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Register a new userSystematically Improvable Excitonic Hamiltonians for Electronic Structure Theory
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We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment electron exchange and charge transfer. Familiar electronic structure approaches can be applied to the renormalized Hamiltonian. For efficiency, the basis for each fragment can be truncated, removing high-energy local arrangements of electrons from consideration, and effectively defining collective coordinates for the fragments. For a large number of problems (especially for non-covalently interacting fragments), this has the potential to fold the majority of electron correlation into the effective Hamiltonian, and it should provide a robust approach to incorporating difficult electronic structure problems into large systems. The number of terms in the exactly transformed Hamiltonian formally scales quartically with system size, but this can be reduced to quadratic in the mesoscopic regime, to within an arbitrary error tolerance. Finally, all but a linear-scaling number of these terms may be efficiently decomposed in terms of electrostatic interactions between a linear-scaling number of pre-computed transition densities. In a companion article, this formalism is applied to an excitonic variant of coupled-cluster theory.
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A variant of coupled-cluster theory is described here, wherein the degrees of freedom are fluctuations of fragments between internally correlated states. The effects of intra-fragment correlation on the inter-fragment interaction are pre-computed and permanently folded into an effective Hamiltonian, thus avoiding redundant evaluations of local relaxations associated with coupled fluctuations. A companion article shows that a low-scaling step may be used to cast the electronic Hamiltonians of real systems into the form required. Two proof-of-principle demonstrations are presented here for non-covalent interactions. One uses harmonic oscillators, for which accuracy and algorithm structure can be carefully controlled in comparisons. The other uses small electronic systems (Be atoms) to demonstrate compelling accuracy and efficiency, also when inter-fragment electron exchange and charge transfer must be handled. Since the cost of the global calculation does not depend directly on the correlation models used for the fragments, this should provide a way to incorporate difficult electronic structure problems into large systems. This framework opens a promising path for building tunable, systematically improvable methods to capture properties of systems interacting with a large number of other systems. The extension to excited states is also straightforward.
The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a given basis set. The derivation of the exact equations are based on the Levy-Lieb formulation of DFT, which helps us to define a complementary functional which corrects uniquely for the basis-set error of WFT. The coupling of DFT and WFT is done through the definition of a real-space representation of the electron-electron Coulomb operator projected in a one-particle basis set. Such an effective interaction has the particularity to coincide with the exact electron-electron interaction in the limit of a complete basis set, and to be finite at the electron-electron coalescence point when the basis set is incomplete. The non-diverging character of the effective interaction allows one to define a mapping with the long-range interaction used in the context of range-separated DFT and to design practical approximations for the unknown complementary functional. Here, a local-density approximation is proposed for both full-configuration-interaction (FCI) and selected configuration-interaction approaches. Our theory is numerically tested to compute total energies and ionization potentials for a series of atomic systems. The results clearly show that the DFT correction drastically improves the basis-set convergence of both the total energies and the energy differences. For instance, a sub kcal/mol accuracy is obtained from the aug-cc-pVTZ basis set with the method proposed here when an aug-cc-pV5Z basis set barely reaches such a level of accuracy at the near FCI level.
During compression of a water dimer calculated with high-precision first-principles methods, the trends of H-bond and O-H bond lengths show quantum effect of the electronic structure. We found that the H-bond length keeps decreasing, while the O-H bond length increases up to the stable point and decreases beyond it when the water dimer is further compressed. The remarkable properties are different from those observed in most previous researches which can be understood and extrapolated through classical simulation. The observations can be explained by the decrease in orbital overlap and change in the exchange repulsion interaction between water monomers. The dominant interaction between water monomers changes from electrostatic interaction to exchange repulsion at the turning point of the O-H bond length when the O...O distance is decreased. These findings highlight the quantum effect on the hydrogen bond in extreme conditions and play an important role in the recognition of the hydrogen bond structure and mechanism.
Hyperconjugation is a basic conception of chemistry. Its straightforward effect is exhibited by the spatial delocalization characteristics of the electron density distributions or wavefunctions. Such effects on the electron wavefunctions of the highest-occupied molecular orbitals (HOMO) of two ethanol conformers are demonstrated with electron momentum spectroscopy together with natural bond orbital analyses, exhibiting the distinctly different symmetries of the HOMO wavefunctions in momentum space.
We study excitonic states of an atomic impurity in a Fermi gas, i.e., bound states consisting of the impurity and a hole. Previous studies considered bound states of the impurity with particles from the Fermi sea where the holes only formed part of the particle-hole dressing. Within a two-channel model, we find that, for a wide range of parameters, excitonic states are not ground but metastable states. We further calculate the decay rates of the excitonic states to polaronic and dimeronic states and find they are long lived, scaling as $Gamma^{rm{Exc}}_ {rm{Pol}} propto ( Deltaomega)^{5.5}$ and $Gamma^{rm{Exc}}_ {rm{Dim}} propto (Deltaomega)^{4}$. We also find that a new continuum of exciton-particle states should be considered alongside the previously known dimeron-hole continuum in spectroscopic measurements. Excitons must therefore be considered as a new ingredient in the study of metastable physics currently being explored experimentally.
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