We propose an efficient version of ensemble Hartree-Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions-even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for ab initio non-adiabatic dynamics in the near future.
We study the spin-dependent stereodynamics of the S + H2 â SH + H reaction by using full-dimensional quantum dynamics calculations with zero total nuclear angular momentum along the triplet 3Aâ³ states and singlet 1A' states. We find that the interplay between the electronic spin direction and the molecular geometry has a measurable influence on the singlet-triplet intersystem crossing reaction probabilities. Our results show that for some incident scattering angles in the body-fixed frame, the relative difference in intersystem crossing reaction probabilities (as determined between spin up and spin down initial states) can be as large as 15%. Our findings are an ab initio demonstration of spin-dependent nonadiabatic dynamics, which we hope will shine light as far as understanding the chiral-induced spin selectivity effect.
Within the context of fewest-switch surface hopping (FSSH) dynamics, one often wishes to remove the angular component of the derivative coupling between states J and K. In a previous set of papers, Shu et al. [J. Phys. Chem. Lett. 11, 1135-1140 (2020)] posited one approach for such a removal based on direct projection, while we isolated a second approach by constructing and differentiating a rotationally invariant basis. Unfortunately, neither approach was able to demonstrate a one-electron operatorÔ whose matrix element JÔK was the angular component of the derivative coupling. Here, we show that a one-electron operator can, in fact, be constructed efficiently in a semi-local fashion. The present results yield physical insight into designing new surface hopping algorithms and are of immediate use for FSSH calculations.
Modern electronic structure theory is built around the Born-Oppenheimer approximation and the construction of an electronic Hamiltonian Hel(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ') and rotational (Γâ³) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, HPS(X,P). While classical Born-Oppenheimer dynamics that run along the eigensurfaces of the operator Hel(X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of HPS(X,P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general.
We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, "Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions," J. Chem. Phys. 122, 084113 (2005) and V. Krishna, "Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit," J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree-Fock with spin-orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born-Oppenheimer approximation when using ab initio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results.
For a system without spin-orbit coupling, the (i) nuclear plus electronic linear momentum and (ii) nuclear plus orbital electronic angular momentum are good quantum numbers. Thus, when a molecular system undergoes a nonadiabatic transition, there should be no change in the total linear or angular momentum. Now, the standard surface hopping algorithm ignores the electronic momentum and indirectly equates the momentum of the nuclear degrees of freedom to the total momentum. However, even with this simplification, the algorithm still does not conserve either the nuclear linear or the nuclear angular momenta. Here, we show that one way to address these failures is to dress the derivative couplings (i.e., the hopping directions) in two ways: (i) we disallow changes in the nuclear linear momentum by working in a translating basis (which is well known and leads to electron translation factors) and (ii) we disallow changes in the nuclear angular momentum by working in a basis that rotates around the center of mass [which is not well-known and leads to a novel, rotationally removable component of the derivative coupling that we will call electron rotation factors below, cf. Eq. (96)]. The present findings should be helpful in the short term as far as interpreting surface hopping calculations for singlet systems (without spin) and then developing the new surface hopping algorithm in the long term for systems where one cannot ignore the electronic orbital and/or spin angular momentum.
Nonadiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly) polarized light allows one to effectively introduce a complex-valued time-dependent Hamiltonian, which offers a new path for control or exploration through the introduction of Berry forces. Here, we investigate several inexpensive semiclassical approaches for modeling such nonadiabatic dynamics in the presence of a time-dependent complex-valued Hamiltonian, beginning with a straightforward instantaneous adiabatic fewest-switches surface hopping (IA-FSSH) approach (where the electronic states depend on position and time), continuing to a standard Floquet fewest switches surface hopping (F-FSSH) approach (where the electronic states depend on position and frequency), and ending with an exotic Floquet phase-space surface hopping (F-PSSH) approach (where the electronic states depend on position, frequency, and momentum). Using a set of model systems with time-dependent complex-valued Hamiltonians, we show that the Floquet phase-space adiabats are the optimal choice of basis as far as accounting for Berry phase effects and delivering accuracy. Thus, the F-PSSH algorithm sets the stage for future modeling of nonadiabatic dynamics under strong externally pumped circular polarization.
Nuclear Berry curvature effects emerge from electronic spin degeneracy and can lead to nontrivial spin-dependent (nonadiabatic) nuclear dynamics. However, such effects are not captured fully by any current mixed quantum-classical method such as fewest-switches surface hopping. In this work, we present a phase-space surface-hopping (PSSH) approach to simulate singlet-triplet intersystem crossing dynamics. We show that with a simple pseudodiabatic ansatz, a PSSH algorithm can capture the relevant Berry curvature effects and make predictions in agreement with exact quantum dynamics for a simple singlet-triplet model Hamiltonian. Thus, this approach represents an important step toward simulating photochemical and spin processes concomitantly, as relevant to intersystem crossing and spin-lattice relaxation dynamics.
Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. However, for electronic systems with spin degrees of freedom, there are few if any applicable and practical quasiclassical methods. Here, we show that for nonadiabatic dynamics with two electronic states and a complex-valued Hamiltonian that does not obey time-reversal symmetry (as relevant to many coupled nuclear-electronic-spin systems), the optimal semiclassical approach is to generalize Tully's surface hopping dynamics from coordinate space to phase space. In order to generate the relevant phase-space adiabatic surfaces, one isolates a proper set of diabats, applies a phase gauge transformation, and then diagonalizes the total Hamiltonian (which is now parameterized by both R and P). The resulting algorithm is simple and valid in both the adiabatic and nonadiabatic limits, incorporating all Berry curvature effects. Most importantly, the resulting algorithm allows for the study of semiclassical nonadiabatic dynamics in the presence of spin-orbit coupling and/or external magnetic fields. One expects many simulations to follow as far as modeling cutting-edge experiments with entangled nuclear, electronic, and spin degrees of freedom, e.g., experiments displaying chiral-induced spin selectivity.
We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin-orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction-even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson-Fischer point (which can lead to numerical instabilities). We do not address magnetic fields here.
We present a preliminary surface-hopping approach for modeling intersystem crossing (ISC) dynamics between four electronic states: one singlet and one (triply degenerate) triplet. In order to incorporate all Berry force effects, the algorithm requires that, when moving along an adiabatic surface associated with the triplet manifold, one must also keep track of a quasi-diabatic index (akin to a "ms" quantum number) for each trajectory. For a simple model problem, we find that a great deal of new physics can be captured by our algorithm, setting the stage for larger, more realistic (or perhaps even ab initio) simulations in the future.
We examine the many open questions that arise for nonadiabatic dynamics in the presence of degenerate electronic states, e.g., for singlet-to-triplet intersystem crossing where a minimal Hamiltonian must include four states (two of which are always degenerate). In such circumstances, the standard surface hopping approach is not sufficient as the algorithm does not include Berry force. Yet, we hypothesize that such a Berry force may be crucial as far as creating chiral induced spin separation, which is now a burgeoning field of study. Thus, this Perspective highlights the fact that if one can generate a robust and accurate semiclassical approach for the case of degenerate states, one will take a big step forward toward merging chemical physics with spintronics.
We propose a "backtracking" mechanism within Tully's fewest switches surface hopping (FSSH) algorithm, whereby whenever one detects consecutive (double) hops during a short period of time, one simply rewinds the dynamics backward in time. In doing so, one reduces the number of hopping events and comes closer to a truly fewest switches surface hopping approach with independent trajectories. With this algorithmic change, we demonstrate that surface hopping can be reasonably accurate for nuclear dynamics in a multidimensional configuration space with a complex-valued (i.e., not real-valued) electronic Hamiltonian; without this adjustment, surface hopping often fails. The added computational cost is marginal. Future research will be needed to assess whether or not this backtracking correction can improve the accuracy of a typical FSSH calculation with a real-valued electronic Hamiltonian (that ignores spin).
The aim of the present study was to determine the potential core genes in the pathogenesis of human thoracic aortic dissection (TAD) by analyzing microarray profiles of long noncoding (lnc)RNAs between TAD and normal thoracic aorta (NTA). The differentially expressed lncRNA profiles of the aorta tissues between TAD patients (TAD group, n=6) and agematched donors with aortic diseases (NTA group, n=6) were analyzed by lncRNAs microarray. Gene ontology (GO), pathway and network analyses were used to further investigate candidate lncRNAs and mRNAs. Differentially expressed lncRNAs and mRNAs were validated by reverse transcriptionquantitative polymerase chain reaction (RTqPCR). In total, the present study identified 765 lncRNAs and 619 mRNAs with differential expression between TAD and NTA (fold change >2.0, P<0.01). GO analysis demonstrated that the differentially upregulated lncRNAs are associated with cell differentiation, homeostasis, cell growth and angiogenesis. Kyoto Encyclopedia of Gene and Genomes pathway analysis demonstrated that the differentially downregulated lncRNAs are mainly associated with arrhythmogenic right ventricular cardiomyopathy, hypertrophic cardiomyopathy and dilated cardiomyopathy. To reduce the lncRNAs for further investigation and to enrich those potentially involved in TAD, a total of 16 candidate lncRNAs with a significant expression (fold change >4, P<0.01) were selected, that were associated with an annotated proteincoding gene through the GO term and scientific literatures. Then a set of significantly expressed lncRNAs [purinergic receptor P2X7 (P2RX7), hypoxia inducing factor (HIF)1AAS2, AX746823, RP1169I8.3 and RP11536K7.5) and the corresponding mRNAs (P2RX7, cyclin dependent kinase inhibitor 2B, HIF1A, runtrelated transcription factor 1, connective tissue growth factor and interleukin 2 receptor a chain] were confirmed using RTqPCR. The present study revealed that the expression profiles of lncRNAs and mRNAs in aorta tissues from TAD were significantly altered. These results may provide important insights into the pathogenesis of TAD disease.
Aortic Dissection/genetics , Gene Regulatory Networks , RNA, Long Noncoding/genetics , RNA, Messenger/genetics , Transcriptome , Adult , Aortic Dissection/pathology , Aorta, Thoracic/metabolism , Aorta, Thoracic/pathology , Female , Gene Expression Profiling , Gene Ontology , Humans , Male , Middle Aged
