization of conventional TDDFT. The form of this formulation is exactly the same as that of the conventional TDDFT for the excitation energies of transitions that do not involve spin flips. In addition, this noncollinear TDDFT formulation allows for spin-flip transitions. This feature makes it possible to resolve more fully excited state spin multiplets, while for closed-shell systems, the spin-flip transitions will result in singlet-triplet excitations and this excitation energy calculated from this formulation of TDDFT is exactly the same as that from ordinary TDDFT. This formulation is applied to the dissociation of H(2) in its (1)Sigma(g) (+) ground state and (1)Sigma(u) (+) and (3)Sigma(u) (-) excited states with (3)Sigma(u) (-) (M(s)=+1) as the reference state and the multiplets splitting of some atoms.     

Ab initio potential-energy surfaces of O2(X3Sigmag -, a1Deltag, b1Sigmag +) +O2 (X3Sigmag -, a1Deltag, b1Sigmag +): mechanism of quenching of O2 (a 1Deltag)

Ab initio computational studies were carried out in order to explore the possible mechanisms of quenching of O(2)(a (1)Delta(g)) by O(2)(X (3)Sigma(g) (-)): the self-quenching of O(2)(a (1)Delta(g)) and other energy-transfer processes involving two O(2) molecules. All eighteen states arising from two O(2) molecules in the X (3)Sigma(g) (-), a (1)Delta(g), and b (1)Sigma(g) (+) states are considered. After scans at the state-averaged complete active space self-consistent field method to identify possible regions of crossing between states belonging to different asymptotes, complete active state second-order perturbation theory high-symmetry optimization and low-symmetry scans established that four different minima on the seams of crossing (MSXs), arising between the a+a manifold and the X+b manifold and responsible for self-quenching: O(2)(a (1)Delta(g))+O(2)(a (1)Delta(g))-->O(2)(X (3)Sigma(g) (-))+O(2)(b (1)Sigma(g) (+)), have coplanar C(2h) or C(2v) symmetries and are only 0.45 eV barrier relative to the a+a asymptote and energetically easily accessible. The rate constant for this process was estimated based on the Landau-Zener formalism. The MSXs for quenching of O(2)(a (1)Delta(g)) by the ground state O(2)(X (3)Sigma(g) (-)):O(2)(a (1)Delta(g))+O(2)(X (3)Sigma(g) (-))-->O(2)(X (3)Sigma(g) (-))+O(2)(X (3)Sigma(g) (-)) require higher energies and the process is not likely to be important.     

Vacuum ultraviolet photoionization of C3

Photoionization efficiency (PIE) curves for C(3) molecules produced by laser ablation are measured from 11.0 to 13.5 eV with tunable vacuum ultraviolet undulator radiation. A step in the PIE curve versus photon energy, obtained with N(2) as the carrier gas, supports the conclusion of very effective cooling of C(3) to its linear (1)Sigma(g)(+) ground state. The second step observed in the PIE curve versus photon energy could be the first experimental evidence of the C(3)(+)((2)Sigma(g)(+)) excited state. The experimental results, complemented by ab initio calculations, suggest a state-to-state vertical ionization energy of 11.70 +/- 0.05 eV between the C(3)(X(1)Sigma(g)(+)) and the C(3)(+)(X(2)Sigma(u)(+)) states. An ionization energy of 11.61 +/- 0.07 eV between the neutral and ionic ground states of C(3) is deduced using the data together with our calculations. Accurate ab initio calculations are performed for both linear and bent geometries on the lowest doublet electronic states of C(3)(+) using Configuration Interaction (CI) approaches and large basis sets. These calculations confirm that C(3)(+) is bent in its electronic ground state, which is separated by a small potential barrier from the (2)Sigma(u)(+) minimum. The gradual increase at the onset of the PIE curve suggests a geometry change between the ground neutral and cationic states. The energies between several doublet states of the ion are theoretically determined to be 0.81, 1.49, and 1.98 eV between the (2)Sigma(u)(+) and the (2)Sigma(g)(+),( 2)Pi(u), (2)Pi(g) excited states of C(3)(+), respectively.     

Theoretical study of the gas-phase chemiionization reactions La + O and La + O2

The La + O and La + O 2 chemiionization reactions have been investigated with quantum chemical methods. For La + O 2(X (3)Sigma g) and La + O 2(a (1)Delta g), the chemiionization reaction La + O 2 --> LaO 2 (+) + e (-) has been shown to be endothermic and does not contribute to the experimental chemielectron spectra. For the La + O 2(X (3)Sigma g) reaction conditions, chemielectrons are produced by La + O 2 --> LaO + O, followed by La + O --> LaO (+) + e (-). This is supported by the same chemielectron band, arising from La + O --> LaO (+) + e (-), being observed from both the La + O( (3)P) and La + O 2(X (3)Sigma g) reaction conditions. For La + O 2(a (1)Delta g), a chemielectron band with higher electron kinetic energy than that obtained from La + O 2(X (3)Sigma g) is observed. This is attributed to production of O( (1)D) from the reaction La + O 2(a (1)Delta g) --> LaO + O( (1)D), followed by chemiionization via the reaction La + O( (1)D) --> LaO (+) + e (-). Potential energy curves are computed for a number of states of LaO, LaO* and LaO (+) to establish mechanisms for the observed La + O --> LaO (+) + e (-) chemiionization reactions.     

A vacuum ultraviolet pulsed field ionization-photoelectron study of cyanogen cation in the energy range of 13.2-15.9 eV

The vacuum ultraviolet pulsed field ionization-photoelectron and photoionization efficiency spectra of NCCN have been measured in the energy region of 13.25-17.75 eV. The analyses of these spectra have provided accurate ionization energy (IE) values of 13.371+/-0.001, 14.529+/-0.001, 14.770+/-0.001, and 15.516+/-0.001 eV for the formation of NCCN(+) in the X(2)Pi(g), A(2)Sigma(g) (+), B(2)Sigma(u) (+), and C(2)Pi(u) states, respectively. The ionization energy [NCCN(+)(B(2)Sigma(u) (+))] value determined here indicates that the origin of the NCCN(+)(B(2)Sigma(u) (+)) state lies lower in energy by 25 meV than previously reported. A set of spectroscopic parameters for NCCN(+)(X(2)Pi(g)) has been calculated using high level ab initio calculations. The experimental spectra are found to consist of ionizing transitions populating the vibronic levels of NCCN(+), which consist of pure vibronic progressions, combination modes involving the symmetric CN stretch, the CC stretch, and even quanta of the antisymmetric CN stretch, and bending vibrations. These bands are identified with the guidance of the present ab initio calculations.     

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.     

Gas phase electronic spectra of the carbon chains C5, C6, C8, and C9

Three electronic absorption systems for C5 at 511, 445, and 232 nm and one for C6, C8, and C9 centered at 228, 259, and 288 nm have been observed in the gas phase. The C5 chain was produced in both discharge and ablation sources and detected using resonant two-color two-photon ionization spectroscopy involving 10.5 eV photons. The decay of the excited singlet electronic states indicates fast intramolecular processes on a subpicosecond time scale. The internal energy is assumed to be trapped in a triplet state for at least 15 micros. Hole-burning experiments on the 2 (3)Sigma(u)- <-- X (3)Sigma(g)- transition of C6, C8, and (1)Sigma(u)+ <-- X (1)Sigma(g)+ of C9 confirm the predissociative nature of the excited electronic states.     

State-resolved dynamics of the CN(B2Sigma+) and CH(A2Delta) excited products resulting from the VUV photodissociation of CH3CN

Fourier transform visible spectroscopy, in conjunction with VUV photons produced by a synchrotron, is employed to investigate the photodissociation of CH3CN. Emission is observed from both the CN(B2Sigma+-X2Sigma+) and CH(A2Delta-X2Pi) transitions; only the former is observed in spectra recorded at 10.2 and 11.5 eV, whereas both are detected in the 16 eV spectrum. The rotational and vibrational temperatures of both the CN(B2Sigma+) and CH(A2Delta) radical products are derived using a combination of spectral simulations and Boltzmann plots. The CN(B2Sigma+) fragment displays a bimodal rotational distribution in all cases. Trot(CN(B2Sigma+)) ranges from 375 to 600 K at lower K' and from 1840 to 7700 K at higher K' depending on the photon energy used. Surprisal analyses indicate clear bimodal rotational distributions, suggesting CN(B2Sigma+) is formed via either linear or bent transition states, respectively, depending on the extent of rotational excitation in this fragment. CH(A2Delta) has a single rotational distribution when produced at 16 eV, which results in Trot(CH(A2Delta))=4895+/-140 K in v'=0 and 2590+/-110 K in v'=1. From thermodynamic calculations, it is evident that CH(A2Delta) is produced along with CN(X2Sigma+)+H2. These products can be formed by a two step mechanism (via excited CH3* and ground state CN(X2Sigma+)) or a process similar to the "roaming" atom mechanism; the data obtained here are insufficient to definitively conclude whether either pathway occurs. A comparison of the CH(A2Delta) and CN(B2Sigma+) rotational distributions produced by 16 eV photons allows the ratio between the two excited fragments at this energy to be determined. An expression that considers the rovibrational populations of both band systems results in a CH(A2Delta):CN(B2Sigma+) ratio of (1.2+/-0.1):1 at 16 eV, thereby indicating that production of CH(A2Delta) is significant at 16 eV.     

Ab initio investigation of the electronic structure and bonding of BH, BH(-), and HBBH molecules

By correlating all electrons and employing core-tuned correlation consistent basis sets of quintuple-zeta quality, we applied multireference and coupled-cluster methods to study 32 electronic states of the diatomic BH molecule, two bound states of BH(-), and three states of the linear HBBH molecule. We have constructed full potential energy curves and profiles, reporting binding energies, geometries, spectroscopic parameters, dipole moments, and energy separations, whereas our numerical results are in excellent agreement with available experimental numbers. We are trying as well to interpret the binding modes of a large number of the examined states. 18 states of BH are of Rydberg character, with the BH(-) anion revealing similar structural characteristics to the isoelectronic CH species. The first three states of HBBH X 3Sigma g (-), a 1Delta g, and b 1Sigma g + diabatically correlate to two a 3Pi BH fragments, they are similar to the states b 3Sigma g (-), B 1Delta g, and B' 1Sigma g + of the isoelectronic molecule C2, however, their ordering follows that of the first three states of the O2 molecule.     

Observation and calculation of the Cs2 2 3Delta(1g) and b 3Pi(0u) states

The Cs(2) 2 (3)Delta(1g) and b (3)Pi(0u) states have been observed by infrared-infrared double resonance spectroscopy for the first time. 221 2 (3)Delta(1g)<--A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) double resonance lines have been assigned to transitions into the 2 (3)Delta(1g) v=6-13 vibrational levels. Resolved fluorescence into the b (3)Pi(0u) v(')=0-48 levels has been recorded. Molecular constants and potential energy curves are determined by the global fit of the entire set of the experimental data. Theoretical potential energy curves of the 2 (3)Delta(g) and b (3)Pi(u) states have been determined in the framework of the pseudopotential method and are compared with the experimental results.     

Electronic Structure Characteristics of ESIPT and TICT Fluorescence Emissions and Calculations of Emitting Energies

A scheme of time-dependent density functional theory (TDDFT) combined with the single-excitation configuration interaction (CIS) approach was employed to investigate the first excited singlet state (S₁) for eight salicylanilide derivatives and analogues, which have similar structural formulas. The results showed that fluorescence-emitting mechanisms of these molecules were in two distinct manners (excited-state intramolecular proton transfer (ESIPT) and twisted intramolecular charge transfer (TICT)), which agreed with the well-known experiments. For ESIPT compounds with inconspicuous charge transfer (CT) during electron transition, pure functionals without Hartree-Fock (HF) exchange energy, such as OLYP and BLYP, were suitable to calculate emitting energies. For TICT compounds with large CT during electron transition, hybrid functionals with about 37% HF exchange energy, such as mPW1B95 and MPW1K, performed well. On condition that the exchange-correlation (XC) functionals were chosen properly according to the rules above, reliable emitting energies for salicylanilide derivatives and analogues could be obtained at the TDDFT/6-31G(d)//CIS/3-21G(d) level. The average accuracy reached about 0.2 eV. For the salicylanilides with both proton transfer (PT) and CT reaction channels, only one channel occurred actually according to the principle of energy minimum. This actual reaction decided proper XC functionals, whereas the reaction that did not occur actually was trivial. Eight appendent compounds were calculated to prove that this successful scheme is expected to be suitable for other ESIPT and TICT compounds.     

Spin-orbit coupling in O2(v)+O2 collisions: a new energy transfer mechanism

A reduced dimensionality model is used to study the relaxation of highly vibrationally excited O(2)(X (3)Sigma(g) (-),v>/=20) in collisions with O(2)(X (3)Sigma(g) (-),v=0). Spin-orbit coupled potential energy surfaces are employed to incorporate the vibrational-to-electronic energy transfer mechanism involving the O(2)(a (1)Delta(g)) and O(2)(b (1)Sigma(g) (+)) excited states. The transition probabilities obtained show a sharp increase for v>/=26 providing the first direct evidence of the important role played by the electronic energy transfer processes in the depletion of O(2)(X (3)Sigma(g) (-),v>/=26).     

Threshold-photoelectron-spectroscopy-coincidence study of the double photoionization of HBr

A threshold-photoelectron-coincidence spectrum of HBr has been recorded in the 32.2-35.8 eV photon energy range, with a resolution of approximately 0.01 eV, using a synchrotron radiation source. The X (3)Sigma(-) and a (1)Delta(2) states of the HBr(2+) dication are clearly observed in the spectrum, while there is no clear evidence for the formation of the b (1)Sigma(+) electronic state. For the first two states, the vibrational states v=0-3 have been resolved, while for the ground X (3)Sigma(-) state also spin-orbit splitting has been detected. The results appear in good agreement with previous experimental observations. A comparison with theoretical predictions indicates the role of "noncovalent" contributions to the interaction between the two atomic partners for the formation of metastable states.     

ESIPT和TICT荧光发射的电子结构特征及发射能计算

采用含时密度泛函理论(TDDFT)与单激发组态相互作用(CIS)相结合的计算方案对八种结构相似的水杨酰苯胺衍生物及其类似物第一激发单重态(S1)进行考察, 证实它们的荧光发射分属分子内质子转移(ESIPT)和分子扭转-电荷转移(TICT)两种不同机制且结论与已知实验事实相符. ESIPT发光的化合物在电子跃迁前后无明显的电荷转移发生, 发射能计算的适用泛函是OLYP和BLYP等无Hartree-Fock(HF)交换成分的纯泛函; TICT发光的化合物在电子跃迁前后发生明显的电荷转移, 其适用泛函为含约37% HF交换成分的混合型泛函(例如mPW1B95和MPW1K). 按上述原则来选择适用泛函, 即可在TDDFT/6-31G(d)//CIS/3-21G(d)理论水平上正确预测水杨酰苯胺衍生物和类似物的发射能, 平均精度可达0.2 eV. 兼具质子转移与电荷转移双反应通道的化合物, 两者的竞争遵从能量最小原理, 结果使荧光发射仅选择其中一个通道进行. 泛函的选择只与实际发生的反应有关, 与并未实际发生的反应通道无关. 附加的八个算例进一步表明, 此成功的计算方案可望推广应用于其它类型的ESIPT和TICT荧光有机物.