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The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham(REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. In this work, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirely in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. The implementation and benchmarking of the derived formalism will be described in a subsequent article of this series. [ABSTRACT FROM AUTHOR]

The spin-restricted ensemble-referenced Kohn-Sham (REKS) method is based on an ensemble representation of the density and is capable of correctly describing the non-dynamic electron correlation stemming from (near-)degeneracy of several electronic configurations. The existing REKS methodology describes systems with two electrons in two fractionally occupied orbitals. In thiswork, the REKS methodology is extended to treat systems with four fractionally occupied orbitals accommodating four electrons and self-consistent implementation of the REKS(4,4) method with simultaneous optimization of the orbitals and their fractional occupation numbers is reported. The new method is applied to a number of molecular systems where simultaneous dissociation of several chemical bonds takes place, as well as to the singlet ground states of organic tetraradicals 2,4-didehydrometaxylylene and 1,4,6,9-spiro[4.4]nonatetrayl. [ABSTRACT FROM AUTHOR]

The unimolecular decay of carbonyl oxide intermediates, known as Criegee intermediates, produced in alkene ozonolysis is a significant source of OH radicals in the troposphere. Here, the rate of appearance of OH radical products is examined directly in the time-domain for a prototypical alkylsubstituted Criegee intermediate, CH3CH2CHOO, following vibrational activation under collisionfree conditions. Complementary statistical Rice-Ramsperger-Kassel-Marcus calculations of the microcanonical unimolecular decay rate for CH3CH2CHOO are also carried out at energies in the vicinity of the barrier for 1,4 hydrogen atom transfer that leads to OH products. Tunneling through the barrier, derived from high level electronic structure calculations, contributes significantly to the decay rate. Infrared transitions of CH3CH2CHOO are identified in the CH stretch overtone region, which are detected by ultraviolet laser-induced fluorescence of the resultant OH products. The features observed are attributed to CH vibrational excitations and conformational forms utilizing insights from theory. Both experiment and theory yield unimolecular decay rates for CH3CH2CHOO of ca. 107 s-1, which are slower than those obtained for syn-CH3CHOO or (CH3)2COO reported previously [Fang et al., J. Chem. Phys. 144, 061102 (2016)] at similar energies. Master equation modeling is also utilized to predict the thermal decay rate of CH3CH2CHOO under atmospheric conditions, giving a rate of 279 s-1 at 298 K. [ABSTRACT FROM AUTHOR]

The hydroxyl radical (OH) is a key oxidant in atmospheric and combustion chemistry. Recently, a sensitive and state-selective ionization method has been developed for detection of the OH radical that utilizes UV excitation on the A²Σ+-X²π transition followed by fixed 118 nm vacuum ultraviolet (VUV) radiation to access autoionizing Rydberg states [J. M. Beames et al., J. Chem. Phys. 134, 241102 (2011)]. The present study uses tunable VUV radiation generated by four-wave mixing to examine the origin of the enhanced ionization efficiency observed for OH radicals prepared in specific A²Σ+ intermediate levels. The enhancement is shown to arise from resonant excitation to distinct rotational and fine structure levels of two newly identified ²π Rydberg states with an A³π cationic core and a 3d electron followed by ionization. Spectroscopic constants are derived and effects due to uncoupling of the Rydberg electron are revealed for the OH ²π Rydberg states. The linewidths indicate a Rydberg state lifetime due to autoionization on the order of a picosecond. [ABSTRACT FROM AUTHOR]

We formulate self-consistent field (SCF) theory in terms of an interaction picture where the working variable is the difference density matrix between the true system and a corresponding superposition of atomic densities. As the difference density matrix directly represents the electronic deformations inherent in chemical bonding, this "difference self-consistent field (dSCF)" picture provides a number of significant conceptual and computational advantages. We show that this allows for a stable and efficient dSCF iterative procedure with wholly single-precision Coulomb and exchange matrix builds. We also show that the dSCF iterative procedure can be performed with aggressive screening of the pair space. These approximations are tested and found to be accurate for systems with up to 1860 atoms and >10 000 basis functions, providing for immediate overall speedups of up to 70% in the heavily optimized TERACHEM SCF implementation. [ABSTRACT FROM AUTHOR]

In the atmosphere, a dominant loss process for carbonyl oxide intermediates produced from alkene ozonolysis is also an important source of hydroxyl radicals. The rate of appearance of OH radicals is revealed through direct time-domain measurements following vibrational activation of prototypical methyl-substituted Criegee intermediates under collision-free conditions. Complementary theoretical calculations predict the unimolecular decay rate for the Criegee intermediates in the vicinity of the barrier for 1,4 hydrogen transfer that leads to OH products. Both experiment and theory yield unimolecular decay rates of ca. 108 and 107 s-1 for syn-CH3CHOO and (CH3)2COO, respectively, at energies near the barrier. Tunneling through the barrier, computed from high level electronic structure theory and experimentally validated, makes a significant contribution to the decay rate. Extension to thermally averaged unimolecular decay of stabilized Criegee intermediates under atmospheric conditions yields rates that are six orders of magnitude slower than those evaluated directly in the barrier region. [ABSTRACT FROM AUTHOR]