skip to main content

Explore Research Products in the NSF-PAR

Title: Generalization of the tensor product selected CI method for molecular excited states
In a recent paper (JCTC, 16, 6098 (2020)), we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces, called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excitonic character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons (PAH) with respect to the extrapolated result (i.e. near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 biexcitonic states.  more » « less
Award ID(s):
1752612
NSF-PAR ID:
10406649
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
arXivorg
ISSN:
2331-8422
Page Range / eLocation ID:
arXiv:2303.02232
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ( , The Journal of Chemical Physics)

    We present the computational methodology that allows rigorous and efficient nine-dimensional (9D) quantum calculations of the intermolecular vibrational states of noncovalently bound trimers of diatomic molecules, with the monomers treated as rigid. The full 9D vibrational Hamiltonian of the trimer is partitioned into a 3D “frame” (or stretching) Hamiltonian and a 6D “bend” Hamiltonian. These two Hamiltonians are diagonalized separately, and a certain number of their lowest-energy eigenstates is included in the final 9D product contracted basis in which the full 9D intermolecular vibrational Hamiltonian is diagonalized. This methodology is applied to the 9D calculations of the intermolecular vibrational levels of (HF)3, a prototypical hydrogen-bonded trimer, on the rigid-monomer version of an ab initio calculated potential energy surface (PES). They are the first to include fully the stretch-bend coupling present in the trimer. The frequencies of all bending fundamentals considered from the present 9D calculations are about 10% lower than those from the earlier quantum 6D calculations that considered only the bending modes of the HF trimer. This means that the stretch-bend coupling is strong, and it is imperative to include it in any accurate treatment of the (HF)3 vibrations aiming to assess the accuracy of the PES employed. Moreover, the 9D results are in better agreement with the limited available spectroscopic data that those from the 6D calculations. In addition, the 9D results show sensitivity to the value of the HF bond length, equilibrium or vibrationally averaged, used in the calculations. The implication is that full-dimensional 12D quantum calculations will be required to obtain definitive vibrational excitation energies for a given PES. Our study also demonstrates that the nonadditive three-body interactions are very significant in (HF)3 and have to be included in order to obtain accurate intermolecular vibrational energy levels of the trimer.

     
    more » « less
  2. ; ( , Physical Chemistry Chemical Physics)
    The molecules 1,4-cyclohexadiene (unconjugated 1,4-CHD) and 1,3-cyclohexadiene (conjugated 1,3-CHD) both have two double bonds, but these bonds interact in different ways. These molecules have long served as examples of through-bond and through-space interactions, respectively, and their electronic structures have been studied in detail both experimentally and theoretically, with the experimental assignments being especially complete. The existence of Rydberg states interspersed with the valence states makes the quantum mechanical calculation of their spectra a challenging task. In this work, we explore the electronic excitation energies of 1,4-CHD and 1,3-CHD for both valence and Rydberg states by means of complete active space second-order perturbation theory (CASPT2), extended multi-state CASPT2 (XMS-CASPT2), and multiconfiguration pair-density functional theory (MC-PDFT); it is shown by comparison to experiment that MC-PDFT yields the most accurate results. We found that the inclusion of Rydberg orbitals in the active space not only enables the calculation of Rydberg excitation energies but also improves the accuracy of the valence ones. A special characteristic of the present analysis is the calculation of the second moments of the excited-state orbitals. Because we find that the CASPT2 densities agree well with the CASSCF ones and since the MC-PDFT methods gets accurate excitation energies based on the CASSCF densities, we believe that we can trust these moments as far as giving a more accurate picture of the diffuseness of the excited-state orbitals in these prototype molecules than has previously been available. 
    more » « less
  3. ; ; ( , The Journal of Chemical Physics)

    We report fully quantum mechanical simulations of excitation energy transfer within the peripheral light harvesting complex (LH2) of Rhodopseudomonas molischianum at room temperature. The exciton–vibration Hamiltonian comprises the 16 singly excited bacteriochlorophyll states of the B850 (inner) ring and the 8 states of the B800 (outer) ring with all available electronic couplings. The electronic states of each chromophore couple to 50 intramolecular vibrational modes with spectroscopically determined Huang–Rhys factors and to a weakly dissipative bath that models the biomolecular environment. Simulations of the excitation energy transfer following photoexcitation of various electronic eigenstates are performed using the numerically exact small matrix decomposition of the quasiadiabatic propagator path integral. We find that the energy relaxation process in the 24-state system is highly nontrivial. When the photoexcited state comprises primarily B800 pigments, a rapid intra-band redistribution of the energy sharply transitions to a significantly slower relaxation component that transfers 90% of the excitation energy to the B850 ring. The mixed character B850* state lacks the slow component and equilibrates very rapidly, providing an alternative energy transfer channel. This (and also another partially mixed) state has an anomalously large equilibrium population, suggesting a shift to lower energy by virtue of exciton–vibration coupling. The spread of the vibrationally dressed states is smaller than that of the eigenstates of the bare electronic Hamiltonian. The total population of the B800 band is found to decay exponentially with a 1/ e time of 0.5 ps, which is in good agreement with experimental results.

     
    more » « less
  4. ; ; ; ; ; ; ; ; ( , Quantum)
    Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware. 
    more » « less
  5. ; ; ; ; ; ( , ArXivorg)
    Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for representing a matrix from a set of selected rows and columns-is an efficient method for constructing a tensor train decomposition of a tensor from few of its entries. While tensor train cross approximation has achieved remarkable performance in practical applications, its theoretical analysis, in particular regarding the error of the approximation, is so far lacking. To our knowledge, existing results only provide element-wise approximation accuracy guarantees, which lead to a very loose bound when extended to the entire tensor. In this paper, we bridge this gap by providing accuracy guarantees in terms of the entire tensor for both exact and noisy measurements. Our results illustrate how the choice of selected subtensors affects the quality of the cross approximation and that the approximation error caused by model error and/or measurement error may not grow exponentially with the order of the tensor. These results are verified by numerical experiments, and may have important implications for the usefulness of cross approximations for high-order tensors, such as those encountered in the description of quantum many-body states. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email