Global elucidation of broken symmetry solutions to the independent particle model through a Lie algebraic approach

Thompson, Lee M.

doi:10.1063/1.5049827

Cited by 11 publications

(25 citation statements)

References 34 publications

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“…ese additional symmetry-broken solutions have been a) Electronic mail: hugh.burton@chem.ox.ac.uk b) Electronic mail: dw34@cam.ac.uk linked to the onset of strong electron correlation and provide reference states for methods such as projected Hartree-Fock (PHF), [22][23][24] or nonorthogonal con guration interaction (NOCI). 16 While numerous developments have focused on locating multiple SCF solutions, 8,12,13,[25][26][27][28] relatively li le is known about the topology of the HF energy surface itself. e stability analysis popularised by Čížek and Paldus 29,30 allows a particular solution to be identi ed as a minimum, saddle point, or maximum, and allows downhill directions to be identi ed to characterise pathways.…”

Section: Introductionmentioning

confidence: 99%

“…Notable exceptions include the use of power series expansions of the HF energy, 26 the SCF metadynamics approach, 25 and linearisation of the SCF equations through Lie algebraic approaches. 27 In contrast, elucidating the topology of the SCF energy landscape itself promises a route towards more systematic approaches for locating multiple solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Results are then described for the H 4 model, which has proved to be a popular benchmark for investigating the existence of multiple HF solutions. 25,27,28 In particular, we investigate the e ect of symmetry on the pathways connecting minima, and compare the electronic structure landscape for di erent geometries, basis sets, SCF potentials, and spin states.…”

Section: Introductionmentioning

confidence: 99%

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Energy Landscapes for Electronic Structure

Burton

Wales

2020

J. Chem. Theory Comput.

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Orbital-optimised multiple self-consistent-eld (SCF) solutions are increasingly being interpreted as mean-eld approximations of diabatic or excited electronic states. However, surprisingly li le is known about the topology of the electronic energy landscape from which these multiple solutions emerge. In this contribution, we extend energy landscape methods, developed for investigating molecular potential energy surfaces, to investigate and understand the structure of the electronic SCF energy surface. Using analytic gradients and Hessians, we systematically identify every real SCF minimum for the prototypical H 4 molecule with the 3-21G basis set, and the index-1 saddles that connect these minima. e resulting SCF energy landscape has a double-funnel structure, with no high-energy local minima. e e ect of molecular symmetry on the pathways is analysed, and we demonstrate how the SCF energy landscape changes with the basis set, SCF potential, molecular structure, and spin state. ese results provide guiding principles for the future development of algorithms to systematically identify multiple SCF solutions from an orbital optimisation perspective.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Energy Landscapes for Electronic Structure

Burton

Wales

2020

J. Chem. Theory Comput.

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“…Recently, there has been a renewed interest in singlereference methods for excited states in the context of Hartree-Fock, density-functional, and coupled-cluster theories. [102][103][104][105][106][107][108][109][110][111][112][113][114][115][116][117][118][119][120][121]125,142,168 This has been made possible thanks to the development of new algorithms specifically designed to target higher-energy solutions of these non-linear equations. These so-called non-standard solutions provide genuine alternatives to the usual linear response and equation-of-motion formalisms (which are naturally biased towards the reference ground state) for the determination of accurate excited-state energies in molecular systems.…”

Section: Discussionmentioning

confidence: 99%

“…101,102 Lee et al refers to this type of methods as ∆CC 102 by analogy with the ∆SCF methods where one basically follows the same procedure but at the self-consistent field (SCF) level. Indeed, the use of Hartree-Fock (HF) or Kohn-Sham higher-energy solutions corresponding to excited states is becoming more and more popular and new algorithms designed to target such solutions, like the maximum overlap method (MOM) [103][104][105][106] or more involved variants, [107][108][109][110][111][112][113][114][115][116][117][118][119][120][121] are being actively developed. Besides providing a qualitatively good description of excited states, 121 these solutions can also be very helpful for ∆CC methods, as we shall illustrate below (see also Ref.…”

Section: A Tcc For Excited Statesmentioning

confidence: 99%

Variational coupled cluster for ground and excited states

Marie,

Kossoski,

Loos

2021

Preprint

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In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes which are then used to compute the energy and other properties. Although it is of common practice to converge to the (lowest-energy) ground-state solution, it is also possible, thanks to tailored algorithms, to access higher-energy roots of these equations which may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC (VCC) and we compare it with its (projected) traditional version (TCC) in the case where the excitation operator is restricted to paired double excitations (pCCD). By investigating two model systems (the symmetric stretching of the linear H 4 molecule and the continuous deformation of the square H 4 molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of VpCCD and TpCCD are gauged against their configuration interaction (CI) equivalent, known as doubly-occupied CI (DOCI), for reference Slater determinants made of ground-or excited-state Hartree-Fock orbitals or state-specific orbitals optimized directly at the VpCCD level. The influence of spatial symmetry breaking is also investigated. I. COUPLED CLUSTER AND STRONG CORRELATIONSingle-reference (SR) coupled-cluster (CC) methods offers a reliable description of weakly correlated systems through a well-defined hierarchy of systematically improvable models. [1][2][3][4][5] On top of this hierarchy stands full CC (FCC), which is equivalent to full configuration interaction (FCI), and consequently provides, at a very expensive computational cost, the exact wave function and energy of the system in a given basis set. Fortunately, more affordable methods have been designed and the popular CCSD(T) method, which includes singles, doubles and non-iterative triples, is nowadays considered as the gold standard of quantum chemistry for ground-state energies and properties. 6,7 Despite its success for weakly correlated systems, it is now widely known that CCSD(T) flagrantly breaks down in the presence of strong correlation as one cannot efficiently describe such systems with a single (reference) Slater determinant. This has motivated quantum chemists to design multi-reference CC (MRCC) methods. [8][9][10][11][12] However, it is fair to say that these methods are computationally demanding and still far from being black-box.Because SRCC works so well for weak correlation, it would be convenient to be able to treat strong correlation within the very same framework. This is further motivated by the fact that one can compensate the poor quality of the reference wave function by simply increasing the maximum excitation degree of the CC expansion. However, this is inevitably associated with a rapid growth of the computational cost, and hence one cannot always afford this brute-force strategy. The development of SR-based methods for strong correlation is ongoing and some of them (usually based on the...

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Global Elucidation of Self-Consistent Field Solution Space Using Basin Hopping

Dong

Mahler

Kempfer-Robertson

et al. 2020

J. Chem. Theory Comput.

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Reliable global elucidation of (subsets of) self-consistent field solutions is required for continued development and application of computational approaches that utilize these solutions as reference wavefunctions. We report the derivation and implementation of a stochastic approach to perform global elucidation of self-consistent field solutions by exploiting the connection between global optimization and global elucidation problems. We discuss the design of the algorithm through combining basin-hopping search algorithms with a Lie algebraic approach to linearize self-consistent field solution space, while also allowing preservation of desired spin-symmetry properties of the wavefunction. The performance of the algorithm is demonstrated on minimal basis C 2v H4 due to its use as a model system for global self-consistent field solution exploration algorithms. Subsequently, we show that the model is capable of successfully identifying low-lying self-consistent solutions of benzene and NO2 with polarized double-zeta and triple-zeta basis sets and examine the properties of these solutions.

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Global elucidation of broken symmetry solutions to the independent particle model through a Lie algebraic approach

Cited by 11 publications

References 34 publications

Energy Landscapes for Electronic Structure

Energy Landscapes for Electronic Structure

Variational coupled cluster for ground and excited states

Global Elucidation of Self-Consistent Field Solution Space Using Basin Hopping

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