Nonadiabatic coupling vectors for excited states within time-dependent density functional theory in the Tamm-Dancoff approximation and beyond

Recently, we have proposed a scheme for the calculation of nonadiabatic couplings and nonadiabatic coupling vectors within linear response time-dependent density functional theory using a set of auxiliary many-electron wavefunctions [I. Tavernelli, E. Tapavicza, and U. Rothlisberger, J. Chem. Phys. 130, 124107 (2009)]. As demonstrated in a later work [I. Tavernelli, B. F. E. Curchod, and U. Rothlisberger, J. Chem. Phys. 131, 196101 (2009)], this approach is rigorous in the case of the calculation of nonadiabatic couplings between the ground state and any excited state. In this work, we extend this formalism to the case of coupling between pairs of singly excited states with the same spin multiplicity. After proving the correctness of our formalism using the electronic oscillator approach by Mukamel and co-workers [S. Tretiak and S. Mukamel, Chem. Rev. (Washington, D.C.) 102, 3171 (2002)], we tested the method on a model system, namely, protonated formaldimine, for which we computed S(1)/S(2) nonadiabatic coupling vectors and compared them with results from high level (MR-CISD) electronic structure calculations.     

The role of the excited electronic states in the C+ + H2O reaction

The electronic excited states of the [COH2]+ system have been studied in order to establish their role in the dynamics of the C+ + H2O-->[COH]+ +H reaction, which is a prototypical ion-molecule reaction. The most relevant minima and saddle points of the lowest excited state have been determined and energy profiles for the lowest excited doublet and quartet electronic states have been computed along the fragmentation and isomerization coordinates. Also, nonadiabatic coupling strengths between the ground and the first excited state have been computed where they can be large. Our analysis suggests that the first excited state could play an important role in the generation of the formyl isomer, which has been detected in crossed beam experiments [D. M. Sonnenfroh et al., J. Chem. Phys. 83, 3985 (1985)], but could not be explained in quasiclassical trajectory computations [Y. Ishikawa et al., Chem. Phys. Lett. 370, 490 (2003); J. R. Flores, J. Chem. Phys. 125, 164309 (2006)].     

A quantum wave-packet study of intersystem crossing effects in the O(3P2,1,0,1D2)+H2 reaction

We present for the first time an exact quantum study of spin-orbit-induced intersystem crossing effects in the title reaction. The time-dependent wave-packet method, combined with an extended split operator scheme, is used to calculate the fine-structure resolved cross section. The calculation involves four electronic potential-energy surfaces of the 1A' state [J. Dobbyn and P. J. Knowles, Faraday Discuss. 110, 247 (1998)], the 3A' and the two degenerate 3A" states [S. Rogers, D. Wang, A. Kuppermann, and S. Wald, J. Phys. Chem. A 104, 2308 (2000)], and the spin-orbit couplings between them [B. Maiti, and G. C. Schatz, J. Chem. Phys. 119, 12360 (2003)]. Our quantum dynamics calculations clearly demonstrate that the spin-orbit coupling between the triplet states of different symmetries has the greatest contribution to the intersystem crossing, whereas the singlet-triplet coupling is not an important effect. A branch ratio of the spin state Pi32 to Pi12 of the product OH was calculated to be approximately 2.75, with collision energy higher than 0.6 eV, when the wave packet was initially on the triplet surfaces. The quantum calculation agrees quantitatively with the previous quasiclassical trajectory surface hopping study.     

Effective local potentials for excited states

The constrained variational Hartree-Fock method for excited states of the same symmetry as the ground state [Chem. Phys. Lett. 287, 189 (1998)] is combined with the effective local potential (ELP) method [J. Chem. Phys. 125, 081104 (2006)] to generate Kohn-Sham-type exact-exchange potentials for singly excited states of many-electron systems. Illustrative examples include the three lowest (2)S states of the Li and Na atoms and the three lowest (3)S states of He and Be. For the systems studied, excited-state ELPs differ from the corresponding ground-state potentials in two respects: They are less negative and have small additional "bumps" in the outer electron region. The technique is general and can be used to approximate excited-state exchange-correlation potentials for other orbital-dependent functionals.     

Mechanistic aspects of proton chain transfer in the green fluorescent protein. Part II. A comparison of minimal quantum chemical models

In this paper we report the results of extensive quantum chemical reaction pathway calculations for the electronic ground state of several different cluster models that mimic the proton chain transfer path within the green fluorescent protein (GFP). Our principal objective is to establish the robustness with respect to variations in the model of our recent mechanistic inferences for the ground state proton chain transfer [S. Wang and S. C. Smith, J. Phys. Chem. B, 2006, 110, 5084]. Additionally, comparison of our ground state results with the excited state proton transfer (ESPT) study by Vendrell et al. [O. Vendrell, R. Gelabert, M. Moreno and J. M. Lluch, J. Am. Chem. Soc., 2006, 128, 3564] leads to the conclusion that the mechanism of proton chain transfer may be expected to be analogous in ground and excited states, principally because in both cases the loss of the chromophore's phenolic proton contributes strongly to the reaction coordinate only late in the reaction path.     

Three-dimensional potential energy surface of the Ar-OH(2Pi i) complex

Pure rotational transitions in the ground state for Ar-OH and Ar-OD [Y. Ohshima et al., J. Chem. Phys. 95, 7001 (1991) and Y. Endo et al., Faraday Discuss. 97, 341 (1994)], those in the excited states of the OH vibration, nu(s)=1 and 2, observed by Fourier-transform microwave spectroscopy in the present study, rotation-vibration transitions observed by infrared-ultraviolet double-resonance spectroscopy [K. M. Beck et al., Chem. Phys. Lett. 162, 203 (1989) and R. T. Bonn et al., J. Chem. Phys. 112, 4942 (2000)], and the P-level structure observed by stimulated emission pumping spectroscopy [M. T. Berry et al., Chem. Phys. Lett. 178, 301 (1991)] have been simultaneously analyzed to determine the potential energy surface of Ar-OH in the ground state. A Schrodinger equation, considering all the freedom of motions for an atom-diatom system in the Jacobi coordinate, R, theta, and r, was numerically solved to obtain energies of the rovibrational energy levels using the discrete variable representation method. A three-dimensional potential energy surface is determined by a least-squares fitting. In the analysis the potential parameters, obtained by ab initio calculations at the RCCSD(T) level of theory with a set of basis functions of aug-cc-pVTZ and midbond functions, are used as initial values. The determined intermolecular potential energy surface and its dependence on the OH monomer bond length are compared with those of an isovalent radical complex, Ar-SH.     

Ab initio potential energy surfaces, bound states, and electronic spectrum of the Ar-SH complex

New ab initio potential energy surfaces for the (2)Pi ground electronic state of the Ar-SH complex are presented, calculated at the RCCSD(T)/aug-cc-pV5Z level. Weakly bound rotation-vibration levels are calculated using coupled-channel methods that properly account for the coupling between the two electronic states. The resulting wave functions are analyzed and a new adiabatic approximation including spin-orbit coupling is proposed. The ground-state wave functions are combined with those obtained for the excited (2)Sigma(+) state [D. M. Hirst, R. J. Doyle, and S. R. Mackenzie, Phys. Chem. Chem. Phys. 6, 5463 (2004)] to produce transition dipole moments. Modeling the transition intensities as a combination of these dipole moments and calculated lifetime values [A. B. McCoy, J. Chem. Phys. 109, 170 (1998)] leads to a good representation of the experimental fluorescence excitation spectrum [M.-C. Yang, A. P. Salzberg, B.-C. Chang, C. C. Carter, and T. A. Miller, J. Chem. Phys. 98, 4301 (1993)].     

Further investigation of the photodissociation dynamics of dichlorocarbene near 248 nm

A further investigation of the 248 nm photodissociation of CCl(2), which expands upon our original study of this process [S. K. Shin and P. J. Dagdigian, Phys. Chem. Chem. Phys. 8, 3446 (2006)], is presented. The CCl(2) parent molecule and the CCl photofragment were detected by laser fluorescence excitation in a molecular beam experiment. From the dependence of the CCl(2) signals on the photolysis laser fluence, attenuation cross sections of the 0(0), 1(1), and 2(1) vibrational levels were determined; the cross sections for the excited vibrational levels were found to be significantly smaller than those for the ground vibrational level. The previously observed fragment CCl bimodal rotational state distribution was found to arise from the photolysis of more than one parent molecule. At low CHCl(3) mole fractions in the gas supplied to the pyrolysis beam source, it was concluded that CCl(2) is the photolysis precursor for both low-J and high-J CCl fragments. On the basis of the dependence of the CCl signals on the photolysis laser fluence, ground and vibrationally excited CCl(2), respectively, were assigned as the precursors to these two classes of fragments. The photofragment excitation spectra for low-J and high-J CCl fragments from the photolysis of CCl(2) were recorded in the wavelength range around 248 nm; both were found to be structureless. The 248 nm photodissociation dynamics of CCl(2) is discussed in light of our experimental observations and quantum chemical calculations of the CCl(2) excited electronic states.     

Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers

Using both analytical and simulational methods, we study low-temperature nucleation rates in kinetic Ising lattice-gas models that evolve under two different Arrhenius dynamics that interpose between the Ising states a transition state representing a local energy barrier. The two dynamics are the transition-state approximation [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)] and the one-step dynamic [H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989)]. Even though they both obey detailed balance and are here applied to a situation that does not conserve the order parameter, we find significant differences between the nucleation rates observed with the two dynamics, and between them and the standard Glauber dynamic [R. J. Glauber, J. Math. Phys. 4, 294 (1963)], which does not contain transition states. Our results show that great care must be exercised when devising kinetic Monte Carlo transition rates for specific physical or chemical systems.     

Broad shape resonance effects in CaF Rydberg states

Results of ab initio R-matrix calculations [S. N. Altunata et al., J. Chem. Phys. 123, 084319 (2005)] indicate the presence of a broad shape resonance in electron-CaF(+) scattering for the (2)Sigma(+) electronic symmetry near the ionization threshold. The properties of this shape resonance are analyzed using the adiabatic partial-wave expansion of the scattered electron wave function introduced by Le Dourneuf et al. [J. Phys. B 15, L685 (1982)]. The qualitative aspects of the shape resonance are explained by an adiabatic approximation on the electronic motion. Mulliken's rule for the structure of the Rydberg state wave functions [R. S. Mulliken, J. Am. Chem. Soc. 86, 3183 (1964)] specifies that, except for an (n*)(-32) amplitude scale factor, every excited state wave function within one Rydberg series is built on an innermost lobe that remains invariant in shape and nodal position as a function of the excitation energy. Mulliken's rule implies a weak energy dependence of the quantum defects for an unperturbed molecular Rydberg series, which is given by the Rydberg-Ritz formula. This zero-order picture is violated by a single (2)Sigma(+) CaF Rydberg series at all Rydberg state energies (n*=5-->infinity, more so with increasing n*) below the ionization threshold, under the broad width of the shape resonance. Such a violation is diagnostic of a global "scarring" of the Rydberg spectrum, which is distinct from the more familiar local level perturbations.     

Computer simulation study of metastable ice VII and amorphous phases obtained by its melting

Molecular dynamics simulations of metastable ice VII and cubic ice Ic are carried out in order to examine (1) the ability of commonly used water interaction potentials to reproduce the properties of ices, and (2) the possibility of generating low-density amorphous (LDA) structures by heating ice VII, which is known to transform to LDA at approximately 135 K at normal pressure [S. Klotz, J. M. Besson, G. Hamel, R. J. Nelmes, J. S. Loveday, and W. G. Marshall, Nature (London) 398, 681 (1999)]. We test four simple empirical interaction potentials of water: TIP4P [W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys. 79, 926 (1983)], SPC/E [H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. B 91, 6269 (1987)], TIP5P [M. W. Mahoney and W. L. Jorgensen, J. Chem. Phys. 112, 8910 (2000)], and ST2 [F. H. Stillinger and A. Rahman, J. Chem. Phys. 60, 1545 (1974)]. We have found that TIP5P ice VII melts at 210 K, TIP4P at 90 K, and SPC/E at 70 K. Only TIP5P water after transition has a structure similar to that of LDA. TIP4P and SPC/E have almost identical structures, dissimilar to any known water or amorphous phases, but upon heating both slowly evolve towards LDA-like structure. ST2 ice VII is remarkably stable up to 430 K. TIP4P and SPC/E predict correctly the cubic ice collapse into a high-density amorphous ice (HDA) at approximately 1 GPa whereas TIP5P remains stable up to approximately 5 GPa. The densities of the simulated ice phases differ significantly, depending on the potential used, and are generally higher than experimental values. The importance of proper treatment of long-range electrostatic interactions is also discussed.     

Vibrationally inelastic collisions in H+ +CO system: comparing quantum calculations with experiments

State-resolved cross beam experiments [H. Udseth et al., J. Chem. Phys. 60, 3051 (1974); J. Krutein and F. Linder, J. Chem. Phys. 71, 599 (1979); G. Niedner-Schatteburg and J. P. Toennies, Adv. Chem. Phys. LXXXII, 553 (1992)], coupled with proton energy loss spectroscopy for the inelastic scattering of H(+) from CO in the collision range of 10-30 eV show very low vibrational excitation of the target molecule. Stimulated by the experimentally observed low vibrational inelasticity in the system the ground and the first two low-lying excited electronic potential-energy surfaces have been computed using the ab initio multireference configuration interaction method. Quantum dynamics has been performed on the ground potential energy surface in the framework of vibrational close-coupling rotational infinite-order sudden approximation. The various computed dynamical attributes such as differential and integral cross sections, and average vibrational energy transfer are analyzed in detail, and compared successfully with the available experimental results.     

Analysis of experimental data for the nucleation rate of water droplets

A formula for the stationary nucleation rate J is proposed and used for analysis of experimental data for the dependence of J on the supersaturation ratio S in isothermal homogeneous nucleation of water droplets in vapors. It is found that the experimental data are described quite successfully by the proposed formula which is based on (i) the Gibbs presentation of the nucleation work in terms of overpressure, (ii) the Girshick-Chiu [J. Chem. Phys. 93, 1273 (1990); 94, 826 (1991)] self-consistency correction to the equilibrium cluster size distribution, and (iii) the Reguera-Rubi [J. Chem. Phys. 115, 7100 (2001)] kinetic accounting of the nucleus translational-rotational motion. The formula, like that of Wolk and Strey [J. Phys. Chem. B 105, 11683 (2001)], could be used as a semiempirical relation describing the J(S) dependence for nucleation in vapors of single-component droplets or crystals of substances with insufficiently well known equations of state.     

Use of nuclear stiffness in search for a maximum hardness principle and for the softest states along the chemical reaction path: a new formula for the energy third derivative gamma

Nuclear stiffness, expressed as a hardness derivative, appears to be a good measure of the slope of global hardness. The authors analyze molecular states for which hardness has a maximum value. Maximum hardness principle (MHP) has been discussed. At the ground state hardness function does not obtain a maximum value versus spatial coordinates within a constant number of electrons (N), but is so within constant chemical potential (mu) constraint. The authors apply this feature to evaluate an energy third derivative (gamma). MHP has been analyzed via symmetry considerations of nuclear stiffness and nuclear reactivity. Nuclear stiffness has been also applied to study the hardness profile for a chemical reaction. In this case, the authors seek molecular states for which hardness is at a minimum. They have examined systems for which they have recently obtained regional chemical potentials [P. Ordon and A. Tachibana, J. Mol. Model. 11, 312 (2005); J. Chem. Sci. 117, 583 (2005)]. The transition state is found not to be the softest along the chemical reaction path. Nuclear stiffness reflects well the softest conformation of a molecule, which has been found independently along the intrinsic reaction coordinate profile. Electronic energy-density [A. Tachibana, J. Mol. Mod. 11, 301 (2005)] has been used to visualize the reactivity difference between the softest state and the transition state.     

Linear scaling computation of the Fock matrix. VII. Periodic density functional theory at the Gamma point

Linear scaling quantum chemical methods for density functional theory are extended to the condensed phase at the Gamma point. For the two-electron Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb summation [M. Challacombe and E. Schwegler, J. Chem. Phys. 106, 5526 (1997)], together with multipole representation of the crystal field [M. Challacombe, C. White, and M. Head-Gordon, J. Chem. Phys. 107, 10131 (1997)]. A periodic version of the hierarchical cubature algorithm [M. Challacombe, J. Chem. Phys. 113, 10037 (2000)], which builds a telescoping adaptive grid for numerical integration of the exchange-correlation matrix, is shown to be efficient when the problem is posed as integration over the unit cell. Commonalities between the Coulomb and exchange-correlation algorithms are discussed, with an emphasis on achieving linear scaling through the use of modern data structures. With these developments, convergence of the Gamma-point supercell approximation to the k-space integration limit is demonstrated for MgO and NaCl. Linear scaling construction of the Fockian and control of error is demonstrated for RBLYP6-21G* diamond up to 512 atoms.     

Partition theory: a very simple illustration

We illustrate the main features of a recently proposed method based on ensemble density functional theory to divide rigorously a complex molecular system into its parts (J. Phys. Chem. A 2007, 111, 2229). The illustrative system is an analog of the hydrogen molecule for which analytic expressions for the densities of the parts (hydrogen "atoms") are found along with the "partition potential" that enters the theory. While previous formulations of chemical reactivity theory lead to zero, or undefined, values for the chemical hardness of the isolated parts, we demonstrate they can acquire a finite and positive hardness within the present formulation.     

The electronic properties of potassium doped copper-phthalocyanine studied by electron energy-loss spectroscopy

The authors have studied the electronic structure of potassium doped copper-phthalocyanine using electron energy-loss spectroscopy. The evolution of the loss function indicates the formation of distinct KxCuPc phases. Taking into account the C1s and K2p core level excitations and recent results by Giovanelli et al. [J. Chem. Phys. 126, 044709 (2007)], they conclude that these are K2CuPc and K4CuPc. They discuss the changes in the electronic excitations upon doping on the basis of the molecular electronic levels and the presence of electronic correlations.