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Register a new userAn Anderson Impurity Model for Efficient Sampling of Adiabatic Potential Energy Surfaces of Transition Metal Complexes
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We present a model intended for rapid sampling of ground and excited state potential energy surfaces for first-row transition metal active sites. The method is computationally inexpensive and is suited for dynamics simulations where (1) adiabatic states are required on-the-fly and (2) the primary source of the electronic coupling between the diabatic states is the perturbative spin-orbit interaction among the 3d electrons. The model Hamiltonian we develop is a variant of the Anderson impurity model and achieves efficiency through a physically motivated basis set reduction based on the large value of the d-d Coulomb interaction U_{d} and a Lanczos matrix diagonalization routine to solve for eigenvalues. The model parameters are constrained by fits to the partial density of states (PDOS) obtained from ab initio density functional theory calculations. For a particular application of our model we focus on electron-transfer occuring between cobalt ions solvated by ammonium, incorporating configuration interaction between multiplet states for both metal ions. We demonstrate the capability of the method to efficiently calculate adiabatic potential energy surfaces and the electronic coupling factor we have calculated compares well to previous calculations and experiment.
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The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior is evaluated for a model function in 2, 3 and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.
Machine Learning techniques can be used to represent high-dimensional potential energy surfaces for reactive chemical systems. Two such methods are based on a reproducing kernel Hilbert space representation or on deep neural networks. They can achieve a sub-1 kcal/mol accuracy with respect to reference data and can be used in studies of chemical dynamics. Their construction and a few typical examples are briefly summarized in the present contribution.
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods discussed. They include empirical force fields, representations based on reproducing kernels, using permutationally invariant polynomials, and neural network-learned representations and combinations thereof. Future directions and potential improvements are discussed primarily from a practical, application-oriented perspective.
We study the zero-bandwidth limit of the two-impurity Anderson model in an antiferromagnetic (AF) metal. We calculate, for different values of the model parameters, the lowest excitation energy, the magnetic correlation $<mathbf{S}_{1}mathbf{S}_{2}>$ between the impurities, and the magnetic moment at each impurity site, as a function of the distance between the impurities and the temperature. At zero temperature, in the region of parameters corresponding to the Kondo regime of the impurities, we observe an interesting competition between the AF gap and the Kondo physics of the two impurities. When the impurities are close enough, the AF splitting governs the physics of the system and the local moments of the impurities are frozen, in a state with very strong ferromagnetic correlation between the impurities and roughly independent of the distance. On the contrary, when the impurities are sufficiently far apart and the AF gap is not too large, the scenario of the Kondo physics take place: non-magnetic ground state and the possibility of spin-flip excitation emerges and the ferromagnetic $<mathbf{S}_{1}mathbf{S}_{2}>$ decreases as the distance increases, but the complete decoupling of the impurities never occurs. In adition, the presence of the AF gap gives a non-zero magnetic moment at each impurity site, showing a non complete Kondo screening of the impurities in the system. We observe that the residual magnetic moment decreases when the distance between the impurities is increased.
The density matrix renormalization group method is applied to obtain the ground state phase diagram of the single impurity Anderson model on the honeycomb lattice at half filling. The calculation of local static quantities shows that the phase diagram contains two distinct phases, the local moment (LM) phase and the asymmetric strong coupling (ASC) phase. These results are supported by the local spin and charge excitation spectra, which exhibit qualitatively different behavior in these two phases and also reveal the existence of the valence fluctuating point at the phase boundary. For comparison, we also study the low-energy effective pseudogap Anderson model. Although the high-energy excitations are obviously different, we find that the ground state phase diagram and the asymptotically low-energy excitations are in good quantitative agreement with those for the single impurity Anderson model on the honeycomb lattice, thus providing the first quantitative justification for the previous studies based on low-energy approximate approaches. Furthermore, we find that the lowest entanglement level is doubly degenerate for the LM phase, whereas it is singlet for the ASC phase and is accidentally three fold degenerate at the valence fluctuating point. Our results therefore clearly demonstrate that the low-lying entanglement spectrum can be used to determine with high accuracy the phase boundary of the impurity quantum phase transition.
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