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Register a new userError propagation in the fully self-consistent stochastic second-order Greens function method
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We present an implementation of a fully self-consistent finite temperature second order Greens function perturbation theory (GF2) within the diagrammatic Monte Carlo framework. In contrast to the previous implementations of stochastic GF2 ({it J. Chem. Phys.},{bf 151}, 044144 (2019)), the current self-consistent stochastic GF2 does not introduce a systematic bias of the resulting electronic energies. Instead, the introduced implementation accounts for the stochastic errors appearing during the solution of the Dyson equation. We present an extensive discussion of the error handling necessary in a self-consistent procedure resulting in dressed Greens function lines. We test our method on a series of simple molecular examples.
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We extend the range-separated double-hybrid RSH+MP2 method [J. G. Angyan et al., Phys. Rev. A 72, 012510 (2005)], combining long-range HF exchange and MP2 correlation with a short-range density functional, to a fully self-consistent version using the optimized-effective-potential technique in which the orbitals are obtained from a local potential including the long-range HF and MP2 contributions. We test this approach, that we name RS-OEP2, on a set of small closed-shell atoms and molecules. For the commonly used value of the range-separation parameter $mu=0.5$ bohr$^{-1}$, we find that self-consistency does not seem to bring any improvement for total energies, ionization potentials, and electronic affinities. However, contrary to the non-self-consistent RSH+MP2 method, the present RS-OEP2 method gives a LUMO energy which physically corresponds to a neutral excitation energy and gives local exchange-correlation potentials which are reasonably good approximations to the corresponding Kohn-Sham quantities. At a finer scale, we find that RS-OEP2 gives largely inaccurate correlation potentials and correlated densities, which points to the need of further improvement of this type of range-separated double hybrids.
We present the fundamental techniques and working equations of many-body Greens function theory for calculating ground state properties and the spectral strength. Greens function methods closely relate to other polynomial scaling approaches discussed in chapters 8 and 10. However, here we aim directly at a global view of the many-fermion structure. We derive the working equations for calculating many-body propagators, using both the Algebraic Diagrammatic Construction technique and the self-consistent formalism at finite temperature. Their implementation is discussed, as well as the inclusion of three-nucleon interactions. The self-consistency feature is essential to guarantee thermodynamic consistency. The pairing and neutron matter models introduced in previous chapters are solved and compared with the other methods in this book.
We present a matrix-product state (MPS)-based quadratically convergent density-matrix renormalization group self-consistent-field (DMRG-SCF) approach. Following a proposal by Werner and Knowles (JCP 82, 5053, (1985)), our DMRG-SCF algorithm is based on a direct minimization of an energy expression which is correct to second-order with respect to changes in the molecular orbital basis. We exploit a simultaneous optimization of the MPS wave function and molecular orbitals in order to achieve quadratic convergence. In contrast to previously reported (augmented Hessian) Newton-Raphson and super-configuration-interaction algorithms for DMRG-SCF, energy convergence beyond a quadratic scaling is possible in our ansatz. Discarding the set of redundant active-active orbital rotations, the DMRG-SCF energy converges typically within two to four cycles of the self-consistent procedure
The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks complications to the application of the self-consistent method arise because of the bistable behavior due to the co-existence of a stable fixed point and a stable limit cycle, and the resulting complicated boundary between the corresponding basins of attraction. In this paper, we report on a self-consistent analysis of second-order oscillators which is simpler compared to previous approaches while giving more accurate results in the small inertia regime and close to incoherence. We apply the method to analyze the steady states of coupled second-order oscillators and we introduce the concepts of margin region and scaled inertia. The improved accuracy of the self-consistent method close to incoherence leads to an accurate estimate of the critical coupling corresponding to transitions from incoherence.
The method of increments (MoI) allows one to successfully calculate cohesive energies of bulk materials with high accuracy, but it encounters difficulties when calculating whole dissociation curves. The reason is that its standard formalism is based on a single Hartree-Fock (HF) configuration whose orbitals are localized and used for the many-body expansion. Therefore, in those situations where HF does not allow a size-consistent description of the dissociation, the MoI cannot yield proper results either. Herein we address the problem by employing a size-consistent multiconfigurational reference for the MoI formalism. This leads to a matrix equation where a coupling derived by the reference itself is employed. In principle, such approach allows one to evaluate approximate values for the ground as well as excited states energies. While the latter are accurate close to the avoided crossing only, the ground state results are very promising for the whole dissociation curve, as shown by the comparison with density matrix renormalization group (DMRG) benchmarks. We tested this two-state constant-coupling (TSCC)-MoI on beryllium rings of different sizes and studied the error introduced by the constant coupling.
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