Internuclear Separation Research Articles

Convergence of the multipole expansions of the polarization and dispersion interactions for atoms under confinement

The multipole expansion of the polarization interaction between a charged particle and an electrically neutral object has long been known to be asymptotic in nature, i.e., the multiple expansion diverges at any finite distance from the atom. However, the multipole expansion of the polarization potential of a confined hydrogen atom is shown to be absolutely convergent at a distance outside the confinement radius, R(0), of the atom. The multipole expansion of the dispersion potential between two confined hydrogen atoms is also shown to be absolutely convergent provided the two atoms satisfy R > 2R(0), where R is the inter-nuclear separation. These results were established analytically using oscillator strength sum rules and verified numerically using a B-spline description of the hydrogen ground state and its excitation spectrum.

Electronic spectrum of 17 electronic states of BN molecule: A theoretical study

The potential energy curves (PECs) of the X3Π, a1Σ+, b1Π, A3Σ+, B3Σ−, c1Δ, D3Π, 15Π, 31Σ+, 33Π, 21Π, 23Σ+, 13Δ, 15Σ+, 43Π, 23Σ− and 15Σ− electronic states of the BN molecule are calculated using an ab initio quantum chemical method. The PEC calculations have been made for internuclear separations from 0.06 to 1.20nm using the complete active space self-consistent field (CASSCF) method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with a correlation-consistent aug-cc-pV5Z basis set. To improve the quality of PECs, core-valence correlation and relativistic corrections are included. Relativistic correction calculations are carried out using the third-order Douglas–Kroll Hamiltonian (DKH3) approximation. Core–valence correlation corrections are included using a cc-pCVQZ basis set. Relativistic corrections are calculated at the level of a cc-pVQZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit by the total-energy extrapolation scheme. The spectroscopic parameters are determined by fitting the vibrational levels, which are calculated in a direct forward manner from the analytic potential by solving the ro-vibrational Schrödinger equation using Numerov's method. The spectroscopic results have been compared in detail with those reported in the literature. Excellent agreement has been found between the present spectroscopic results and the experimental ones. Using the Breit-Pauli operator, the spin–orbit coupling effect on the spectroscopic parameters is included in the X3Π and D3Π electronic states. The vibrational level, inertial rotation and centrifugal distortion constants are calculated for each vibrational state of each electronic state. And those of the first 20 vibrational states of each electronic state are reported when the rotational quantum number equals zero. Comparison with the measurements shows that the present results are accurate. The spectroscopic parameters of the c1Δ, 15Π, 31Σ+, 33Π, 21Π, 23Σ+, 13Δ, 15Σ+, 43Π and 15Σ− electronic states and the vibrational manifolds of all the electronic states obtained here are expected to be reliable predicted results.

Behaviour of density functional theory for electric response properties at distorted geometries of molecules

The role of exchange–correlation is well known for accurate calculations of electric response properties. The exchange–correlation functional in density functional theory (DFT) has been well studied for ground state equilibrium geometry. However, the behaviour of these functional in stretched geometries, where static correlation play an important role, has not been studied systematically, particularly for response electric properties. Thus, we present here the rigorous calculation of electric response properties at distorted geometries of the molecules. We have considered dipole polarizability and dipole–quadrupole polarizability for description of role of static and dynamic correlation for electric response properties. The calculations are performed with our new approach, non-iterative approximation to coupled-perturbed Kohn–Sham method. These DFT results are compared with higher level ab initio such as coupled perturbed singles and doubles and fully correlated full CI. We have studied single, double and triple-bonded systems at different inter-nuclear separation. We report here the dipole polarizability and dipole–quadrupole polarizability of HF, BH, H2CO, CO and NO+. We also present the effect of basis and functional on polarizability and dipole–quadrupole polarizability.

Proton-bound homodimers involving second-row atoms

High-level ab initio quantum chemical calculations (G4(MP2)//MP2/6-311+G(2df,p)) have been used to examine homodimers of second-row bases, and to compare the results with those obtained previously for the first-row analogs. The relationship between the binding energies of the dimers and the proton affinities (PAs) of the bases follows the same pattern as that for the first-row systems, with the binding energies initially increasing with increasing proton affinity but subsequently decreasing. This may be attributed to the opposing effects of increased PA on the hydrogen-bond donor and hydrogen-bond acceptor. The binding energies are generally smaller for the second-row dimers than for the corresponding first-row dimers. There is an increased tendency for asymmetrical hydrogen bonds in homodimers of the second-row compared with first-row dimers. This may be attributed to the lower electronegativities of second-row atoms relative to their first-row counterparts, and to the longer internuclear separation between the hydrogen-bonded second-row atoms.

Current-density functional theory study of the H2 molecule evolving under a strong ultrashort magnetic field

Hydrogen molecule in a strong ultrashort magnetic field is investigated through a current-density functional theory (CDFT) and quantum fluid dynamics (QFD) based approach employing current-density dependent vector exchange-correlation potential and energy density functional derived with a vorticity variable. The numerical computations through the CDFT based approach are performed for the H2 molecule, starting initially from its field-free ground state, in a parallel internuclear axis and magnetic field-axis configuration with the internuclear separation R ranging from 0.1 a.u. to 14.0 a.u., and the strength of the time-dependent (TD) magnetic field varying between 0−1011 G over a few femtoseconds. The numerical results are compared with that obtained using an approach based on the current-density independent approximation under similar computational constraints but employing only scalar exchange-correlation potential dependent on the electronic charge-density alone. The current-density based approach yields exchange- and correlation energy as well as electronic charge-density of the H2 molecule drastically different from that obtained using current-independent approach, in particular, at TD magnetic field-strengths >109 G during a typical time-period of the field when the magnetic-field had attained maximum applied field-strength and is switched to a decreasing ramp function. This nonadiabatic behavior of the TD electronic charge-density is traced to the TD vorticity-dependent vector exchange-correlation potential of the CDFT based approach. The interesting electron dynamics of the H2 molecule in strong TD magnetic field is further elucidated by treating electronic charge-density as an ‘electron-fluid’. The present work also reveals interesting real-time dynamics on the attosecond time-scale in the electronic charge-density distribution of the hydrogen molecule.

The interaction of H2D+ with thin solid foils and the detection of its structure

The Interaction between molecular ion H2D+ and ultra-thin solid film is reported for the first time. The importance of H2D+ in the areas such as astrophysics is stated and the study on H2D+ of recent years is outlined. The formation mechanism for the H2D+ under laboratory conditions is also analysed. The structural pattern of H2D+ and the mean internuclear separation are determined using Coulomb explosion technique. Once again, the existence of wake effects in the interaction of molecular ions with solid is confirmed and three-body wake effect module is used to determine the geometric structure of H2D+. Finally, the unusual structure of the wake of energy spectrum for the heavier ions in the H2D+ Coulomb explosion is discussed.

Spectroscopic parameters and molecular constants of X1+ and a3 electronic states of BF radical

The potential energy curves (PECs) of the X1+ and a3 electronic states of the BF radical are studied by employing the ab initio quantum chemical method. The calculations are performed by using the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with the basis set, aug-cc-pV6Z, for internuclear separations from 0.095 to 1.33 nm. The effects of the Davidson modification and core-valence correlation and relativistic corrections on the PECs are included. The way to consider the relativistic correction is to employ the second-order DouglasKroll Hamiltonian approximation. The relativistic correction is carried out at the level of cc-pV5Z basis set. And the core-valence correlation correction is made by using the cc-pCV5Z basis set. With the PECs obtained here, the spectroscopic parameters (De, Re, e, exe, eye, Be and e) are determined and compared with those reported in the literature. With the PECs obtained by the MRCI+Q/aug-cc-pV6Z+CV+DK calculations, the complete vibrational states are computed for each electronic state when J = 0. And the vibrational levels, the inertial rotation constants and the centrifugal distortion constants of the first 20 vibrational states of each electronic state are reported. On the whole, as expected, the spectroscopic parameters and molecular constants closest to the experimental data are determined by the MRCI+Q/ aug-cc-pV6Z+DK+CV calculations for the two electronic states.

Investigations on spectroscopic parameters and molecular constants of SO+ (b4∑-) cation

The potential energy curve (PEC) of b4Σ- electronic state of the SO+ cation is calculated using the internally contracted multireference configuration interaction approach with the Davidson modification (MRCI+Q) for internuclear separations from 0.103 to 1.083 nm. The basis set used is a correlation- consistent aug-cc-pV5Z basis set. The spin-orbit coupling effect on the spectroscopic parameters is taken into account by the state interaction approach with the full Breit-Pauli operator with all-electron basis set, aug-cc-pCVTZ. To improve the quality of PEC and spin-orbit coupling constant, core-valence correlation and relativistic corrections are included. Core-valence correlation correction is calculated using a cc-pCVTZ basis set. Relativistic corrections are included by the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. At the MRCI+Q/aug-cc-pV5Z+CV+DK level, the spin-orbit coupling constant of the SO+ (b4Σ-1/2,3/2) is 1 cm-1 when the aug-cc-pCVTZ basis set is used for the spin-orbit coupling calculations The spectroscopic parameters are determined and compared with those reported in the literature. Excellent agreement is found between the present results and the measurements. The vibrational level G(v) inertial rotation constant Bv and centrifugal distortion constant Dv are predicted for each vibrational state of the b4Σ- electronic state by solving the ro-vibrational Schrödinger equation of nuclear motion using Numerov's method and those of the first 2 vibrational states are reported for the non-rotation SO+ cation. Comparison with the measurements demonstrates that the present vibrational manifolds are both reliable and accurate. They should be good predictions for future experimental or theoretical research.

MRCI study on electronic spectrum of several low-lying electronic states of the SiO + cation

The potential energy curves (PECs) of the X 2Σ +, A 2Π, B 2Σ +, a 4Σ +, 1 4Π, 1 4Δ, 1 4Σ − and 2 2Π electronic states of the SiO + cation are calculated using an ab initio quantum chemical method. The PEC calculations have been made for internuclear separations from 0.06 to 1.24 nm using the complete active space self-consistent field method followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with a correlation-consistent aug-cc-pV6Z basis set. To improve the quality of the PECs, core–valence correlation and relativistic corrections are included. The relativistic correction calculations are performed using the third-order Douglas–Kroll Hamiltonian approximation. The core–valence correlation corrections are included using a cc-pCVQZ basis set. The relativistic corrections are calculated at the level of the cc-pVQZ basis set. In order to obtain more reliable results, the PECs obtained by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI + Q). The spectroscopic parameters are determined by fitting the vibrational levels, which are calculated by solving the ro-vibrational Schrödinger equation with these PECs. The spectroscopic results have been compared in detail with those reported in the literature. Excellent agreement has been found between the present results and the experimental ones. Using the Breit–Pauli operator, the spin–orbit coupling effect is included in the calculations of the Π and Δ electronic states. Four Ω components of the 1 4Δ, three Ω components of the 1 4Π and two Ω components of the A 2Π and 2 2Π electronic states have been studied. The complete vibrational states are determined for each electronic state. The vibrational level, inertial rotation and centrifugal distortion constants are calculated for each vibrational state of each electronic state. And those of the first 20 vibrational states of the X 2Σ +, A 2Π and 2 2Π electronic states are reported for the non-rotating SiO + cation. Comparison with the experimental data demonstrates that the present results are accurate.

Structure and Stability of the Negative Hydrogen Molecular Ion

We present the results of a Coulomb explosion experiment that allows for the imaging of the rovibrational wave function of the metastable H2- ion. Our measurements confirm the predicted large internuclear separation of 6 a.u., and they show that the ion decays by autodetachment rather than by spontaneous dissociation. Imaging of the resulting H2 products reveals a large angular momentum of J = 25 ± 2, quantifying the rotation that leads to the metastability of this most fundamental molecular anion.

Internuclear-separation-resolved asymmetric dissociation of I2in a two-color laser field

We have designed a pump-probe experiment to excite I${}_{2}$ to the $B$ state and subsequently ionize the molecule with a two-color (800- and 400-nm) probe pulse. By varying the relative phase of the two colors we are able to probe the asymmetric dissociation of ${\mathrm{I}}_{2}{}^{2+}\ensuremath{\rightarrow}{\mathrm{I}}^{2+}+\mathrm{I}$ and we observe spatial asymmetries in the ion yield of this (2,0) channel. Because the durations (35 fs) of the pump and probe pulses are much shorter than the vibrational period of the $B$ state (700 fs) we can fully resolve the dynamics as a function of internuclear separation $R$. We find that the amplitude of the spatial asymmetry increases as a function of $R$ and that the relative phase of the two colors that produces the maximum asymmetry is independent of $R$. Both of these observations are consistent with ionization of I${}_{2}$ directly into the field-dressed potential curves of I${}_{2}{}^{2+}$, which we model with a two-electron one-dimensional double-well potential in an external field. Interestingly, we find a spatial asymmetry for dissociation channels with a charge difference $\ensuremath{\Delta}q=2$, [(2,0) and (3,1)], but not for $\ensuremath{\Delta}q=1$, [(1,0), (2,1), (3,2)]. Finally, substructure in the time-of-flight data shows two distinct states leading to the (2,0) dissociation limit, one of which may indicate a breakdown of the presented model.

Angle-resolved and internuclear-separation-resolved measurements of the ionization rate of theBstate of I2by strong laser fields

Angle-resolved and internuclear-separation-resolved measurements of the single ionization rate of neutral I${}_{2}$ have been obtained. By launching a wave packet in the $B{\phantom{\rule{0.16em}{0ex}}}^{3}\ensuremath{\Pi}{{}_{u}}^{+}$ state ($B$ state) of I${}_{2}$ with a 50-fs tunable pump pulse we can measure the ionization rate as a function of internuclear separation as the wave packet evolves in the $B$ state. Moreover, since the ground to $B$-state optical transition dipole moment is parallel to the internuclear axis, the $B$-state subpopulation of the I${}_{2}$ thermal ensemble will have a high degree of alignment, allowing for angular measurements. The $B$ state shows the well-known effect of enhanced ionization at a critical separation, $R$${}_{c}$, with an enhancement factor of 22 when the ionizing field is polarized along the internuclear axis and the enhanced ionization decreases when the angle between the field and the axis increases from 0 ${}^{\ensuremath{\circ}}$ to 90 ${}^{\ensuremath{\circ}}$, finally disappearing at 90 ${}^{\ensuremath{\circ}}$. These results on the enhanced ionization of the $B$ state of I${}_{2}$ give the most precise determination of $R$${}_{c}$ for any molecule and agree extremely well with the prediction from a simple model of electron localization.

Communication: Imaging wavefunctions in dissociative photoionization

The dissociative ionization dynamics of excited electronic states of the xenon dimer, Xe(2), have been studied using velocity map ion imaging (VMI). A one-colour, (2+1) resonant excitation scheme was employed to first excite and then ionize selected vibrational levels of the Xe(2) 6p (2)[(1)∕(2)](0) 0(g)(+) Rydberg state. Cationic fragments were then detected by the VMI. The data provide an outstanding example of the reflection principle in photodissociation with the full nodal structure of the Rydberg state wavefunctions clearly observed in the final Xe(+) kinetic energy distributions without the need for scanning the excitation energy. Fitting of the observed distributions provides detailed and precise information on the form of the Xe(2)(+) I((1)/(2)g) potential energy curve involved which is in excellent agreement with the results of photoelectron imaging studies [Shubert and Pratt, J. Chem. Phys. 134, 044315 (2011)]. Furthermore, the anisotropy of the product angular distributions yields information on the evolution of the electronic character of the ionic state with internuclear separation, R. The combination of the nature of dissociative ionization and the extent of the bound state wavefunctions provide information over an unusually wide range of internuclear separation R (ΔR > 0.75 Å). This would normally require scanning over a considerable energy region but is obtained in these studies at a fixed excitation energy.

R-matrix with Pseudo-States (RMPS) method: application to CH+ resonances curves

In a series of calculations on both electron and positron collisions with small molecules the R-Matrix with Pseudo-States (RMPS) method has been found to recover polarisation effects neglected in other close-coupling methods including the standard R-matrix procedure. The molecular R-Matrix and RMPS methods is being applied to determine low-lying resonance states of CH+ as a function of internuclear separation. Initial results are presented for both a standard R-matrix close-coupling model and for an RMPS calculation. Eigenphase sums and resonances below the 3Π threshold are presented for 2Π total symmetry. These resonances are classified by their quantum defects and compared to previous results. Prospects for these and other calculations using the RMPS method are discussed.

Optimal pulse for orbital reconstruction from ionization maps in aligned molecules

We perform ab initio calculations on the total ionization probability of diatomic molecules in strong laser fields as a function of alignment angle, the angle between the laser polarization and the molecular axis, with the goal of investigating whether these ionization maps can be used to determine the orbital symmetry of the initial state. We find that the ionization rate for each alignment angle is highly dependent on the pulse intensity and duration and, because of this dependence, the orbital symmetry can only be determined with the appropriate pulse parameters. The pulse length and intensity need to be chosen in such a way as to avoid excessive ionization, or significant population of other bound states. We also observe that the internuclear separation of the molecule strongly affects the mapping of the orbital symmetries.

Collision-induced dipole polarizability of helium dimer from explicitly correlated calculations

Large expansions in basis sets of explicitly correlated Gaussian functions and the variation-perturbation technique were used to calculate the static dipole polarizability of the helium dimer at 16 different internuclear separations from 1.0 to 9.0 bohrs. The convergence towards the complete basis set limit was analyzed in order to estimate uncertainties of all the calculated values. The results are significantly more accurate than literature data. Asymptotically correct analytic fits for the trace and anisotropy of collision-induced polarizability were obtained.

Effects on spectroscopic parameters of several low-lying electronic states of GeS by core–valence correlation and relativistic corrections

The potential energy curves (PECs) of six low-lying electronic states (X 1Σ +, a 3Σ +, b 3Π, A 1Π, 1 3Σ − and 1 5Σ +) of GeS molecule have been investigated employing the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach with large correlation-consistent basis sets for internuclear separations from 0.08 to 2.00 nm. The effects on the spectroscopic parameters by the core–valence correlation, relativistic and nonadiabatic corrections have been discussed in detail. The core–valence correlation correction is carried out at the aug-cc-pCVTZ basis set. The nonadiabatic correction is performed at the aug-cc-pVTZ basis set. And the relativistic correction is made at the level of cc-pV5Z basis set. The way to consider the relativistic correction is to employ the second-order Douglas–Kroll Hamiltonian (DKH2) approximation. To obtain more reliable PECs, the Davidson modification is also included in the present study. To reduce the incomplete basis set error, the PECs of these electronic states are extrapolated to the complete basis set (CBS) limit. With these PECs, the spectroscopic parameters of these low-lying electronic states are determined. On the one hand, analyses demonstrate that the effects on the spectroscopic parameters by the core–valence correlation correction, relativistic correction and Davidson modification are very obvious, whereas the effect on the spectroscopic parameters by the nonadiabatic correction is very small. On the other hand, comparison with the RKR data shows that the two-point total-energy extrapolation could improve the quality of spectroscopic parameters. On the whole, as expected, the most accurate spectroscopic parameters of GeS molecule are determined by the MRCI+Q/CV+DK+Q5 calculations.

MRCI study on spectroscopic and molecular properties of B1Δg, , C1Πg, , and 11Δu electronic states of the C2 radical

The potential energy curves (PECs) of six electronic states (B1Δg, , C1Πg, , and 11Δu) of the C2 radical have been investigated using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent aug-cc-pV6Z basis set for internuclear separations from 0.05 to 2.0 nm. The effects on the spectroscopic parameters (Te , D 0, De , Re , ωe , ωexe , ωeye , αe , βe , γe and Be ) of the core–valence correlation and relativistic corrections are taken into account. The way to consider the relativistic corrections is to employ the second-order Douglas–Kroll Hamiltonian approximation. The core–valence correlation correction is performed at the cc-pCV5Z basis set. And the relativistic correction is carried out at the level of the cc-pV5Z basis set. In order to obtain reliable PECs, the Davidson modification is also included in the study. These spectroscopic parameters have been compared in detail with those of previous investigations reported in the literature, and excellent agreement has been found between the present results and the available experimental data. The first 20 vibrational states are computed for all these electronic states when the rotational quantum number J equals zero, and the vibrational levels, inertial rotation and centrifugal distortion constants of the B1Δg and electronic states are reported when J = 0, which are in excellent agreement with the available measurements. Comparison with the available experimental data shows that the present molecular constants are both reliable and accurate.

Positron attachment to theH2(A3Σu) state

The stochastic variational method is used to compute the binding energy for positrons attached to the repulsive ${\mathrm{H}}_{2}$($A$ ${}^{3}{\ensuremath{\Sigma}}_{u}$) state. Attachment occurs for internuclear separations between 1.616 ${a}_{0}$ and $1.818$ ${a}_{0}$. At these distances the vertical ionization potential for the ${\mathrm{H}}_{2}$($A$ ${}^{3}{\ensuremath{\Sigma}}_{u}$) state is close to the positronium binding energy of 0.250 a.u. The maximum attachment energy occurs at 1.67 ${a}_{0}$ and is 0.003532 a.u.

He 2++ molecular ion in a strong time-dependent magnetic field: A current-density functional study

The He 2++ molecular ion exposed to a strong ultrashort time-dependent (TD) magnetic field of the order of 10(9) G is investigated through a quantum fluid dynamics (QFD) and current-density functional theory (CDFT) based approach using vector exchange-correlation (XC) potential and energy density functional that depend not only on the electronic charge-density but also on the current density. The TD-QFD-CDFT computations are performed in a parallel internuclear-axis and magnetic field-axis configuration at the field-free equilibrium internuclear separation R = 1.3 au with the field-strength varying between 0 and 10(11) G. The TD behavior of the exchange- and correlation energy of the He 2++ is analyzed and compared with that obtained using a [B-TD-QFD-density functional theory (DFT)] approach based on the conventional TD-DFT under similar computational constraints but using only scalar XC potential and energy density functional dependent on the electronic charge-density alone. The CDFT based approach yields TD exchange- and correlation energy and TD electronic charge-density significantly different from that obtained using the conventional TD-DFT based approach, particularly, at typical magnetic field strengths and during a typical time period of the TD field. This peculiar behavior of the CDFT-based approach is traced to the TD current-density dependent vector XC potential, which can induce nonadiabatic effects causing retardation of the oscillating electronic charge density. Such dissipative electron dynamics of the He 2++ molecular ion is elucidated by treating electronic charge density as an electron-"fluid" in the terminology of QFD.