Self-consistent Field Level Research Articles

Elastic X-ray scattering from state-selected molecules

The characterization of electronic, vibrational, and rotational states using elastic (coherent) X-ray scattering is considered. The scattering is calculated directly from complete active space self-consistent field level ab initio wavefunctions for H2 molecules in the ground-state X1Σg+ and first-excited EF1Σg+ electronic states. The calculated scattering is compared to recent experimental measurements [Y.-W. Liu et al., Phys. Rev. A 89, 014502 (2014)], and the influence of vibrational and rotational states on the observed signal is examined. The scaling of the scattering calculations with basis set is quantified, and it is found that energy convergence of the ab initio calculations is a good indicator of the quality of the scattering calculations.

Kinetic Energy Release of the Singly and Doubly Charged Methylene Chloride Molecule: The Role of Fast Dissociation

The center of mass kinetic energy release distribution (KERD) spectra of selected ionic fragments, formed through dissociative single and double photoionization of CH2Cl2 at photon energies around the Cl 2p edge, were extracted from the shape and width of the experimentally obtained time-of-flight (TOF) distributions. The KERD spectra exhibit either smooth profiles or structures, depending on the moiety and photon energy. In general, the heavier the ionic fragments, the lower their average KERDs are. In contrast, the light H(+) fragments are observed with kinetic energies centered around 4.5-5.5 eV, depending on the photon energy. It was observed that the change in the photon energy involves a change in the KERDs, indicating different processes or transitions taking place in the breakup process. In the particular case of double ionization with the ejection of two charged fragments, the KERDs present have characteristics compatible with the Coulombic fragmentation model. Intending to interpret the experimental data, singlet and triplet states at Cl 2p edge of the CH2Cl2 molecule, corresponding to the Cl (2p → 10a1*) and Cl (2p → 4b1*) transitions, were calculated at multiconfigurational self-consistent field (MCSCF) level and multireference configuration interaction (MRCI). These states were selected to form the spin-orbit coupling matrix elements, which after diagonalization result in a spin-orbit manifold. Minimum energy pathways for dissociation of the molecule were additionally calculated aiming to give support to the presence of the ultrafast dissociation mechanism in the molecular breakup.

Initial mechanisms for the unimolecular decomposition of electronically excited nitrogen-rich energetic salts with tetrazole rings: (NH4)2BT and TAGzT

Unimolecular decomposition of nitrogen-rich energetic salt molecules bis(ammonium)5,5′-bistetrazolate (NH4)2BT and bis(triaminoguanidinium) 5,5′-azotetrazolate TAGzT, has been explored via 283 nm laser excitation. The N2 molecule, with a cold rotational temperature (<30 K), is observed as an initial decomposition product, subsequent to UV excitation. Initial decomposition mechanisms for the two electronically excited salt molecules are explored at the complete active space self-consistent field (CASSCF) level. Potential energy surface calculations at the CASSCF(12,8)/6-31G(d) ((NH4)2BT) and ONIOM (CASSCF/6-31G(d):UFF) (TAGzT) levels illustrate that conical intersections play an essential role in the decomposition mechanism as they provide non-adiabatic, ultrafast radiationless internal conversion between upper and lower electronic states. The tetrazole ring opens on the S1 excited state surface and, through conical intersections (S1/S0)CI, N2 product is formed on the ground state potential energy surface without rotational excitation. The tetrazole rings open at the N2—N3 ring bond with the lowest energy barrier: the C—N ring bond opening has a higher energy barrier than that for any of the N—N ring bonds: this is consistent with findings for other nitrogen-rich neutral organic energetic materials. TAGzT can produce N2 either by the opening of tetrazole ring or from the N=N group linking its two tetrazole rings. Nonetheless, opening of a tetrazole ring has a much lower energy barrier. Vibrational temperatures of N2 products are hot based on theoretical predictions. Energy barriers for opening of the tetrazole ring for all the nitrogen-rich energetic materials studied thus far, including both neutral organic molecules and salts, are in the range from 0.31 to 2.71 eV. Energy of the final molecular structure of these systems with dissociated N2 product is in the range from −1.86 to 3.11 eV. The main difference between energetic salts and neutral nitrogen-rich energetic material is that energetic salts usually have lower excitation energy.

On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

ABSTRACTWe have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition.

Initial mechanisms for the unimolecular decomposition of electronically excited nitrogen-rich energetic materials with tetrazole rings: 1-DTE, 5-DTE, BTA, and BTH.

Unimolecular decomposition of nitrogen-rich energetic molecules 1,2-bis(1H-tetrazol-1-yl)ethane (1-DTE), 1,2-bis(1H-tetrazol-5-yl)ethane (5-DET), N,N-bis(1H-tetrazol-5-yl)amine (BTA), and 5,5'-bis(tetrazolyl)hydrazine (BTH) has been explored via 283 nm two photon laser excitation. The maximum absorption wavelength in the UV-vis spectra of all four materials is around 186-222 nm. The N2 molecule, with a cold rotational temperature (<30 K), is observed as an initial decomposition product from the four molecules, subsequent to UV excitation. Initial decomposition mechanisms for these four electronically excited isolated molecules are explored at the complete active space self-consistent field (CASSCF) level. Potential energy surface calculations at the CASSCF(12,8)/6-31G(d) level illustrate that conical intersections play an essential role in the decomposition mechanism. The tetrazole ring opens on the S1 excited state and through conical intersections (S1/S0)CI, N2 product is formed on the ground state potential energy surface without rotational excitation. The tetrazole rings of all four energetic molecules open at the N1-N2 ring bond with the lowest energy barrier: the C-N bond opening has higher energy barrier than that for any of the N-N ring bonds. Therefore, the tetrazole rings open at their N-N bonds to release N2. The vibrational temperatures of N2 product from all four energetic materials are hot based on theoretical calculations. The different groups (CH2-CH2, NH-NH, and NH) joining the tetrazole rings can cause apparent differences in explosive behavior of 1-DTE, 5-DTE, BTA, and BTH. Conical intersections, non-Born-Oppenheimer interactions, and dynamics are the key features for excited electronic state chemistry of organic molecules, in general, and energetic molecules, in particular.

Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the light elements H–Ar

Relativistic basis sets of double-zeta, triple-zeta, and quadruple-zeta quality have been optimized at the self-consistent field level with a Gaussian nuclear charge distribution for the light elements H–Ar. Correlating functions were optimized for all shells in MR-CISD calculations on the ground configuration. Energies and properties evaluated with the basis sets are compared with those produced by several other basis sets. Prescriptions are given for constructing contracted basis sets. The basis sets are available as an internet archive.

Spin–Orbit Effects in Closed-Shell Heavy and Superheavy Element Monohydrides and Monofluorides with Coupled-Cluster Theory

Bond lengths and force constants of a set of closed-shell sixth-row and superheavy element monohydrides and monofluorides are calculated in this work. Kramers restricted coupled-cluster approaches (KR-CC) with spin-orbit coupling (SOC) included at the self-consistent field (SCF) level as well as CC approaches with SOC included in post-SCF treatment (SOC-CC) are employed in calculations. Recently published relativistic effective core potentials are employed, and highly accurate results for superheavy element molecules are achieved with KR-CCSD(T). SOC effects on bond lengths and force constants of these molecules are investigated. Effects of electron correlation are shown to be affected by SOC to a large extent for some superheavy element molecules. Bond lengths and force constants with SOC-CC agree very well with those of KR-CC for most of the sixth-row element molecules. As for superheavy element molecules, SOC-CCSD is able to afford results that are in good agreement with those of KR-CCSD except for 111F, while the error of SOC-CCSD(T) is more pronounced. Large error would be encountered with SOC-CC approaches for molecules when both SOC and electron correlation effects are sizable.

Collision Cross Sections for O + Ar(+) Collisions in the Energy Range 0.03-500 eV.

The interatomic potentials of the a(2)Π and b(2)Π states of the OAr(+) molecule are calculated using the relativistic complete-active space Hartree-Fock method followed by a multireference configuration interaction calculation with an aug-cc-pwCVNZ-DK basis sets where N is 4 and 5. The calculations were followed by an extrapolation to the complete basis set limit. An avoided crossing between the two potential energy curves is found at an internuclear separation of 5.75 bohr (3.04 Å). As the transition probability between the curves is negligible in the relative collision energy range 0.03-500 eV of interest here, collisions on the lower adiabatic a(2)Π potential may be treated without reference to the upper state. For low energies and orbital angular momentum quantum numbers, the one-dimensional radial Schrödinger equation is solved numerically using a Numerov algorithm method to determine the phase shift. The semiclassical JWKB approximation was employed for relative energies greater than 5 eV and orbital angular quantum numbers higher than 500. Differential, integral, transport (diffusion), and viscosity cross sections for elastic collisions of oxygen atoms with argon ions are calculated for the first time for the range of relative collision energies studied. The calculated cross sections are expected to be of utility in the fields of nanotechnology and arc welding. The combination of an Ar(+)((2)P) ion and a O((3)P) atom gives rise to a total of 12 different molecular electronic states that are all coupled by spin-orbit interactions. Potential energy curves for all 12 states are computed at the complete active space self-consistent field (CASSCF) level and scattering calculations performed. The results are compared with those obtained using just the lowest potential energy curve.

Magnetic properties with multiwavelets and DFT: the complete basis set limit achieved.

Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.

Prediction of electronically nonadiabatic decomposition mechanisms of isolated gas phase nitrogen-rich energetic salt: Guanidium-triazolate

Electronically nonadiabatic decomposition pathways of guanidium triazolate are explored theoretically. Nonadiabatically coupled potential energy surfaces are explored at the complete active space self-consistent field (CASSCF) level of theory. For better estimation of energies complete active space second order perturbation theories (CASPT2 and CASMP2) are also employed. Density functional theory (DFT) with B3LYP functional and MP2 level of theory are used to explore subsequent ground state decomposition pathways. In comparison with all possible stable decomposition products (such as, N2, NH3, HNC, HCN, NH2CN and CH3NC), only NH3 (with NH2CN) and N2 are predicted to be energetically most accessible initial decomposition products. Furthermore, different conical intersections between the S1 and S0 surfaces, which are computed at the CASSCF(14,10)/6-31G(d) level of theory, are found to play an essential role in the excited state deactivation process of guanidium triazolate. This is the first report on the electronically nonadiabatic decomposition mechanisms of isolated guanidium triazolate salt.

Vibronic structure of the 2Πu ground electronic state of dicyanoacetylene cation revisited by PFI-ZEKE photoelectron spectroscopy and ab initio calculations

The X+2Πu ← X1Σ+g transition of dicyanoacetylene has been recorded for the first time using pulsed-field-ionisation zero-kinetic-energy photoelectron spectroscopy. The analysis of the photoelectron spectrum allowed an accurate determination of the adiabatic ionisation potential of C4N2 (Ei, ad./hc = 95,479 ± 2 cm−1) and a description of the vibrational structure of the electronic ground state of the cation which is affected by the Renner–Teller effect and the spin–orbit interaction. The spin–orbit coupling constant was measured as −52 ± 2 cm−1. These results are supported by ab initio calculations performed at the complete active space self-consistent field and second-order perturbation theory levels of theory, with extrapolation to the complete basis set limit.

Low-energy dissociative electron attachment toCF2

We present the results of a theoretical study of dissociative electron attachment (DEA) of low-energy electrons to ${\mathrm{CF}}_{2}$. We carried out electron scattering calculations using the complex Kohn variational method at the static-exchange and relaxed self-consistent field (SCF) level at the equilibrium geometry and compare our differential cross sections to other results. We then repeated these calculations as a function of the three internal degrees of freedom to obtain the resonance energy surfaces and autoionization widths. We use this data as input to form the Hamiltonian relevant to the nuclear dynamics. The multidimensional wave equation is solved using the multiconfiguration time-dependent Hartree (MCTDH) approach within the local approximation.

Initial mechanisms for the decomposition of electronically excited energetic materials: 1,5'-BT, 5,5'-BT, and AzTT.

Decomposition of nitrogen-rich energetic materials 1,5'-BT, 5,5'-BT, and AzTT (1,5'-Bistetrazole, 5,5'-Bistetrazole, and 5-(5-azido-(1 or 4)H-1,2,4-triazol-3-yl)tetrazole, respectively), following electronic state excitation, is investigated both experimentally and theoretically. The N2 molecule is observed as an initial decomposition product from the three materials, subsequent to UV excitation, with a cold rotational temperature (<30 K). Initial decomposition mechanisms for these three electronically excited materials are explored at the complete active space self-consistent field (CASSCF) level. Potential energy surface calculations at the CASSCF(12,8)/6-31G(d) level illustrate that conical intersections play an essential role in the decomposition mechanism. Electronically excited S1 molecules can non-adiabatically relax to their ground electronic states through (S1/S0)CI conical intersections. 1,5'-BT and 5,5'-BT materials have several (S1/S0)CI conical intersections between S1 and S0 states, related to different tetrazole ring opening positions, all of which lead to N2 product formation. The N2 product for AzTT is formed primarily by N-N bond rupture of the -N3 group. The observed rotational energy distributions for the N2 products are consistent with the final structures of the respective transition states for each molecule on its S0 potential energy surface. The theoretically derived vibrational temperature of the N2 product is high, which is similar to that found for energetic salts and molecules studied previously.

Initial mechanisms for the decomposition of electronically excited energetic salts: TKX-50 and MAD-X1.

Decomposition of energetic salts TKX-50 and MAD-X1 (dihydroxylammonium 5,5'-bistetrazole-1,1'-diolate and dihydroxylammonium 3,3'-dinitro-5,5'-bis-1,2,4-triazole-1,1'-diol, respectively), following electronic state excitation, is investigated both experimentally and theoretically. The NO and N2 molecules are observed as initial decomposition products from the two materials subsequent to UV excitation. Observed NO products are rotationally cold (<25 K) and vibrationally hot (>1500 K). The vibrational temperature of the NO product from TKX-50 is (2600 ± 250) K, (1100 ± 250) K hotter than that produced from MAD-X1. Observed N2 products of these two species are both rotationally cold (<30 K). Initial decomposition mechanisms for these two electronically excited salts are explored at the complete active space self-consistent field (CASSCF) level. Potential energy surface calculations at the CASSCF(8,8)/6-31G(d) level illustrate that conical intersections play an essential role in the decomposition mechanisms. Electronically excited S1 molecules can nonadiabatically relax to the lower electronic state through (S1/S0)CI conical intersections. Both TKX-50 and MAD-X1 have two (S1/S0)CI conical intersections between S1 and S0 states, related to and leading to two different reaction paths, forming N2 and NO products. N2 products are released by the opening of the tetrazole or triazole rings of TKX-50 and MAD-X1. NO products are released from the amine N-oxide moiety of TKX-50, and for MAD-X1, they are produced through nitro-nitrite isomerizations. The observed rotational energy distributions for NO and N2 products are consistent with the final structures of the respective transition states for each molecule on its S0 potential energy surface.

A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level.

An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r(-2) instead of r(-1). The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure.

Cold magnetically trapped2Dgscandium atoms. I. Interaction potential

We present a first principles description of the interaction of two ground-state scandium atoms. Scandium has a ${{}^{2}D}_{g}$ ground state. Thirty molecular states correlate to the lowest dissociation limit of the dimer. In the short range, potential energy curves are calculated using second-order $n$-electron valence state perturbation theory. The first-order long-range interaction is calculated at the complete active space self-consistent field level. We determine the second-order long-range dispersion interaction from atomic dynamic polarizabilities at imaginary frequencies. These polarizabilities are calculated using time-dependent density functional theory. We merge the short-range approach with the long-range model to obtain a physical description of the 30 potential energy curves correlating to the ${{}^{2}D}_{g}+{{}^{2}D}_{g}$ limit. Diabatic potentials are presented that can be used in quantum scattering calculations, in order to study Zeeman relaxation of ultracold scandium atoms.

Analytical gradients of complete active space self-consistent field energies using Cholesky decomposition: Geometry optimization and spin-state energetics of a ruthenium nitrosyl complex

We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042Å at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e.g., 0.032Å with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08Å for S0 and 0.11Å for T1, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry.

Initial decomposition mechanism for the energy release from electronically excited energetic materials: FOX-7 (1,1-diamino-2,2-dinitroethene, C2H4N4O4)

Decomposition of the energetic material FOX-7 (1,1-diamino-2,2-dinitroethylene, C2H4N4O4) is investigated both theoretically and experimentally. The NO molecule is observed as an initial decomposition product subsequent to electronic excitation. The observed NO product is rotationally cold (<35 K) and vibrationally hot (2800 K). The initial decomposition mechanism is explored at the complete active space self-consistent field (CASSCF) level. Potential energy surface calculations at the CASSCF(12,8)/6-31G(d) level illustrate that conical intersections play an essential role in the decomposition mechanism. Electronically excited S2 FOX-7 can radiationlessly relax to lower electronic states through (S2/S1)CI and (S1/S0)CI conical intersections and undergo a nitro-nitrite isomerization to generate NO product on the S0 state. The theoretically predicted mechanism is consistent with the experimental results. As FOX-7 decomposes on the ground electronic state, thus, the vibrational energy of the NO product from FOX-7 is high. The observed rotational energy distribution for NO is consistent with the final transition state structure on the S0 state. Ground state FOX-7 decomposition agrees with previous work: the nitro-nitrite isomerization has the lowest average energy barrier, the C-NH2 bond cleavage is unlikely under the given excitation conditions, and HONO formation on the ground state surface is energy accessible but not the main process.

A generalised vibronic-coupling Hamiltonian model for benzopyran.

A new general model for describing intersecting multidimensional potential energy surfaces when motions of large amplitude are involved is presented. This model can be seen as an extension of the vibronic coupling models of Köppel et al. ["Multimode molecular dynamics beyond the Born-Oppenheimer approximation," Adv. Chem. Phys. 57, 59 (1984)]. In contrast to the original vibronic coupling models, here the number of diabatic states is larger than the number of adiabatic states and curvilinear coordinates are used in a systematic way. Following general considerations, the approach is applied to the fitting of the potential energy surfaces for the very complex nonadiabatic photodynamics of benzopyran. Preliminary results are presented at the complete active space self-consistent field level of theory and with up to 12 active degrees of freedom. Special emphasis is placed on the physical interpretation of the diabatic states and on the influence of the various degrees of freedom on the fit.

Azole energetic materials: initial mechanisms for the energy release from electronical excited nitropyrazoles.

Decomposition of energetic material 3,4-dinitropyrazole (DNP) and two model molecules 4-nitropyrazole and 1-nitropyrazole is investigated both theoretically and experimentally. The initial decomposition mechanisms for these three nitropyrazoles are explored with complete active space self-consistent field (CASSCF) level. The NO molecule is observed as an initial decomposition product from all three materials subsequent to UV excitation. Observed NO products are rotationally cold (<50 K) for all three systems. The vibrational temperature of the NO product from DNP is (3850 ± 50) K, 1350 K hotter than that of the two model species. Potential energy surface calculations at the CASSCF(12,8)/6-31+G(d) level illustrate that conical intersections plays an essential role in the decomposition mechanism. Electronically excited S2 nitropyraozles can nonradiatively relax to lower electronic states through (S2/S1)CI and (S1/S0)CI conical intersection and undergo a nitro-nitrite isomerization to generate NO product either in the S1 state or S0 state. In model systems, NO is generated in the S1 state, while in the energetic material DNP, NO is produced on the ground state surface, as the S1 decomposition pathway is energetically unavailable. The theoretically predicted mechanism is consistent with the experimental results, as DNP decomposes in a lower electronic state than do the model systems and thus the vibrational energy in the NO product from DNP should be hotter than from the model systems. The observed rotational energy distributions for NO are consistent with the final structures of the respective transition states for each molecule.