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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Bedroom Concentrations and Emissions of Volatile Organic Compounds during Sleep

Because humans spend about one-third of their time asleep in their bedrooms and are themselves emission sources of volatile organic compounds (VOCs), it is important to specifically characterize the composition of the bedroom air that they experience during sleep. This work uses real-time indoor and outdoor measurements of volatile organic compounds (VOCs) to examine concentration enhancements in bedroom air during sleep and to calculate VOC emission rates associated with sleeping occupants. Gaseous VOCs were measured with proton-transfer reaction time-of-flight mass spectrometry during a multiweek residential monitoring campaign under normal occupancy conditions. Results indicate high emissions of nearly 100 VOCs and other species in the bedroom during sleeping periods as compared to the levels in other rooms of the same residence. Air change rates for the bedroom and, correspondingly, emission rates of sleeping-associated VOCs were determined for two bounding conditions: (1) air exchange between the bedroom and outdoors only and (2) air exchange between the bedroom and other indoor spaces only (as represented by measurements in the kitchen). VOCs from skin oil oxidation and personal care products were present, revealing that many emission pathways can be important occupant-associated emission factors affecting bedroom air composition in addition to direct emissions from building materials and furnishings.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Design Insights for Tuning the Electrocatalytic Activity of Perovskite Oxides for the Oxygen Evolution Reaction

Rechargeable metal-air batteries and water electrolyzers based on aqueous alkaline electrolytes hold the potential to be sustainable solutions to address the challenge of storing large amounts of electrical energy generated from solar and wind resources. For these batteries and electrolyzers to be economically viable, it is essential to have efficient, durable, and inexpensive electrocatalysts for the oxygen evolution reaction. In this article, we describe new insights for predicting and tuning the activity of inexpensive transition metal oxides for designing efficient and inexpensive electrocatalysts. We have focused on understanding the factors determining the electrocatalytic activity for oxygen evolution in a strong alkaline medium. To this end, we have conducted a systematic investigation of nanophase calcium-doped lanthanum cobalt manganese oxide, an example of a mixed metal oxide that can be tuned for its electrocatalytic activity by varying the transition metal composition. Using X-ray absorption spectroscopy (XANES), X-ray photoelectron spectroscopy (XPS), electrochemical polarization experiments, and analysis of mechanisms, we have identified the key determinants of electrocatalytic activity. We have found that the Tafel slopes are determined by the oxidation states and the bond energy of the surface intermediates of Mn-OH and Co-OH bonds while the catalytic activity increased with the average d-electron occupancy of the sigma* orbital of the M-OH bond. We anticipate that such understanding will be very useful in predicting the behavior of other transition metal oxide catalysts.

ORR↗
DOE OSTI2025

Air, surface, and wastewater surveillance of SARS-CoV-2; a multimodal evaluation of COVID-19 detection in a built environment

Environmental surveillance of infectious organisms holds tremendous promise to reduce human-to-human transmission in indoor spaces through early detection. In this study we determined the applicability and limitations of wastewater, indoor high-touch surfaces, in-room air, and rooftop exhaust air sampling methods for detecting SARS-CoV-2 in a real world building occupied by residents recently diagnosed with COVID-19. We concurrently examined the results of three 24-hour environmental surveillance techniques, indoor surface sampling, exhaust air sampling and wastewater surveillance, to the known daily census fluctuations in a COVID-19 isolation dormitory. Additionally, we assessed the ability of aerosol samplers placed in the large volume lobby to detect SARS-CoV-2 multiple times per day. Our research reveals an increase in the number of individuals confirmed positive with COVID-19 as well as their estimated human viral load to be associated with statistically significant increases in viral loads detected in rooftop exhaust aerosol samples (p = 0.0413), wastewater samples (p = 0.0323,), and indoor high-touch surfaces (p < 0.001)). We also report that the viral load detected in lobby aerosol samples was statistically higher in samples collected during presence of occupants whose COVID-19 diagnostic tests were confirmed positive via qPCR compared to periods when the lobby was occupied by either contact-traced (suspected positive) individuals or during unoccupied periods (p = 0.0314 and <2e–16). We conclude that each daily (24h) surveillance method, rooftop exhaust air, indoor high-touch surfaces, and wastewater, provide useful detection signals for building owner/operator(s). Furthermore, we demonstrate that exhaust air sampling can provide spatially resolved signals based upon ventilation exhaust zones. Additionally, we find that indoor lobby air sampling can provide temporally resolved signals useful during short duration sampling periods (e.g., 2-4 hours) even with intermittent occupancy by occupants diagnosed with COVID-19.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Impact of microkinetic modeling assumptions on predicted kinetics and mechanisms over undercoordinated sites

Accurate modeling of catalytic reactions on undercoordinated sites requires accounting for the structural and ensemble-specific nature of the active sites. This study examines how common microkinetic modeling (MKM) assumptions affect predicted kinetics and mechanisms on the stepped Pt(211) facet for the ethane dehydrogenation (EDH) and the ethane hydrogenolysis (EH). Six (211) MKMs were developed, differing in (i) the number of active sites represented, (ii) adsorbate site occupancy treatment, and (iii) inclusion of cross-facet interactions. These models are benchmarked against a particle-based microkinetic model (PB-MKM), which best represents step-edge behavior. MKM assumptions caused deviations in turnover frequencies exceeding ten orders of magnitude and led to contrasting mechanistic and selectivity predictions. Multi-site MKMs overestimate activity by inflating free site availability, single-site models underestimate activity, and uniform occupancy models overpredict coverage of multi-dentate intermediates, leading to reaction-specific artifacts. Overall, the Combined Site Edge Model (CSEM), a single-site MKM accounting for site occupancy and cross-facet interactions, most closely approximates PB-MKM predictions. All models predict similar kinetics when surfaces are clean or primarily occupied by monodentate species. This work provides practical guidance for selecting MKM frameworks for undercoordinated catalytic surfaces and highlights the critical role of modeling assumptions in catalytic predictions.

(211) facet↗
DOE OSTI2014

Professional diversity and the productivity of cities

Attempts to understand the relationship between diversity, productivity and scale have remained limited due to the scheme-dependent nature of the taxonomies describing complex systems. We analyze the diversity of US metropolitan areas in terms of profession diversity and employment to show how this frequency distribution takes a universal scale-invariant form, common to all cities, in the limit of infinite resolution of occupational taxonomies. We show that this limit is obtained under general conditions that follow from the analysis of the variation of the occupational frequency across taxonomies at different resolutions in a way analogous to finite-size scaling in statistical physical systems. We propose a theoretical framework that derives the form and parameters of the limiting distribution of professions based on the appearance, in urban social networks, of new occupations as the result of specialization and coordination of labor. By deriving classification scheme-independent measures of functional diversity and modeling cities as social networks embedded in infrastructural space, these results show how standard economic arguments of division and coordination of labor can be articulated in detail in cities and provide a microscopic basis for explaining increasing returns to population scale observed at the level of entire metropolitan areas.

SOCIOECONOMIC SCENARIOS↗
DOE OSTI2016

Li-ion site disorder driven superionic conductivity in solid electrolytes: a first-principles investigation of β-Li 3 PS 4

The attractive safety and long-term stability of all solid-state batteries has added a new impetus to the discovery and development of solid electrolytes for lithium batteries. Recently several superionic lithium conducting solid electrolytes have been discovered. All the superionic lithium containing compounds (β-Li 3 PS 4 and Li 10 GeP 2 S 12 and oxides, predominantly in the garnet phase) have partially occupied sites. This naturally begs the question of understanding the role of partial site occupancies (or site disorder) in optimizing ionic conductivity in these family of solids. In this paper, we find that for a given topology of the host lattice, maximizing the number of sites with similar Li-ion adsorption energies, which gives partial site occupancy, is a natural way to increase the configurational entropy of the system and optimize the conductivity. For a given topology and density of Li-ion adsorption sites, the ionic conductivity is maximal when the number of mobile Li-ions are equal to the number of mobile vacancies, also the very condition for achieving maximal configurational entropy. We demonstrate applicability of this principle by elucidating the role of Li-ion site disorder and the local chemical environment in the high ionic conductivity of β-Li 3 PS 4 . In addition, for β-Li 3 PS 4 we find that a significant density of vacancies in the Li-ion sub-lattice (~25%) leads to sub-lattice melting at (~600 K) leading to a molten form for the Li-ions in an otherwise solid anionic host. This gives a lithium site occupancy that is similar to what is measured experimentally. We further show that quenching this disorder can improve conductivity at lower temperatures. As a consequence, we discover that (a) one can optimize ionic conductivity in a given topology by choosing a chemistry/composition that maximizes the number of mobile-carriers i.e. maximizing both mobile Li-ions and vacancies, and (b) when the concentration of vacancies becomes significant in the Li-ion sub-lattice, it becomes energetically as well as entropically favorable for it to remain molten well below the bulk decomposition temperature of the solid. Finally, this principle may already apply to several known superionic conducting solids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Metastable electronic states in uranium tetrafluoride

Here, the DFT+ U approach, where U is the Hubbard-like on-site Coulomb interaction, has successfully been used to improve the description of transition metal oxides and other highly correlated systems, including actinides. The secret of the DFT+ U approach is the breaking of d or f shell orbital degeneracy and adding an additional energetic penalty to non-integer occupation of orbitals. A prototypical test case, UO 2 , benefits from the + U approach whereby the bare LDA method predicts UO 2 to be a ferromagnetic metal, whereas LDA+ U correctly predicts UO 2 to be insulating. However, the concavity of the energetic penalty in the DFT+ U approach can lead to a number of convergent “metastable” electronic configurations residing above the ground state. Uranium tetrafluoride (UF 4 ) represents a more complex analogy to UO 2 in that the crystal field has lower symmetry and the unit cell contains two symmetrically distinct U atoms. We explore the metastable states in UF 4 using several different methods of selecting initial orbital occupations. Two methods, a “pre-relaxation” method wherein an initial set of orbital eigenvectors is selected via the self-consistency procedure and a crystal rotation method wherein the x, y, z axes are brought into alignment with the crystal field, are explored. We show that in the case of UF 4 , which has non-collinearity between its crystal axes and the U atoms' crystal field potentials, the orbital occupation matrices are much more complex and should be analyzed using a novel approach. In addition to demonstrating a complex landscape of metastable electronic states, UF 4 also shows significant hybridization in U–F bonding, which involves non-trivial contributions from s, p, d, and f orbitals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Water transport through functionalized nanotubes with tunable hydrophobicity

Molecular dynamics simulations are used to study the occupancy and flow of water through nanotubes comprised of hydrophobic and hydrophilic atoms, which are arranged on a honeycomb lattice to mimic functionalized carbon nanotubes (CNTs). We consider single-file motion of TIP3P water through narrow channels of (6,6) CNTs with varying fractions (f) of hydrophilic atoms. Various arrangements of hydrophilic atoms are used to create heterogeneous nanotubes with separate hydrophobic/hydrophilic domains along the tube as well as random mixtures of the two types of atoms. The water occupancy inside the nanotube channel is found to vary nonlinearly as a function of f, and a small fraction of hydrophilic atoms (f ≈ 0.4) are sufficient to induce spontaneous and continuous filling of the nanotube. Interestingly, the average number of water molecules inside the channel and water flux through the nanotube are less sensitive to the specific arrangement of hydrophilic atoms than to the fraction, f. Two different regimes are observed for the water flux dependence on f – an approximately linear increase in flux as a function of f for f < 0.4, and almost no change in flux for higher f values, similar to the change in water occupancy. We are able to define an effective interaction strength between nanotube atoms and water's oxygen, based on a linear combination of interaction strengths between hydrophobic and hydrophilic nanotube atoms and water, that can quantitatively capture the observed behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Negative magnetoresistance in a low-k dielectric

We observed negative magnetoresistance in amorphous SiCOH, a low-k dielectric, applying modest magnetic fields (<150 Gauss) at room temperature. The conductivity increases with increasing magnetic field. The change in conductivity due to the applied magnetic field increases with electric field and has little or no temperature dependence over the range studied. The magnitude of the effect is independent of the orientation of magnetic field relative to the direction of current flow. The effect is attributed to spin constraints associated with double occupancy of a trap site under the assumption that trap sites which have double occupancy have lower hopping frequencies than traps that have single occupancy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

A unified approach to modelling the charge state of monatomic hydrogen and other defects in crystalline silicon

There are a number of existing models for estimating the charge states of defects in silicon. In order of increasing complexity, these are (a) the Fermi-Dirac distribution, (b) the Shockley-Last model, (c) the Shockley-Read-Hall model, and (d) the Sah-Shockley model. In this work, we demonstrate their consistency with the general occupancy ratio α, and show that this parameter can be universally applied to predict the charge states of both monovalent and multivalent deep levels, under either thermal equilibrium or steady-state conditions with carrier injection. The capture cross section ratio is shown to play an important role in determining the charge state under non-equilibrium conditions. The application of the general occupancy ratio is compared with the quasi-Fermi levels, which are sometimes used to predict the charge states in the literature, and the conditions where the latter can be a good approximation are identified. The general approach is then applied to the prediction of the temperature- and injection level-dependent charge states for the technologically important case of multivalent monatomic hydrogen, and several other key monovalent deep levels including Fe, Cr, and the boron-oxygen complex in silicon solar cells. For the case of hydrogen, we adapt the model of Herring et al., which describes the charge states of hydrogen in thermal equilibrium, and generalize it for non-equilibrium conditions via the inclusion of the general occupancy ratio, while retaining the pre-factors which make the model more complete. Based on these results, the impact of temperature and injection on the hydrogenation of the key monovalent defects, and other pairing reactions, are discussed, demonstrating that the presented model provides a rigorous methodology for understanding the impact of charge states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Electron transport and electron energy distributions within the wurtzite and zinc-blende phases of indium nitride: Response to the application of a constant and uniform electric field

Within the framework of an ensemble semi-classical three-valley Monte Carlo electron transport simulation approach, we critically contrast the nature of the electron transport that occurs within the wurtzite and zinc-blende phases of indium nitride in response to the application of a constant and uniform electric field. We use the electron energy distribution and its relationship with the electron transport characteristics in order to pursue this analysis. For the case of zinc-blende indium nitride, only a peak corresponding to the electrons within the lowest energy conduction band valley is observed, this peak being seen to broaden and shift to higher energies in response to increases in the applied electric field strength, negligible amounts of upper energy conduction band valley occupancy being observed. In contrast, for the case of wurtzite indium nitride, in addition to the aforementioned lowest energy conduction band valley peak in the electron energy distribution, and its broadening and shifting to higher energies in response to increases in the applied electric field strength, beyond a certain critical electric field strength, 30 kV/cm for the case of this particular material, upper energy conduction band valley occupancy is observed, this occupancy being further enhanced in response to further increases in the applied electric field strength. Reasons for these results are provided. The potential for device consequences is then commented upon.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Microwave spectra, molecular structure, and aromatic character of 4a,8a-azaboranaphthalene

The microwave spectra for seven unique isotopologues of 4a,8a-azaboranaphthalene [hereafter referred to as BN-naphthalene] were measured using a pulsed-beam Fourier transform microwave spectrometer. Spectra were obtained for the normal isotopologues with {sup 10}B, {sup 11}B, and all unique single {sup 13}C and the {sup 15}N isotopologue (with {sup 11}B), in natural abundance. The rotational, centrifugal distortion and quadrupole coupling constants determined for the {sup 11}B{sup 14}N isotopologue are A = 3042.712 75(43) MHz, B = 1202.706 57(35) MHz, C = 862.220 13(35) MHz, D{sub J} = 0.06(1) kHz, 1.5χ{sub aa} ({sup 14}N) = 2.5781(61) MHz, 0.25(χ{sub bb} − χ{sub cc}) ({sup 14}N) = − 0.1185(17) MHz, 1.5χ{sub aa} (11B) = − 3.9221(75) MHz, and 0.25(χ{sub bb} − χ{sub cc}) ({sup 11}B) = − 0.9069(24) MHz. The experimental inertial defect is Δ = − 0.159 amu Å{sup 2}, which is consistent with a planar structure for the molecule. The B—N bond length from the experimentally determined structure is 1.47 Å, which indicates π-bonding character between the B and N. The measured quadrupole coupling strengths provide important and useful information about the bonding, orbital occupancy, and aromatic character for this aromatic molecule. Extended Townes-Dailey analyses were used to determine the B and N electron sp{sup 2}-hybridized and p-orbital occupations. These results are compared with electron orbital occupations from the natural bond orbital option in theoretical calculations. From the analyses, it was determined that BN-naphthalene has aromatic character similar to that of other N-containing aromatics. The results are compared with similar results for B—N bonding in 1,2-dihydro-1,2-azaborine and BN-cyclohexene. Accurate and precise structural parameters were obtained from the microwave measurements on seven isotopologues and from high-level G09 calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Manipulation of polar order in the “empty” tetragonal tungsten bronzes: Ba{sub 4-x}Sr{sub x}Dy{sub 0.67}□{sub 1.33}Nb{sub 10}O{sub 30}, x = 0, 0.25, 0.5, 1, 2, 3

A series of “empty” tetragonal tungsten bronze (TTB) ferroelectrics, Ba{sub 4-x}Sr{sub x}Dy{sub 0.67}□{sub 1.33}Nb{sub 10}O{sub 30} (x = 0, 0.25, 0.5, 1, 2, 3; □ = vacancy), is reported. With increasing x the unit cell contracts in both the ab plane and c-axis; x ≤ 1 compounds are normal ferroelectrics (FE) with decreasing T{sub C} as x increases, while x ≥ 2 are relaxor ferroelectrics (RFE) with associated frequency dependent permittivity peaks and with similar T{sub m} and T{sub f} (Vogel-Fulcher freezing temperatures) values. This observation is rationalised by differing cation occupancies: for x ≤ 1, Sr{sup 2+} principally occupies the A2-site (co-occupied by Ba{sup 2+} with the A1-site occupied by Dy{sup 3+} and vacancies); for x ≥ 2 significant Sr A1-site occupation leads to the observed RFE characteristics. This FE to RFE crossover is consistent with a previously proposed TTB crystal chemical framework where both a decrease in average A-site size and concurrent increase in A1-site tolerance factor (t{sub A1}) favour destabilization of long range polar order and relaxor behaviour. The effect of increasing t{sub A1} as a result of Sr occupancy at the A1 site is dominant in the compounds reported here.

36 MATERIALS SCIENCE↗
DOE OSTI2017

On extending Kohn-Sham density functionals to systems with fractional number of electrons

Here, we analyze four ways of formulating the Kohn-Sham (KS) density functionals with a fractional number of electrons, through extending the constrained search space from the Kohn-Sham and the generalized Kohn-Sham (GKS) non-interacting $\mathcal{v}$-representable density domain for integer systems to four different sets of densities for fractional systems. In particular, these density sets are (I) ensemble interacting N -representable densities, (II) ensemble non-interacting N -representable densities, (III) non-interacting densities by the Janak construction, and (IV) non-interacting densities whose composing orbitals satisfy the Aufbau occupation principle. By proving the equivalence of the underlying first order reduced density matrices associated with these densities, we show that sets (I), (II), and (III) are equivalent, and all reduce to the Janak construction. Moreover, for functionals with the ensemble v-representable assumption at the minimizer, (III) reduces to (IV) and thus justifies the previous use of the Aufbau protocol within the (G)KS framework in the study of the ground state of fractional electron systems, as defined in the grand canonical ensemble at zero temperature. By further analyzing the Aufbau solution for different density functional approximations (DFAs) in the (G)KS scheme, we rigorously prove that there can be one and only one fractional occupation for the Hartree Fock functional, while there can be multiple fractional occupations for general DFAs in the presence of degeneracy. This has been confirmed by numerical calculations using the local density approximation as a representative of general DFAs. This work thus clarifies important issues on density functional theory calculations for fractional electron systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Divalent doping-induced thermoelectric power factor increase in p-type Bi 2 Te 3 via electronic structure tuning

We use first-principles calculations to reveal the effects of divalent Pb, Ca, and Sn doping of Bi 2 Te 3 on the band structure and transport properties, including the Seebeck coefficient, α, and the reduced power factor, α 2 σ/τ, where σ is the electrical conductivity and τ is the effective relaxation time. Pb and Ca additions exhibit up to 60%–75% higher peak α 2 σ/τ than that of intrinsic Bi 2 Te 3 with Bi antisite defects. Pb occupancy and Ca occupancy of Bi sites increase σ/τ by activating high-degeneracy low-effective-mass bands near the valence band edge, unlike Bi antisite occupancy of Te sites that eliminates near-edge valence states in intrinsic Bi 2 Te 3 . Neither Pb doping nor subatomic-percent Ca doping increases α significantly, due to band averaging. Higher Ca levels increase α and diminish σ, due to the emergence of a corrugated band structure underpinned by high-effective-mass bands, attributable to Ca–Te bond ionicity. Sn doping results in a distortion of the bands with a higher density of states that may be characterized as a resonant state but decreases α 2 σ by up to 30% due to increases in the charge carrier effective mass and decreases in both spin–orbit coupling and valence band quasidegeneracy. These results, and thermal conductivity calculations for nanostructured Bi 2 Te 3 , suggest that Pb or Ca doping can enhance the thermoelectric figure of merit ZT to values up to ZT ~ 1.7, based on an experimentally determined τ. Our findings suggest that divalent doping can be attractive for realizing large ZT enhancements in pnictogen chalcogenides.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Hammerhead, an ultrahigh resolution ePix camera for wavelength-dispersive spectrometers

Wavelength-dispersive spectrometers (WDS) are often used in synchrotron and FEL applications where high energy resolution (in the order of eV) is important. Increasing WDS energy resolution requires increasing spatial resolution of the detectors in the dispersion direction. The common approaches are not ideal: using strip detectors loses the 2D position sensitivity (important for, e.g., background estimation) and the high counting rate; using pixel detectors with a small pitch results in complex charge sharing behaviour and typically have a small size. Developing pixel detectors with high aspect ratio and a small pitch in the wavelength dispersive direction would be ideal, however, it would require a substantial ASIC development. We present a new approach, with a novel sensor design using rectangular pixels with a high aspect ratio (between strips and pixels, further called “strixels”), and strixel redistribution to match the square pixel arrays of typical ASICs. This results in a sensor area of 17.4 mm × 77 mm, with a fine pitch of 25 µm in the horizontal direction resulting in 3072 columns and 176 rows. The sensors use ePix100 readout ASICs, leveraging their low noise (43 e - , or 180 eV rms). We present results obtained with a Hammerhead ePix100 camera, showing that the small pitch (25 µm) in the dispersion direction maximizes performance for both high and low photon occupancies, resulting in optimal WDS energy resolution. The low noise level at high photon occupancy allows precise photon counting, while at low occupancy, both the energy and the subpixel position can be reconstructed for every photon, allowing an ultrahigh resolution (in the order of 1 µm) in the dispersion direction and rejection of scattered beam and harmonics. Using strixel sensors with redistribution and flip-chip bonding to standard ePix readout ASICs results in ultrahigh position resolution (~1 µm) and low noise in WDS applications, leveraging the advantages of hybrid pixel detectors (high production yield, good availability, relatively inexpensive) while minimizing development complexity through sharing the ASIC, hardware, software and DAQ development with other versions of ePix cameras.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Mixed quantum–classical approach to model non-adiabatic electron–nuclear dynamics: Detailed balance and improved surface hopping method

We develop a density matrix formalism to describe coupled electron–nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates in these (rate) equations are asymmetric with respect to the lower-to-higher energy transitions and vice versa. In thermal equilibrium, such asymmetry corresponds to the detailed balance condition. We also study the equations for the electronic occupations in the non-Markovian regime and develop a surface hopping algorithm based on our formalism. To treat the decoherence effects, we introduce additional “virtual” nuclear wave packets whose interference with the “real” (physical) wave packets leads to the reduction in coupling between the electronic states (i.e., decoherence) as well as to the phase shifts that improve the accuracy of the numerical approach. Remarkably, the same phase shifts lead to the detailed balance condition in the strong decoherence limit.

74 ATOMIC AND MOLECULAR PHYSICS↗