Photoionization cross sections with optimized orbital exponents within the complex basis function method

We show a new direction to expand the applicability of the complex basis function method for calculating photoionization cross sections through the imaginary part of the frequency-dependent polarizability. Based on the variational stability of the frequency-dependent polarizability, we made nonlinear optimizations of complex orbital exponents in basis functions representing continuum wave functions, and obtained fairly accurate results for H atom with only one or two complex basis functions particularly with dipole velocity gauge. Results were almost independent of whether Slater-type or Gaussian-type orbitals are used, implying the applicability to general many electron problems. The method was also applied to the (1)S (1s)(2) --> (1)P (1s)(1)(kp)(1) cross section of He atom and the optimized complex orbital exponents were related to those of H atom through the scaling property. The nonlinear optimizations have converged smoothly and the cross sections were in excellent agreement with experiment throughout wide photon energies, which suggest the effectiveness of the approach for many-electron systems.     

Optimization of complex slater‐type functions with analytic derivative methods for describing photoionization differential cross sections

The complex basis function (CBF) method applied to various atomic and molecular photoionization problems can be interpreted as an method to solve the driven‐type (inhomogeneous) Schrödinger equation, whose driven term being dipole operator times the initial state wave function. However, efficient basis functions for representing the solution have not fully been studied. Moreover, the relation between their solution and that of the ordinary Schrödinger equation has been unclear. For these reasons, most previous applications have been limited to total cross sections. To examine the applicability of the CBF method to differential cross sections and asymmetry parameters, we show that the complex valued solution to the driven‐type Schrödinger equation can be variationally obtained by optimizing the complex trial functions for the frequency dependent polarizability. In the test calculations made for the hydrogen photoionization problem with five or six complex Slater‐type orbitals (cSTOs), their complex valued expansion coefficients and the orbital exponents have been optimized with the analytic derivative method. Both the real and imaginary parts of the solution have been obtained accurately in a wide region covering typical molecular regions. Their phase shifts and asymmetry parameters are successfully obtained by extrapolating the CBF solution from the inner matching region to the asymptotic region using WKB method. The distribution of the optimized orbital exponents in the complex plane is explained based on the close connection between the CBF method and the driven‐type equation method. The obtained information is essential to constructing the appropriate basis sets in future molecular applications. © 2017 Wiley Periodicals, Inc.     

Calculation of photoionization differential cross sections using complex Gauss‐type orbitals

Accurate theoretical calculation of photoelectron angular distributions for general molecules is becoming an important tool to image various chemical reactions in real time. We show in this article that not only photoionization total cross sections but also photoelectron angular distributions can be accurately calculated using complex Gauss‐type orbital (cGTO) basis functions. Our method can be easily combined with existing quantum chemistry techniques including electron correlation effects, and applied to various molecules. The so‐called two‐potential formula is applied to represent the transition dipole moment from an initial bound state to a final continuum state in the molecular coordinate frame. The two required continuum functions, the zeroth‐order final continuum state and the first‐order wave function induced by the photon field, have been variationally obtained using the complex basis function method with a mixture of appropriate cGTOs and conventional real Gauss‐type orbitals (GTOs) to represent the continuum orbitals as well as the remaining bound orbitals. The complex orbital exponents of the cGTOs are optimized by fitting to the outgoing Coulomb functions. The efficiency of the current method is demonstrated through the calculations of the asymmetry parameters and molecular‐frame photoelectron angular distributions of and . In the calculations of , the static exchange and random phase approximations are employed, and the dependence of the results on the basis functions is discussed. © 2017 Wiley Periodicals, Inc.     

State-to-state reactive differential cross sections for the H+H2-->H2+H reaction on five different potential energy surfaces employing a new quantum wavepacket computer code: DIFFREALWAVE

State-to-state differential cross sections have been calculated for the hydrogen exchange reaction, H+H2-->H2+H, using five different high quality potential energy surfaces with the objective of examining the sensitivity of these detailed cross sections to the underlying potential energy surfaces. The calculations were performed using a new parallel computer code, DIFFREALWAVE. The code is based on the real wavepacket approach of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)]. The calculations are parallelized over the helicity quantum number Omega' (i.e., the quantum number for the body-fixed z component of the total angular momentum) and wavepackets for each J,Omega' set are assigned to different processors, similar in spirit to the Coriolis-coupled processors approach of Goldfield and Gray [Comput. Phys. Commun. 84, 1 (1996)]. Calculations for J=0-24 have been performed to obtain converged state-to-state differential cross sections in the energy range from 0.4 to 1.2 eV. The calculations employ five different potential energy surfaces, the BKMP2 surface and a hierarchical family of four new ab initio surfaces [S. L. Mielke, et al., J. Chem. Phys. 116, 4142 (2002)]. This family of four surfaces has been calculated using three different hierarchical sets of basis functions and also an extrapolation to the complete basis set limit, the so called CCI surface. The CCI surface is the most accurate surface for the H3 system reported to date. Our calculations of differential cross sections are the first to be reported for the A2, A3, A4, and CCI surfaces. They show that there are some small differences in the cross sections obtained from the five different surfaces, particularly at higher energies. The calculations also show that the BKMP2 performs well and gives cross sections in very good agreement with the results from the CCI surface, displaying only small divergences at higher energies.     

Angular distribution of photoelectrons in small molecules: a molecular quantum defect calculation

The molecular quantum defect orbital (MQDO) method, previously used in the determination of molecular photoionization cross sections, is applied here to calculate the angular distribution of photoelectrons arising from the molecular photoionization. Calculations are performed for the ionization from outer valence orbitals of HF, H(2)O, NH(3), N(2)O, and H(2)CO molecules. The results are compared with previous measurements and with theoretical curves found in the literature. Profiles of the angular distribution parameter as a function of photoelectron energy covering a range from the photoionization threshold to 120 eV are presented for the above molecules. The energy dependence of the angular distributions predicted by the MQDO calculations agrees fairly well with predictions from more sophisticated theories and with observed results.     

Angle- and spin-resolved photoelectron spectroscopy of thepπ outer valence shell of HBr molecules

Using circularly polarized synchrotron radiation, the photoionization of HBr molecules was studied by angle- and spin-resolved photoelectron spectroscopy in the photon energy range from 11.7 eV to 21 eV. For photoelectrons corresponding to the final ionic states HBr⁺ X ²Π_3/2(v=0) andX ²Π_1/2(v=0), the energy dependence of the dynamical photoionization parameters was measured and compared with ab initio calculations for HBr⁺ by Raseev et al. and RRPA calculations for Kr⁺ by Huang et al., This comparison indicates that, for energies above the electronic autoionization region, photoemission from the outer valence orbital exhibits distinct atomic behavior. By combining the experimental data for the cross section σ and the spin polarization parameter A, sums of partial cross section contributions to σ were determined and analyzed to obtain specific information on the outgoing partial electron waves. Furthermore, the validity of the so-called non-relativistic relationships for the dynamical photoionization parameters was tested as a function of equal photon and kinetic photoelectron energy, respectively.     

A reduced dimensionality quasiclassical and quantum study of the proton transfer reaction H3O(+)+H2O-->H2O+H3O(+)

We report quantum and quasiclassical calculations of proton transfer in the reaction H(3)O(+)+H(2)O in three degrees of freedom, the two OH(+) bond lengths and the OH(+)O angle. The reduced dimensional potential energy surface is obtained from the full dimensional OSS3(p) energy function of H(5)O(2) (+) [L. Ojamae, I. Shavitt, and S. J. Singer, J. Chem. Phys. 109, 5547 (1998)], with an additional long-range correction to reproduce the correct ion-molecule interaction. This surface is used to perform both quasiclassical trajectory and quantum reactive scattering calculations of the zero total angular momentum cumulative reaction probability and cross sections for initial rotational states 0, 1, and 2. Comparison of these quantities are made to assess the importance of quantum effects in this reduced dimensional reaction. Additional quasiclassical cross sections are calculated to obtain the thermal rate constant for the reaction.     

Analytical optimization of orbital exponents in Gaussian-type functions for molecular systems based on MCSCF and MP2 levels of fully variational molecular orbital method

We have analyzed the basis function series in molecular systems by optimization of orbital exponents in Gaussian-type functions (GTFs) including the electron correlation effects with multiconfiguration self-consistent field (MCSCF) and M?ller?CPlesset second-order perturbation (MP2) methods. First, we have derived and implemented the gradient formulas of MCSCF and MP2 energies with respect to GTF exponent, as well as GTF center and nuclear geometry, based on the fully variational molecular orbital (FVMO) method. Second, we have applied these electron-correlated FVMO methods to H₂, LiH, and hydrocarbon (CH₄, C₂H₆, C₂H₄, and C₂H₂) molecules. We have clearly demonstrated that the optimized exponent values with electron-correlated methods are different from those with simple Hartree?CFock method, since adequate basis functions for adequate virtual orbitals are indispensable to describe the accurate wave function and geometry for electron-correlated calculations.     

Reactivity of C10H7+ and C10D7+ with H2 AND D2

We have investigated, both theoretically and experimentally, the reactions of naphthylium C10H7+ and d-naphthylium C10D7+ ions with H2 and D2. Cross sections as functions of the collision energy have been measured for a variety of reaction channels. Theoretical calculations have been carried out at the density functional theory level which utilizes the hybrid functional B3LYP and the split-valence 6-31G* basis set. The key features of the potential energy surfaces and the relevant thermochemical parameters have been calculated and they provide insights on the reaction mechanisms. The bimolecular reactivity of C10H7+ with H2 is dominated by the production of naphthalene cation C10H8+. The reaction is not a direct atom-abstraction process, but instead it proceeds via the formation of a stable intermediate complex C10H9+ of sigma type geometry, with a significant mobility of hydrogen along the ring. This mobility allows the scrambling of the hydrogen atoms and causes the successive statistical fragmentation of the complex into a variety of product channels. Elimination of one H(D) atom appears to be favored over elimination of one H2 or HD molecule. Alternatively, the intermediate complex can be stabilized either by collision with a third body or by emission of a photon.     

Quantum calculations of the O(3P)+H2-->OH+H reaction

Quantum scattering calculations are reported for the O(3P)+H2(v=0,1) reaction using chemically accurate potential energy surfaces of 3A' and 3A" symmetry. We present state-to-state reaction cross sections and rate coefficients as well as thermal rate coefficients for the title reaction using accurate quantum calculations. Our calculations yield reaction cross sections that are in quantitative accord with results of recent crossed molecular beam experiments. Comparisons with results obtained using the J-shifting calculations show that the J-shifting approximation is quite reliable for this system. Thermal rate coefficients from the exact calculations and the J-shifting approximation agree remarkably well with experimental results. Our calculations also reproduce the markedly different OH(v'=0)/OH(v'=1) branching in O(3P)+H2(v=1) reaction, observed in experiments that use different O(3P) atom sources. In particular, we show that the branching ratio is a strong function of the kinetic energy of the O(3P) atom.     

Probing anisotropic interaction potentials of unsaturated hydrocarbons with He*(2 3S) metastable atom: attractive-site preference of sigma-direction in C2H2 and pi-direction in C2H4

State-resolved collision energy dependence of Penning ionization cross sections of acetylene (C2H2) and ethylene (C2H4) with He*(2 3S) metastable atoms was observed in a wide collision energy range from 20 to 350 meV. A recently developed discharge nozzle source with a liquid N2 circulator was employed for the measurements in the low-energy range from 20 to 80 meV. Based on classical trajectory calculations for the energy dependence of the partial ionization cross sections, anisotropic potential energy surfaces for the present systems were obtained by optimizing ab initio model potentials for the chemically related systems Li+C2H2 and C2H4. In the case of C2H2, the global minimum was found to be located around the H atom along the molecular axis with a well depth of 48 meV (ca. 1.1 kcal/mol). On the other hand, a dominant attractive well with a depth of 62 meV (ca. 1.4 kcal/mol) was found in the piCC electron region of C2H4. These findings were discussed in connection with orbital interactions between molecular orbitals of the target molecules and atomic orbitals of the metastable atom. It is concluded that sigma-type unoccupied molecular orbitals of C2H2 and a piCC-type highest occupied molecular orbital of C2H4 play a significant role for the attractive-site preference of sigma direction in C2H2 and pi direction in C2H4, respectively.     

Photoionization of hot radicals: C2H5, n-C3H7, and i-C3H7

The combination of ion-imaging and vacuum-ultraviolet (vuv) single-photon ionization is used to study the internal energy dependence of the relative photoionization yields of the C(2)H(5),n-C(3)H(7), and i-C(3)H(7) radicals following the 266 nm photodissociation of the corresponding alkyl iodides. The comparison of the ion images obtained by vuv photoionization of the radical with those obtained by two-photon-resonant, three-photon ionization of the complementary I (2)P(32) and I*(2)P(12) atoms allows the extraction of the internal energy dependence of the cross sections. Factors influencing the appearance of the ion images in the different detection channels are discussed, including the secondary fragmentation of the neutral radicals, Franck-Condon factors for the photoionization process, and the unimolecular fragmentation of the parent photoions.     

Full variational molecular orbital method: Application to the positron-molecule complexes

Optimal Gaussian-type orbital (GTO) basis sets of positron and electron in positron-molecule complexes are proposed by using the full variational treatment of molecular orbital (FVMO) method. The analytical expression for the energy gradient with respect to parameters of positronic and electronic GTO such as the orbital exponents, the orbital centers, and the linear combination of atomic orbital (LCAO) coefficients, is derived. Wave functions obtained by the FVMO method include the effect of electronic or positronic orbital relaxation explicitly and satisfy the virial and Hellmann–Feynman theorems completely. We have demonstrated the optimization of each orbital exponent in various positron-atomic and anion systems, and estimated the positron affinity (PA) as the difference between their energies. Our PA obtained with small basis set is in good agreement with the numerical Hartree–Fock result. We have calculated the OH⁻ and [OH⁻; e⁺] species as the positron-molecular system by the FVMO method. This result shows that the positronic basis set not only becomes more diffuse but also moves toward the oxygen atom. Moreover, we have applied this method to determine both the nuclear and electronic wave functions of LiH and LiD molecules simultaneously, and obtained the isotopic effect directly. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 491–501, 1998     

Near-threshold shape resonance in the photoionization of 2-butyne

Photoelectron velocity map imaging is combined with one- and two-photon ionization to study the near threshold photoionization of the 2-butyne molecule. In this region, the photoabsorption and photoionization cross sections display a very intense broad feature that is assigned to an l = 4, π(g) shape resonance. The effect of this shape resonance on the vibrational branching ratios and photoelectron angular distributions is explored. Theoretical calculations of the photoionization cross section and photoelectron angular distributions are in good agreement with the experiments. The results for 2-butyne are compared with those of acetylene, propyne, and 1-butyne, none of which show such significant enhancements near threshold, and the differences are rationalized in terms of the symmetries and orbital angular momenta of the highest occupied orbitals and the corresponding shape resonances. Expectations for larger alkynes and alkynyl radicals are also discussed. A preliminary measurement of the ionization energy of the 2-butyne dimer is also presented.     

Selective hyperfine excitation of N2H+ by He: potential energy surface, cross sections, and propensity rules

We present potential energy surfaces for the He-N2H+ system adiabatically corrected for the zero-point motion along the intermolecular stretching vibrations v1 = 0 and v1 = 1. The potentials are extended to shorter He-N2H+ separations which makes them useful for scattering calculations. Close coupling calculations of the spinless S matrices for the rotational excitation of N2H+ by He are presented, and recoupling techniques to obtain collisional excitation cross sections between the N2H+ hyperfine levels are used. The propensity rules between hyperfine levels are investigated for the case where two nuclear spins are involved. It is found that the only well defined propensity rule is DeltaF = DeltaF1 = Deltaj and that calculations are required in order to obtain the relative intensities of the two-spin hyperfine cross sections.     

ESCA Peak intensities in the dipole and generalized sudden approximations using fourier transforms of GTO's

Analytical expressions for the square of the spherical average of Fourier transforms of Gaussian type orbitals (GTO 's) are given. A direct application of these expressions to the calculation of molecular photoionization cross sections is considered under the generalized sudden (GSA ) and dipole (DA ) Approximations. Numerical calculations were done on the CO molecule using bound orbitals obtained by ab initio LCAO –MO calculations with Gaussian basis sets. The results are in good agreement with experiments. Those obtained by the GSA method however, suggest a limitation in its use: the GSA method is only applicable when comparing photoionization intensities of neighboring ionization energy orbitals. Applications to other molecules are immediate.     

Quasi-classical trajectory study of the Ne + H2(+) → NeH(+) + H reaction based on global potential energy surface

Using the multireference configuration interaction method with a Davidson correction and a large orbital basis set (aug-cc-pVQZ), we obtain an energy grid that includes 32 038 points for the construction of a new analytical potential energy surface (APES) for the Ne + H(2)(+) → NeH(+) + H reaction. The APES is represented as a many-body expansion containing 142 parameters, which are fitted from 31?000 ab initio energies using an adaptive nonlinear least-squares algorithm. The geometric characteristics of the reported APES and the one presented here are also compared. On the basis of the APES we obtained, reaction cross sections are computed by means of quasi-classical trajectory (QCT) calculations and compared with the experimental and theoretical data in the literature.     

On the determination of partial differential cross sections for photodetachment and photoionization processes producing polyatomic molecules with electronic states coupled by conical intersections

A formalism is derived for the computation of partial differential cross sections for electron photodetachment and photoionization processes that leave the residual or target molecule in electronic states that are strongly coupled by conical intersections. Because the electronic states of the target are nonadiabatically coupled, the standard adiabatic states approach of solving the electronic Schro?dinger equation for the detached electron at fixed nuclear geometries and then vibrationally averaging must be fundamentally modified. We use a Lippmann-Schwinger equation based approach, which leads naturally to a partitioning of the transition amplitude into a Dyson orbital like part plus a scattering correction. The requisite Green's function is that developed in our previous paper for the direct determination of total integral cross sections. The method takes proper account of electron exchange, possible nonorthogonality of the orbital describing the detached electron, and nonadiabatic effects in the product molecule. The Green's function is constructed in an L(2) basis using complex scaling techniques. The accurate treatment of nonadiabatic effects in the residual molecule is accomplished using the multimode vibronic coupling model. For photodetachment, an approximate approach, which is less computationally demanding, is suggested.     

Accurate one-dimensional potential energy curve of the linear (H2)2 cluster

We present a sub-0.3 K accuracy, ground-state one-dimensional potential energy curve of the metastable linear configuration of the (H(2))(2) cluster calculated exclusively with explicitly correlated Gaussian functions with shifted centers. The H(2) internuclear distance is kept at the isolated H(2) vibrational ground-state average value of 1.448 736 bohr and the intermonomer separation is varied between 2 and 100 bohrs. The analytical gradient of the energy with respect to the nonlinear parameters of the Gaussians (i.e., the exponents and the coordinates of the shifts) has been employed in the variational optimization of the wave function. Procedures for enlarging the basis set and for adjusting the centers of the Gaussians to the varying intermonomer separation have been developed and used in the calculations.     

Relativistic correlating basis sets for the sixth-period d-block atoms from Lu to Hg

Contracted Gaussian-type function sets to describe valence correlation are developed for the sixth-period d-block atoms Lu through Hg. A segmented contraction scheme is employed for their compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from accurate natural orbitals generated from configuration interaction calculations, in which relativistic effects are incorporated through the third-order Douglas-Kroll approximation. The present basis sets yield more than 99% of atomic correlation energies predicted by accurate natural orbital sets of the same size. Relativistic model core potential calculations with the present correlating sets give the spectroscopic constants of the AuH molecule in excellent agreement with experimental results.