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Physical Review A

Quantum states for quantum processes: A toy model for ammonia inversion spectra

Gustavo A. Arteca, O. Tapia

Published Jul 25, 2011• 2 citations
Publisher

Abstract

Chemical transformations are viewed here as quantum processes modulated by external fields, that is, as shifts in reactant to product amplitudes within a quantum state represented by a linear (coherent) superposition of electronuclear basis functions; their electronic quantum numbers identify the ``chemical species.'' This basis set can be mapped from attractors built from a unique electronic configurational space that is invariant with respect to the nuclear geometry. In turn, the quantum numbers that label these basis functions and the semiclassical potentials for the electronic attractors may be used to derive reaction coordinates to monitor progress as a function of the applied field. A generalization of Feynman's three-state model for the ammonia inversion process illustrates the scheme; to enforce symmetry for the entire inversion process model and ensure invariance with respect to nuclear configurations, the three attractors and their basis functions are computed with a grid of fixed floating Gaussian functions. The external-field modulation of the effective inversion barrier is discussed within this conceptual approach. This analysis brings the descriptions of chemical processes near modern technologies that employ molecules to encode information by means of confinement and external fields.

DOI
10.1103/physreva.84.012115

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Chemical transformations are viewed here as quantum processes modulated by external fields, that is, as shifts in reactant to product amplitudes within a quantum state represented by a linear (coherent) superposition of electronuclear basis functions; their electronic quantum numbers identify the ``chemical species.'' This basis set can be mapped from attractors built from a unique electronic configurational space that is invariant with respect to the nuclear geometry. In turn, the quantum numbers that label these basis functions and the semiclassical potentials for the electronic attractors may be used to derive reaction coordinates to monitor progress as a function of the applied field. A generalization of Feynman's three-state model for the ammonia inversion process illustrates the scheme; to enforce symmetry for the entire inversion process model and ensure invariance with respect to nuclear configurations, the three attractors and their basis functions are computed with a grid of fixed floating Gaussian functions. The external-field modulation of the effective inversion barrier is discussed within this conceptual approach. This analysis brings the descriptions of chemical processes near modern technologies that employ molecules to encode information by means of confinement and external fields.
Accurate simulation of dynamic processes in molecules and reactions is among the most challenging problems in quantum chemistry. Quantum computers promise efficient chemical simulation, but the existing quantum algorithms require many logical qubits and gates, placing practical applications beyond existing technology. Here, we carry out the first quantum simulations of chemical dynamics by employing a more hardware-efficient encoding scheme that uses both qubits and bosonic degrees of freedom. Our trapped-ion device accurately simulates the dynamics of nonadiabatic chemical processes, which are among the most difficult problems in computational chemistry because they involve strong coupling between electronic and nuclear motions. We demonstrate the programmability and versatility of our approach by simulating the dynamics of three different molecules, as well as open-system dynamics in the condensed phase, all with the same quantum resources. Our approach requires orders of magnitude fewer resources than equivalent qubit-only quantum simulations, demonstrating the potential of using hybrid encoding schemes to accelerate quantum simulations of complex chemical processes, which could have applications in fields ranging from energy conversion and storage to biology and drug design.
Quantum computation for chemical problems will require the construction of guiding states with sufficient overlap with a target state. Since easily available and initializable mean-field states are characterized by an overlap that is reduced for multi-configurational electronic structures and even vanishes with growing system size, we here investigate the severity of state preparation for reaction chemistry. We emphasize weaknesses in current traditional approaches (even for weakly correlated molecules) and highlight the advantage of quantum phase estimation algorithms. An important result is the introduction of a new classification scheme for electronic structures based on orbital entanglement information. We identify two categories of multi-configurational molecules. Whereas class-1 molecules are dominated by very few determinants and often found in reaction chemistry, class-2 molecules do not allow one to single out a reasonably sized number of important determinants. The latter are particularly hard for traditional approaches and an ultimate target for quantum computation. Some open-shell iron-sulfur clusters belong to class 2. We discuss the role of the molecular orbital basis set and show that true class-2 molecules remain in this class independent of the choice of the orbital basis, with the iron-molybdenum cofactor of nitrogenase being a prototypical example. We stress that class-2 molecules can be build in a systematic fashion from open-shell centers or unsaturated carbon atoms. Our key result is that it will always be possible to initialize a guiding state for chemical reaction chemistry in the ground state based on initial low-cost approximate electronic structure information, which is facilitated by the finite size of the atomistic structures to be considered.
The application of modern quantum chemical methods to the simulation of chemical reactions makes it obvious that the Copenhagen picture of quantum mechanics cannot be maintained. In ab-initio molecular dynamics methods, any kind of matter is described by applying the Schrödinger equation to the electronic structure and using classical Newton dynamics for the motion of the atomic nuclei. By lots of calculations on this basis, it has become obvious that this concept is superior to a quantum chemical description of nuclear motion. The nuclei move according to Newton's laws in a perfectly local and deterministic way while the surrounding electronic cloud determines bonding and antibonding interactions between the atoms. The resulting theory is a deterministic formulation of quantum mechanics which is free from paradoxa and is able to explain complex phenomena like photochemistry. An obvious consequence is that molecules like ammonia can have a permanent dipole moment in spectroscopic measurements, while consistent application of traditional quantum mechanics predicts a higher symmetry as is outlined in the paper.
The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schrodinger equation. In many cases the Hamiltonian obtained is that of an integrable quantum chain with known properties. Within this approach we search for three-state integrable quantum chains with known spectra and which are related to diffusive-reactive systems. Two integrable models are found to appear naturally in this context: the U q SU(2)-invariant model with external fields and the three-state U q SU(P/M)-invariant Perk-Schultz models with external fields. A non-local similarity transformation which brings the Hamiltonian governing the chemical processes to the known standard forms is described, leading in the case of periodic boundary conditions to a generalization of the Dzialoshinsky-Moriya interaction for N-state Hamiltonians (N>2).
The mechanism of the shift, broadening, and quenching of the ammonia inversion frequency with gas pressure has been a problem of lively interest for over 70years70\phantom{\rule{0.3em}{0ex}}\text{years}70years. A simple quantum model of the ammonia molecule perturbed by collisions with ideal gas molecules displays the essential features of the experimental data for NH3\mathrm{N}{\mathrm{H}}_{3}NH3​ and for ND3\mathrm{N}{\mathrm{D}}_{3}ND3​. The model does not display the behavior expected from theories of environmental decoherence. On the other hand, models of perturbed classical oscillators do display behavior similar to our model and to experimental data. The quenching of the ammonia inversion transition cannot therefore be interpreted as spatial localization of the wave function.