94 research outputs found
Quantum Computing for Molecular Biology
Molecular biology and biochemistry interpret microscopic processes in the
living world in terms of molecular structures and their interactions, which are
quantum mechanical by their very nature. Whereas the theoretical foundations of
these interactions are very well established, the computational solution of the
relevant quantum mechanical equations is very hard. However, much of molecular
function in biology can be understood in terms of classical mechanics, where
the interactions of electrons and nuclei have been mapped onto effective
classical surrogate potentials that model the interaction of atoms or even
larger entities. The simple mathematical structure of these potentials offers
huge computational advantages; however, this comes at the cost that all quantum
correlations and the rigorous many-particle nature of the interactions are
omitted. In this work, we discuss how quantum computation may advance the
practical usefulness of the quantum foundations of molecular biology by
offering computational advantages for simulations of biomolecules. We not only
discuss typical quantum mechanical problems of the electronic structure of
biomolecules in this context, but also consider the dominating classical
problems (such as protein folding and drug design) as well as data-driven
approaches of bioinformatics and the degree to which they might become amenable
to quantum simulation and quantum computation.Comment: 76 pages, 7 figure
Flexible DMRG-based framework for anharmonic vibrational calculations
We present a novel formulation of the vibrational density matrix
renormalization group (vDMRG) algorithm tailored to strongly anharmonic
molecules described by general high-dimensional model representations of
potential energy surfaces. For this purpose, we extend the vDMRG framework to
support vibrational Hamiltonians expressed in the so-called -mode
second-quantization formalism. The resulting -mode vDMRG method offers full
flexibility with respect to both the functional form of the PES and the choice
of single-particle basis set. We leverage this framework to apply, for the
first time, vDMRG based on an anharmonic modal basis set optimized with the
vibrational self-consistent field algorithm on an on-the-fly constructed PES.
We also extend the -mode vDMRG framework to include excited-state targeting
algorithms in order to efficiently calculate anharmonic transition frequencies.
We demonstrate the capabilities of our novel -mode vDMRG framework for
methyloxirane, a challenging molecule with 24 coupled vibrational modes.Comment: 46 pages, 6 figures, 2 table
Symmetry-Projected Nuclear-Electronic Hartree-Fock: Eliminating Rotational Energy Contamination
We present a symmetry projection technique for enforcing rotational and
parity symmetries in nuclear-electronic Hartree-Fock wave functions, which
treat electrons and nuclei on equal footing. The molecular Hamiltonian obeys
rotational and parity-inversion symmetries, which are, however, broken by
expanding in Gaussian basis sets that are fixed in space. We generate a trial
wave function with the correct symmetry properties by projecting the wave
function onto representations of the three-dimensional rotation group, i.e.,
the special orthogonal group in three dimensions SO(3). As a consequence, the
wave function becomes an eigenfunction of the angular momentum operator which
(i) eliminates the contamination of the ground state wave function by highly
excited rotational states arising from the broken rotational symmetry, and (ii)
enables the targeting of specific rotational states of the molecule. We
demonstrate the efficiency of the symmetry projection technique by calculating
energies of the low-lying rotational states of the H and H molecules.Comment: 37 pages, 3 table
Simulation Of Accurate Vibrationally Resolved Electronic Spectra: The Integrated Time-dependent And Time-independent Framework
Two parallel theories including Franck–Condon, Herzberg–Teller and Duschinsky (i.e., mode mixing) effects, allowing different approximations for the description of excited state PES have been developed in order to simulate realistic, asymmetric, electronic spectra line-shapes taking into account the vibrational structure: the so-called sum-over-states or time-independent (TI) method and the alternative time-dependent (TD) approach, which exploits the properties of the Fourier transform.
The integrated TI-TD procedure included within a general purpose QM code [1,2], allows to compute one photon absorption, fluorescence, phosphorescence, electronic circular dichroism, circularly polarized luminescence and resonance Raman spectra. Combining both approaches, which use a single set of starting data, permits to profit from their respective advantages and minimize their respective limits: the time-dependent route automatically includes all vibrational states and, possibly, temperature effects, while the time-independent route allows to identify and assign single vibronic transitions. Interpretation, analysis and assignment of experimental spectra based on integrated TI-TD vibronic computations will be illustrated for challenging cases of medium-sized open-shell systems in the gas and condensed phases with inclusion of leading anharmonic effects.
1. V. Barone, A. Baiardi, M. Biczysko, J. Bloino, C. Cappelli, F. Lipparini Phys. Chem. Chem. Phys, 14, 12404, (2012)
2. A. Baiardi, V. Barone, J. Bloino J. Chem. Theory Comput., 9, 4097–4115 (2013
Tensor Network States for Vibrational Spectroscopy
This review elaborates on the foundation, the advantages, and the prospects
of tensor network representations for quantum states in vibrational
spectroscopy. The focus is on the recently introduced matrix product state
decomposition of nuclear quantum states and its optimization by the density
matrix renormalization group algorithm.Comment: 65 pages, 20 figure
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