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Alcazar J, Ghazi Vakili M, Kalayci CB, Perdomo-Ortiz A. Enhancing combinatorial optimization with classical and quantum generative models. Nat Commun 2024; 15:2761. [PMID: 38553469 PMCID: PMC10980691 DOI: 10.1038/s41467-024-46959-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2021] [Accepted: 03/15/2024] [Indexed: 04/02/2024] Open
Abstract
Devising an efficient exploration of the search space is one of the key challenges in the design of combinatorial optimization algorithms. Here, we introduce the Generator-Enhanced Optimization (GEO) strategy: a framework that leverages any generative model (classical, quantum, or quantum-inspired) to solve optimization problems. We focus on a quantum-inspired version of GEO relying on tensor-network Born machines, and referred to hereafter as TN-GEO. To illustrate our results, we run these benchmarks in the context of the canonical cardinality-constrained portfolio optimization problem by constructing instances from the S&P 500 and several other financial stock indexes, and demonstrate how the generalization capabilities of these quantum-inspired generative models can provide real value in the context of an industrial application. We also comprehensively compare state-of-the-art algorithms and show that TN-GEO is among the best; a remarkable outcome given the solvers used in the comparison have been fine-tuned for decades in this real-world industrial application. Also, a promising step toward a practical advantage with quantum-inspired models and, subsequently, with quantum generative models.
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Affiliation(s)
- Javier Alcazar
- Zapata Computing Canada Inc., 25 Adelaide St E, Suite 1500, Toronto, ON, M5C 3A1, Canada
- Acadian Asset Management LLC, 24 King William St, London, EC4R 9AT, England
| | - Mohammad Ghazi Vakili
- Zapata Computing Canada Inc., 25 Adelaide St E, Suite 1500, Toronto, ON, M5C 3A1, Canada
- Department of Chemistry, University of Toronto, Toronto, ON, M5G 1Z8, Canada
- Department of Computer Science, University of Toronto, Toronto, ON, M5S 2E4, Canada
| | - Can B Kalayci
- Zapata Computing Canada Inc., 25 Adelaide St E, Suite 1500, Toronto, ON, M5C 3A1, Canada
- Department of Industrial Engineering, Pamukkale University, Kinikli Campus, 20160, Denizli, Turkey
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Rudolph MS, Miller J, Motlagh D, Chen J, Acharya A, Perdomo-Ortiz A. Synergistic pretraining of parametrized quantum circuits via tensor networks. Nat Commun 2023; 14:8367. [PMID: 38102108 PMCID: PMC10724286 DOI: 10.1038/s41467-023-43908-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 11/23/2023] [Indexed: 12/17/2023] Open
Abstract
Parametrized quantum circuits (PQCs) represent a promising framework for using present-day quantum hardware to solve diverse problems in materials science, quantum chemistry, and machine learning. We introduce a "synergistic" approach that addresses two prominent issues with these models: the prevalence of barren plateaus in PQC optimization landscapes, and the difficulty to outperform state-of-the-art classical algorithms. This framework first uses classical resources to compute a tensor network encoding a high-quality solution, and then converts this classical output into a PQC which can be further improved using quantum resources. We provide numerical evidence that this framework effectively mitigates barren plateaus in systems of up to 100 qubits using only moderate classical resources, with overall performance improving as more classical or quantum resources are employed. We believe our results highlight that classical simulation methods are not an obstacle to overcome in demonstrating practically useful quantum advantage, but rather can help quantum methods find their way.
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Affiliation(s)
- Manuel S Rudolph
- Zapata Computing Canada Inc., 325 Front St W, Toronto, ON, M5V 2Y1, Canada
| | - Jacob Miller
- Zapata Computing Inc., 100 Federal Street, Boston, MA, 02110, USA
| | - Danial Motlagh
- Zapata Computing Canada Inc., 325 Front St W, Toronto, ON, M5V 2Y1, Canada
| | - Jing Chen
- Zapata Computing Inc., 100 Federal Street, Boston, MA, 02110, USA
| | - Atithi Acharya
- Zapata Computing Inc., 100 Federal Street, Boston, MA, 02110, USA
- Rutgers University, 136 Frelinghuysen Rd, Piscataway, NJ, 08854, USA
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Iouchtchenko D, Gonthier JF, Perdomo-Ortiz A, Melko RG. Neural network enhanced measurement efficiency for molecular groundstates. Mach Learn : Sci Technol 2023. [DOI: 10.1088/2632-2153/acb4df] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023] Open
Abstract
Abstract
It is believed that one of the first useful applications for a quantum computer will be the preparation of groundstates of molecular Hamiltonians. A crucial task involving state preparation and readout is obtaining physical observables of such states, which are typically estimated using projective measurements on the qubits. At present, measurement data is costly and time-consuming to obtain on any quantum computing architecture, which has significant consequences for the statistical errors of estimators. In this paper, we adapt common neural network models (restricted Boltzmann machines and recurrent neural networks) to learn complex groundstate wavefunctions for several prototypical molecular qubit Hamiltonians from typical measurement data. By relating the accuracy ɛ of the reconstructed groundstate energy to the number of measurements, we find that using a neural network model provides a robust improvement over using single-copy measurement outcomes alone to reconstruct observables. This enhancement yields an asymptotic scaling near ɛ
−1 for the model-based approaches, as opposed to ɛ
−2 in the case of classical shadow tomography.
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Alcazar J, Leyton-Ortega V, Perdomo-Ortiz A. Classical versus quantum models in machine learning: insights from a finance application. Mach Learn : Sci Technol 2020. [DOI: 10.1088/2632-2153/ab9009] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
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Zhu D, Linke NM, Benedetti M, Landsman KA, Nguyen NH, Alderete CH, Perdomo-Ortiz A, Korda N, Garfoot A, Brecque C, Egan L, Perdomo O, Monroe C. Training of quantum circuits on a hybrid quantum computer. Sci Adv 2019; 5:eaaw9918. [PMID: 31667342 PMCID: PMC6799983 DOI: 10.1126/sciadv.aaw9918] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2019] [Accepted: 09/26/2019] [Indexed: 05/28/2023]
Abstract
Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. Here, we implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes dataset using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes.
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Affiliation(s)
- D. Zhu
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - N. M. Linke
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - M. Benedetti
- Department of Computer Science, University College London, WC1E 6BT London, UK
- Cambridge Quantum Computing Limited, CB2 1UB Cambridge, UK
| | - K. A. Landsman
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - N. H. Nguyen
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - C. H. Alderete
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - A. Perdomo-Ortiz
- Department of Computer Science, University College London, WC1E 6BT London, UK
- Zapata Computing Inc., 439 University Avenue, Office 535, Toronto, ON, M5G 1Y8, Canada
| | - N. Korda
- Mind Foundry Limited, OX2 7DD Oxford, UK
| | - A. Garfoot
- Mind Foundry Limited, OX2 7DD Oxford, UK
| | - C. Brecque
- Mind Foundry Limited, OX2 7DD Oxford, UK
| | - L. Egan
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
| | - O. Perdomo
- Department of Mathematics, Central Connecticut State University, New Britain, CT 06050, USA
| | - C. Monroe
- Joint Quantum Institute, Department of Physics, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA
- IonQ Inc., College Park, MD 20740, USA
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Smelyanskiy VN, Venturelli D, Perdomo-Ortiz A, Knysh S, Dykman MI. Quantum Annealing via Environment-Mediated Quantum Diffusion. Phys Rev Lett 2017; 118:066802. [PMID: 28234537 DOI: 10.1103/physrevlett.118.066802] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2016] [Indexed: 06/06/2023]
Abstract
We show that quantum diffusion near a quantum critical point can provide an efficient mechanism of quantum annealing. It is based on the diffusion-mediated recombination of excitations in open systems far from thermal equilibrium. We find that, for an Ising spin chain coupled to a bosonic bath and driven by a monotonically decreasing transverse field, excitation diffusion sharply slows down below the quantum critical region. This leads to spatial correlations and effective freezing of the excitation density. Still, obtaining an approximate solution of an optimization problem via the diffusion-mediated quantum annealing can be faster than via closed-system quantum annealing or Glauber dynamics.
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Affiliation(s)
| | - Davide Venturelli
- USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, California 94043, USA
- NASA Ames Research Center, Mail Stop 269-1, Moffett Field, California 94035-1000, USA
| | - Alejandro Perdomo-Ortiz
- USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, California 94043, USA
- NASA Ames Research Center, Mail Stop 269-1, Moffett Field, California 94035-1000, USA
| | - Sergey Knysh
- NASA Ames Research Center, Mail Stop 269-1, Moffett Field, California 94035-1000, USA
- Stinger Ghaffarian Technologies Inc., 7701 Greenbelt Road, Suite 400, Greenbelt, Maryland 20770, USA
| | - Mark I Dykman
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-2320, USA
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Babbush R, Perdomo-Ortiz A, O'Gorman B, Macready W, Aspuru-Guzik A. Construction of Energy Functions for Lattice Heteropolymer Models: Efficient Encodings for Constraint Satisfaction Programming and Quantum Annealing. ADVANCES IN CHEMICAL PHYSICS 2014. [DOI: 10.1002/9781118755815.ch05] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/05/2023]
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Widom JR, Lee W, Perdomo-Ortiz A, Rappoport D, Molinski TF, Aspuru-Guzik A, Marcus AH. Temperature-dependent conformations of a membrane supported zinc porphyrin tweezer by 2D fluorescence spectroscopy. J Phys Chem A 2013; 117:6171-84. [PMID: 23480874 PMCID: PMC3723700 DOI: 10.1021/jp400394z] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We studied the equilibrium conformations of a zinc porphyrin tweezer composed of two carboxylphenyl-functionalized zinc tetraphenyl porphyrin subunits connected by a 1,4-butyndiol spacer, which was suspended inside the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) liposomes. By combining phase-modulation two-dimensional fluorescence spectroscopy (2D FS) with linear absorbance and fluorimetry, we determined that the zinc porphyrin tweezer adopts a mixture of folded and extended conformations in the membrane. By fitting an exciton-coupling model to a series of data sets recorded over a range of temperatures (17-85 °C) and at different laser center wavelengths, we determined that the folded form of the tweezer is stabilized by a favorable change in the entropy of the local membrane environment. Our results provide insights toward understanding the balance of thermodynamic factors that govern molecular assembly in membranes.
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Affiliation(s)
- Julia R. Widom
- Department of Chemistry, Oregon Center for Optics, Institute of Molecular Biology, University of Oregon, Eugene, OR 97403
| | - Wonbae Lee
- Department of Chemistry, Oregon Center for Optics, Institute of Molecular Biology, University of Oregon, Eugene, OR 97403
| | | | - Dmitrij Rappoport
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138
| | - Tadeusz F. Molinski
- Department of Chemistry and Biochemistry, and The Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California, San Diego, La Jolla, California, 92093
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138
| | - Andrew H. Marcus
- Department of Chemistry, Oregon Center for Optics, Institute of Molecular Biology, University of Oregon, Eugene, OR 97403
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Widom JR, Perdomo-Ortiz A, Lee W, Johnson NP, Hippel PHV, Aspuru-Guzik A, Marcus AH. Determining the Conformations of Porphyrin Dimers and Dinucleotide-Substituted DNA Constructs by 2-Dimensional Fluorescence Spectroscopy. Biophys J 2013. [DOI: 10.1016/j.bpj.2012.11.2361] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022] Open
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10
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Widom JR, Rappoport D, Perdomo-Ortiz A, Thomsen H, Johnson NP, von Hippel PH, Aspuru-Guzik A, Marcus AH. Electronic transition moments of 6-methyl isoxanthopterin--a fluorescent analogue of the nucleic acid base guanine. Nucleic Acids Res 2012. [PMID: 23185042 PMCID: PMC3553960 DOI: 10.1093/nar/gks1148] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022] Open
Abstract
Fluorescent nucleic acid base analogues are important spectroscopic tools for understanding local structure and dynamics of DNA and RNA. We studied the orientations and magnitudes of the electric dipole transition moments (EDTMs) of 6-methyl isoxanthopterin (6-MI), a fluorescent analogue of guanine that has been particularly useful in biological studies. Using a combination of absorption spectroscopy, linear dichroism (LD) and quantum chemical calculations, we identified six electronic transitions that occur within the 25 000–50 000 cm−1 spectral range. Our results indicate that the two experimentally observed lowest-energy transitions, which occur at 29 687 cm−1 (337 nm) and 34 596 cm−1 (289 nm), are each polarized within the plane of the 6-MI base. A third in-plane polarized transition is experimentally observed at 47 547 cm−1 (210 nm). The theoretically predicted orientation of the lowest-energy transition moment agrees well with experiment. Based on these results, we constructed an exciton model to describe the absorption spectra of a 6-MI dinucleotide–substituted double-stranded DNA construct. This model is in good agreement with the experimental data. The orientations and intensities of the low-energy electronic transitions of 6-MI reported here should be useful for studying local conformations of DNA and RNA in biologically important complexes.
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Affiliation(s)
- Julia R Widom
- Oregon Center for Optics, Department of Chemistry, Institute of Molecular Biology, University of Oregon, Eugene, OR 97403, USA
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11
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Perdomo-Ortiz A, Widom JR, Lott GA, Aspuru-Guzik A, Marcus AH. Conformation and electronic population transfer in membrane-supported self-assembled porphyrin dimers by 2D fluorescence spectroscopy. J Phys Chem B 2012; 116:10757-70. [PMID: 22882118 DOI: 10.1021/jp305916x] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Two-dimensional fluorescence spectroscopy (2D FS) is applied to determine the conformation and femtosecond electronic population transfer in a dimer of magnesium meso tetraphenylporphyrin. The dimers are prepared by self-assembly of the monomer within the amphiphilic regions of 1,2-distearoyl-sn-glycero-3-phosphocholine liposomes. A theoretical framework to describe 2D FS experiments is presented, and a direct comparison is made between the observables of this measurement and those of 2D electronic spectroscopy (2D ES). The sensitivity of the method to varying dimer conformation is explored. A global multivariable fitting analysis of linear and 2D FS data indicates that the dimer adopts a "bent T-shaped" conformation. Moreover, the manifold of singly excited excitons undergoes rapid electronic dephasing and downhill population transfer on the time scale of ∼95 fs. The open conformation of the dimer suggests that its self-assembly is favored by an increase in entropy of the local membrane environment.
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Affiliation(s)
- Alejandro Perdomo-Ortiz
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, United States
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Perdomo-Ortiz A, Dickson N, Drew-Brook M, Rose G, Aspuru-Guzik A. Finding low-energy conformations of lattice protein models by quantum annealing. Sci Rep 2012; 2:571. [PMID: 22891157 PMCID: PMC3417777 DOI: 10.1038/srep00571] [Citation(s) in RCA: 89] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2012] [Accepted: 07/16/2012] [Indexed: 12/02/2022] Open
Abstract
Lattice protein folding models are a cornerstone of computational biophysics. Although these models are a coarse grained representation, they provide useful insight into the energy landscape of natural proteins. Finding low-energy threedimensional structures is an intractable problem even in the simplest model, the Hydrophobic-Polar (HP) model. Description of protein-like properties are more accurately described by generalized models, such as the one proposed by Miyazawa and Jernigan (MJ), which explicitly take into account the unique interactions among all 20 amino acids. There is theoretical and experimental evidence of the advantage of solving classical optimization problems using quantum annealing over its classical analogue (simulated annealing). In this report, we present a benchmark implementation of quantum annealing for lattice protein folding problems (six different experiments up to 81 superconducting quantum bits). This first implementation of a biophysical problem paves the way towards studying optimization problems in biophysics and statistical mechanics using quantum devices.
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Affiliation(s)
- Alejandro Perdomo-Ortiz
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
| | - Neil Dickson
- D-Wave Systems, Inc., 100-4401 Still Creek Drive, Burnaby, British Columbia V5C 6G9, Canada
| | - Marshall Drew-Brook
- D-Wave Systems, Inc., 100-4401 Still Creek Drive, Burnaby, British Columbia V5C 6G9, Canada
| | - Geordie Rose
- D-Wave Systems, Inc., 100-4401 Still Creek Drive, Burnaby, British Columbia V5C 6G9, Canada
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA
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13
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Affiliation(s)
| | | | - Alejandro Perdomo-Ortiz
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138;
| | - Man-Hong Yung
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138;
| | - Alán Aspuru-Guzik
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138;
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Arce JC, Perdomo-Ortiz A, Zambrano ML, Mujica-Martínez C. Envelope molecular-orbital theory of extended systems. I. Electronic states of organic quasilinear nanoheterostructures. J Chem Phys 2011; 134:104103. [PMID: 21405152 DOI: 10.1063/1.3559148] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A conceptually appealing and computationally economical course-grained molecular-orbital (MO) theory for extended quasilinear molecular heterostructures is presented. The formalism, which is based on a straightforward adaptation, by including explicitly the vacuum, of the envelope-function approximation widely employed in solid-state physics leads to a mapping of the three-dimensional single-particle eigenvalue equations into simple one-dimensional hole and electron Schrödinger-like equations with piecewise-constant effective potentials and masses. The eigenfunctions of these equations are envelope MO's in which the short-wavelength oscillations present in the full MO's, associated with the atomistic details of the molecular potential, are smoothed out automatically. The approach is illustrated by calculating the envelope MO's of high-lying occupied and low-lying virtual π states in prototypical nanometric heterostructures constituted by oligomers of polyacetylene and polydiacetylene. Comparison with atomistic electronic-structure calculations reveals that the envelope-MO energies agree very well with the energies of the π MO's and that the envelope MO's describe precisely the long-wavelength variations of the π MO's. This envelope MO theory, which is generalizable to extended systems of any dimensionality, is seen to provide a useful tool for the qualitative interpretation and quantitative prediction of the single-particle quantum states in mesoscopic molecular structures and the design of nanometric molecular devices with tailored energy levels and wavefunctions.
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Affiliation(s)
- J C Arce
- Departamento de Química, Universidad del Valle, Cali, Colombia.
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