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Register a new userAn optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas
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We explore an alternative to twist averaging in order to obtain more cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for coupled cluster doubles (CCD) calculations. We seek a single twist angle to perform calculations at, instead of integrating over many random points or a grid. We introduce the concept of connectivity, a quantity derived from the non-zero four-index integrals in an MP2 calculation. This allows us to find a special twist angle that provides appropriate connectivity in the energy equation, and which yields results comparable to full twist averaging. This special twist angle effectively makes the finite electron number CCD calculation represent the TDL more accurately, reducing the cost of twist-averaged CCD over $N_mathrm{s}$ twist angles from $N_s$ CCD calculations to $N_s$ MP2 calculations plus one CCD calculation.
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The O(n) spin model in two dimensions may equivalently be formulated as a loop model, and then mapped to a height model which is conjectured to flow under the renormalization group to a conformal field theory (CFT). At the critical point, the order n terms in the partition function and correlation functions describe single self-avoiding loops. We investigate the ensemble of these self-avoiding loops using twist operators, which count loops which wind non-trivially around them with a factor -1. These turn out to have level two null states and hence their correlators satisfy a set of partial differential equations. We show that partly-connected parts of the four point function count the expected number of loops which separate one pair of points from the other pair, and find an explicit expression for this. We argue that the differential equation satisfied by these expectation values should have an interpretation in terms of a stochastic(Schramm)-Loewner evolution (SLE_kappa) process with kappa=6. The two point function in a simply connected domain satisfies a closely related set of equations. We solve these and hence calculate the expected number of single loops which separate both points from the boundary.
Since the hypervalent twist followed by reductive elimination is a general reaction pattern for hypervalent iodine reagents, mechanistic studies about the hypervalent twist step provide significant guidance for experiments. Our previous work showed there are two types of hypervalent twist models, i.e. apical twist and equatorial twist. We applied both hypervalent twist models to explain the isomerization mechanism of two important electrophilic trifluoromethylating reagents, Togni I and Togni II. To the best of our knowledge, there are less detailed studies about the different twist modes between both reagents, which are important to predict the right reaction mechanism and especially, understand well the differences of reactivity and stability. Here, we successfully identified Togni IIs isomerization pathway via equatorial twist, and suggested different hypervalent twist models should be considered to predict the right mechanisms of reactions with hypervalent iodine reagents.
We construct the complementary short-range correlation relativistic local-density-approximation functional to be used in relativistic range-separated density-functional theory based on a Dirac-Coulomb Hamiltonian in the no-pair approximation. For this, we perform relativistic random-phase-approximation calculations of the correlation energy of the relativistic homogeneous electron gas with a modified electron-electron interaction, we study the high-density behavior, and fit the results to a parametrized expression. The obtained functional should eventually be useful for electronic-structure calculations of strongly correlated systems containing heavy elements.
Elucidating photochemical reactions is vital to understand various biochemical phenomena and develop functional materials such as artificial photosynthesis and organic solar cells, albeit its notorious difficulty by both experiments and theories. The best theoretical way so far to analyze photochemical reactions at the level of ab initio electronic structure is the state-averaged multi-configurational self-consistent field (SA-MCSCF) method. However, the exponential computational cost of classical computers with the increasing number of molecular orbitals hinders applications of SA-MCSCF for large systems we are interested in. Utilizing quantum computers was recently proposed as a promising approach to overcome such computational cost, dubbed as SA orbital-optimized variational quantum eigensolver (SA-OO-VQE). Here we extend a theory of SA-OO-VQE so that analytical gradients of energy can be evaluated by standard techniques that are feasible with near-term quantum computers. The analytical gradients, known only for the state-specific OO-VQE in previous studies, allow us to determine various characteristics of photochemical reactions such as the minimal energy (ME) points and the conical intersection (CI) points. We perform a proof-of-principle calculation of our methods by applying it to the photochemical {it cis-trans} isomerization of 1,3,3,3-tetrafluoropropene. Numerical simulations of quantum circuits and measurements can correctly capture the photochemical reaction pathway of this model system, including the ME and CI points. Our results illustrate the possibility of leveraging quantum computers for studying photochemical reactions.
Metric perturbations typically strengthen field resonances during preheating. In contrast we present a model in which the super-Hubble field resonances are completely {em suppressed} when metric perturbations are included. The model is the nonminimal Fakir-Unruh scenario which is exactly solvable in the long-wavelength limit when metric perturbations are included, but exhibits exponential growth of super-Hubble modes in their absence. This gravitationally enhanced integrability is exceptional, both for its rarity and for the power with which it illustrates the importance of including metric perturbations in consistent studies of preheating. We conjecture a no-go result - there exists no {em single-field} model with growth of cosmologically-relevant metric perturbations during preheating.
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