Skip to main content
SpringerLink
Log in

Energy Relaxation and Thermal Transport in Molecules

  • Living reference work entry
  • First Online:
Handbook of Materials Modeling

  • 373 Accesses

Abstract

The nature of energy relaxation in molecules and its role in mediating thermal conduction through a molecular junction are discussed. In addition to an overview of thermalization in molecules and quantum mechanical effects that influence this process, illustrative examples for alkane chain, perfluoroalkane, and polyethylene glycol (PEG) oligomer junctions are provided over a wide range of temperature. The calculated energy relaxation rates help clarify the scope of applicability of approaches that can be used to predict thermal conduction, e.g., where Fourier’s law breaks down and where an approach that neglects energy relaxation and thermalization is suitable, such as one based on a Landauer-like model. Comparison with experimental data, where available, is provided and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Agbo JK, Xu Y et al (2014) Vibrational energy flow across heme-cytochrome c and cytochrome c-water interfaces. Theor Chem Accounts 133:1504

    Article  Google Scholar 

  • Allen PB, Feldman JL (1993) Thermal conductivity of disordered harmonic solids. Phys Rev B 48:12581–12588

    Article  ADS  Google Scholar 

  • Backus EHG, Nguyen PH et al (2008a) Structural flexibility of a helical peptide regulates vibrational energy transport properties. J Phys Chem B 112:15487–15492

    Article  Google Scholar 

  • Backus EHG, Nguyen PH et al (2008b) Energy transport in peptide helices: a comparison between high- and low-energy excitations. J Phys Chem B 112:9091–9099

    Article  Google Scholar 

  • Backus EH, Bloem R et al (2009) Dynamical transition in a small helical peptide and its implication for vibrational energy transport. J Phys Chem B 113:13405–13409

    Article  Google Scholar 

  • Berrios E, Pratt S et al (2013) More protected vibrational states at the dissociation limit of SCCl2. J Phys Chem A 117:12082–12090

    Article  Google Scholar 

  • Bigwood R, Gruebele M et al (1998) The vibrational energy flow transition in organic molecules: theory meets experiment. Proc Natl Acad Sci U S A 95:5960–5967

    Article  ADS  Google Scholar 

  • Botan V, Backus EHG et al (2007) Energy transport in peptide helices. Proc Natl Acad Sci U S A 104:12749–12754

    Article  ADS  Google Scholar 

  • Buchenberg S, Leitner DM et al (2016) Scaling rules for vibrational energy transport in proteins. J Phys Chem Lett 7:25–30

    Article  Google Scholar 

  • Buerkle M, Asai Y (2017) Thermal conductance of Teflon and polyethylene: insight from an atomistic, single-molecule level. Sci Rep 7:41898

    Article  ADS  Google Scholar 

  • Buerkle M, Hellmuth TJ et al (2015) First-principles calculation of the thermoelectric figure of merit for [2,2]paracyclophane-based single-molecule junctions. Phys Rev B 91:165419

    Article  ADS  Google Scholar 

  • Buldum A, Leitner DM et al (1999) Thermal conduction through a molecule. Europhys Lett 47:208–212

    Article  ADS  Google Scholar 

  • Burin AL (2015) Many-body localization in a strongly disordered system with long-range interactions: finite-size scaling. Phys Rev B 91:094202

    Article  ADS  Google Scholar 

  • Burin A (2017) Localization and chaos in a quantum spin glass model in random longitudinal fields: mapping to the localization problem in a Bethe lattice with a correlated disorder. Ann Phys 529:1600292

    Article  MATH  Google Scholar 

  • Cahill DG, Ford WK et al (2003) Nanoscale thermal transport. J Appl Phys 93:793–818

    Article  ADS  Google Scholar 

  • Cahill DG, Braun PV et al (2014) Nanoscale thermal transport. II. 2003–2012. Appl Phys Rev 1:011305

    Article  Google Scholar 

  • Chen R, Craven GT et al (2017) Electron-transfer-induced and phononic heat transport in molecular environments. J Chem Phys 147:124101

    Article  ADS  Google Scholar 

  • Craven GT, Nitzan A (2016) Electron transfer across a thermal gradient. Proc Natl Acad Sci U S A 113:9421–9429

    Article  Google Scholar 

  • Craven GT, Nitzan A (2017) Electron transfer at thermally heterogeneous molecule-metal interfaces. J Chem Phys 146:092305

    Article  ADS  Google Scholar 

  • Datta S (1995) Electronic transport in mesoscopic systems. Cambridge University Press, Cambridge, UK

    Book  Google Scholar 

  • Dhar A (2008) Heat transport in low-dimensional systems. Adv Phys 57:457–537

    Article  ADS  Google Scholar 

  • Duchemin I, Donadio D (2011) Atomistic calculation of the thermal conductance of large scale bulk-nanowire junctions. Phys Rev B 84:115423

    Article  ADS  Google Scholar 

  • Enright MB, Leitner DM (2005) Mass fractal dimension and the compactness of proteins. Phys Rev E 71:011912

    Article  ADS  Google Scholar 

  • Enright MB, Yu X et al (2006) Hydration dependence of the mass fractal dimension and anomalous diffusion of vibrational energy in proteins. Phys Rev E 73:051905

    Article  ADS  Google Scholar 

  • Fabian J, Allen PB (1996) Anharmonic decay of vibrational states in amorphous silion. Phys Rev Lett 77:3839–3842

    Article  ADS  Google Scholar 

  • Feingold M, Leitner DM et al (1989) Semiclassical structure of Hamiltonians. Phys Rev A 39:6507–6514

    Article  ADS  Google Scholar 

  • Feingold M, Leitner DM et al (1991) Spectral statistics in semiclassical random matrix ensembles. Phys Rev Lett 66:986–989

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Foley BM, Gorham CS et al (2014) Protein thermal conductivity measured in the solid state reveals anharmonic interactions of vibrations in a fractal structure. J Phys Chem Lett 5:1077–1082

    Article  Google Scholar 

  • Fujii N, Mizuno M et al (2014) Observing vibrational energy flow in a protein with the spatial resolution of a single amino acid residue. J Phys Chem Lett 5:3269–−3273

    Article  Google Scholar 

  • Galperin M, Nitzan A et al (2007) Heat conduction in molecular transport junctions. Phys Rev B 75:155312

    Article  ADS  Google Scholar 

  • Gaskins JT, Bulusu A et al (2015) Thermal conductance across phosphonic acid molecules and interfaces: ballistic versus diffusive vibrational transport in molecular monolayers. J Phys Chem C 119:20931–20939

    Article  Google Scholar 

  • Giannoni M-J, Voros A et al (1991) Chaos and quantum physics. North-Holland, Amsterdam

    Google Scholar 

  • Giri A, Niemela J-P et al (2016) Heat-transport mechanisms in molecular building blocks of inorganic/organic hybrid superlattices. Phys Rev B 93:115310

    Article  ADS  Google Scholar 

  • Gruebele M, Bigwood R (1998) Molecular vibrational energy flow: beyond the golden rule. Int Rev Phys Chem 17:91–145

    Article  Google Scholar 

  • Hassan S, Schade M et al (2014) Response of villin headpiece-capped gold nanoparticles to ultrafast laser heating. J Phys Chem B 118:7954–7962

    Article  Google Scholar 

  • Hopkins PE (2013) Thermal transport across solid interfaces with nanoscale imperfections: effects of roughness, disorder, dislocations and bonding on thermal boundary conductance (review article). ISRN Mech Eng 2013:682586

    Article  Google Scholar 

  • Ishikura T, Yamato T (2006) Energy transfer pathways relevant for long-range intramolecular signaling of photosensory protein revealed by microscopic energy conductivity analysis. Chem Phys Lett 432:533–537

    Article  ADS  Google Scholar 

  • Ishikura T, Iwata Y et al (2015) Energy exchange network of inter-residue interactions within a thermally fluctuating protein: a computational study. J Comput Chem 36:1709–1718

    Article  Google Scholar 

  • Keshavamurthy S (2013a) Eigenstates of thiophosgene near the dissociation threshold: deviations from ergodicity. J Phys Chem A 117:8729–8736

    Article  Google Scholar 

  • Keshavamurthy S (2013b) Scaling perspective on intramolecular vibrational energy flow: analogies, insights and challenges. Adv Chem Phys 153:43–110

    Google Scholar 

  • Kondoh M, Mizuno M et al (2016) Importance of atomic contacts in vibrational energy flow in proteins. J Phys Chem Lett 7:1950–1954

    Article  Google Scholar 

  • Kuang S, Gezelter JD (2011) Simulating interfacial thermal conductance at metal-solvent interfaces: the role of chemical capping agents. J Phys Chem C 115:22475–22483

    Article  Google Scholar 

  • Kuharski RA, Chandler D et al (1988) Stochastic MD simulation of cyclohexane isomerization. J Phys Chem 92(11):3261–3267

    Article  Google Scholar 

  • Lee W, Kim K et al (2013) Heat dissipation in atomic-scale junctions. Nature 498:209–213

    Article  ADS  Google Scholar 

  • Lehmann KK, Scoles G et al (1994) Intramolecular dynamics from the eigenstate-resolved infrared spectra. Annu Rev Phys Chem 45:241–274

    Article  ADS  Google Scholar 

  • Leitner DM (1993) Real-symmetric random matrix ensembles of Hamiltonians with partial symmetry-breaking. Phys Rev E 48:2536–2546

    Article  ADS  Google Scholar 

  • Leitner DM (1999) Influence of quantum energy flow and localization on molecular isomerization in gas and condensed phases. Int J Quantum Chem 75(4–5):523–531

    Article  Google Scholar 

  • Leitner DM (2001a) Vibrational energy transfer and heat conduction in a one-dimensional glass. Phys Rev B 64:094201

    Article  ADS  Google Scholar 

  • Leitner DM (2001b) Vibrational energy transfer in helices. Phys Rev Lett 87:188102

    Article  ADS  Google Scholar 

  • Leitner DM (2002) Anharmonic decay of vibrational states in helical peptides, coils and one-dimensional glasses. J Phys Chem A 106:10870–10876

    Article  Google Scholar 

  • Leitner DM (2005) Heat transport in molecules and reaction kinetics: the role of quantum energy flow and localization. Adv Chem Phys 130B:205–256

    Google Scholar 

  • Leitner DM (2008) Energy flow in proteins. Annu Rev Phys Chem 59:233–259

    Article  ADS  Google Scholar 

  • Leitner DM (2012) Mode damping rates in a protein chromophore. Chem Phys Lett 530:102–106

    Article  ADS  Google Scholar 

  • Leitner DM (2013) Thermal boundary conductance and rectification in molecules. J Phys Chem B 117:12820–12828

    Article  Google Scholar 

  • Leitner DM (2015) Quantum ergodicity and energy flow in molecules. Adv Phys 64:445–517

    Article  ADS  Google Scholar 

  • Leitner DM, Gruebele M (2008) A quantum model of restricted vibrational energy flow on the way to the transition state in unimolecular reactions. Mol Phys 106:433–442

    Article  ADS  Google Scholar 

  • Leitner DM, Pandey HD (2015a) Asymmetric energy flow in liquid alkylbenzenes: a computational study. J Chem Phys 143:144301

    Article  ADS  Google Scholar 

  • Leitner DM, Pandey HD (2015b) Quantum bottlenecks and unidirectional energy flow in molecules. Ann Phys 527:601–609

    Article  MathSciNet  Google Scholar 

  • Leitner DM, Straub JE (2009) Proteins: energy, heat and signal flow. CRC Press/Taylor & Francis Group, Boca Raton

    Google Scholar 

  • Leitner DM, Wolynes PG (1996a) Statistical properties of localized vibrational eigenstates. Chem Phys Lett 258:18–24

    Article  ADS  Google Scholar 

  • Leitner DM, Wolynes PG (1996b) Vibrational relaxation and energy localization in polyatomics: effects of high-order resonances on flow rates and the quantum ergodicity transition. J Chem Phys 105(24):11226–11236

    Article  ADS  Google Scholar 

  • Leitner DM, Wolynes PG (1997) Quantum energy flow during molecular isomerization. Chem Phys Lett 280:411–418

    Article  ADS  Google Scholar 

  • Leitner DM, Wolynes PG (1997a) Quantization of the stochastic pump model of Arnold diffusion. Phys Rev Lett 79:55–58

    Article  ADS  Google Scholar 

  • Leitner DM, Wolynes PG (1997c) Vibrational mixing and energy flow in polyatomics: quantitative prediction using local random matrix theory. J Phys Chem A 101(4):541–548

    Article  Google Scholar 

  • Leitner DM, Wolynes PG (2006) Quantum theory of enhanced unimolecular reaction rates below the ergodicity threshold. Chem Phys 329:163

    Article  ADS  Google Scholar 

  • Leitner DM, Köppel H et al (1994) Effects of symmetry breaking on spectra of chaotic Hamiltonian systems. Phys Rev Lett 73:2970–2973

    Article  ADS  Google Scholar 

  • Leitner DM, Levine B et al (2003) Quantum energy flow and trans-stilbene photoisomerization: an example of a non-RRKM reaction. J Phys Chem A 107:10706–10716

    Article  Google Scholar 

  • Leitner DM, Buchenberg S et al (2015) Vibrational energy flow in the villin headpiece subdomain: master equation simulations. J Chem Phys 142:075101

    Article  ADS  Google Scholar 

  • Lev YB, Reichman DR (2014) Dynamics of many-body localization. Phys Rev B 220201(R):89

    Google Scholar 

  • Li Q, Duchemin I et al (2015) Mechanical tuning of thermal transport in a molecular junction. J Phys Chem C 119:24636–24642

    Article  Google Scholar 

  • Li Q, Strange M et al (2017) A strategy to suppress phonon transport in molecular junctions using Ï€-stacked systems. J Phys Chem C 121:7175–7182

    Article  Google Scholar 

  • Logan DE, Wolynes PG (1990) Quantum localization and energy flow in many-dimensional Fermi resonant systems. J Chem Phys 93(7):4994–5012

    Article  ADS  Google Scholar 

  • Losego MD, Grady ME et al (2012) Effects of chemical bonding on heat transport across interfaces. Nat Mater 11:502–506

    Article  ADS  Google Scholar 

  • Luo T, Chen G (2013) Nanoscale heat transfer – from computation to experiment. Phys Chem Chem Phys 15:3389–3412

    Article  Google Scholar 

  • Majumdar S, Sierra-Suarez JA et al (2015) Vibrational mismatch of metal leads controls thermal conductance of self-assembled monolayer junctions. Nano Lett 15:2985–2991

    Article  ADS  Google Scholar 

  • Maradudin AA, Fein AE (1962) Scattering of neutrons by an anharmonic crystal. Phys Rev 128:2589–2608

    Article  ADS  Google Scholar 

  • Mehta ML (1991) Random matrices. Academic, San Diego

    MATH  Google Scholar 

  • Meier T, Menges F et al (2014) Length-dependent thermal transport along molecular chains. Phys Rev Lett 113:060801

    Article  ADS  Google Scholar 

  • Nandkishore R, Huse DA (2015) Many-body localization and thermalization in quantum statistical mechanics. Annu Rev Cond Mat Phys 6:15–38

    Article  ADS  Google Scholar 

  • O’Brien PJ, Shenogin S et al (2012) Bonding-induced thermal conductance enhancement at inorganic heterointerfaces using nanomolecular monolayers. Nat Mater 12:118–122

    Article  ADS  Google Scholar 

  • Pandey HD, Leitner DM (2016) Thermalization and thermal transport in molecules. J Phys Chem Lett 7:5062–5067

    Article  Google Scholar 

  • Pandey HD, Leitner DM (2017a) Influence of thermalization on thermal conduction through molecular junctions: computational study of PEG oligomers. J Chem Phys 147:084701

    Article  ADS  Google Scholar 

  • Pandey HD, Leitner DM (2017b) Vibrational energy transport in molecules and the statistical properties of vibrational modes. Chem Phys 482:81–85

    Article  ADS  Google Scholar 

  • Qin Z, Bischof JC (2012) Thermophysical and biological responses of gold nanoparticle laser heating. Chem Soc Rev 41:1191–1217

    Article  Google Scholar 

  • Rubtsov IV (2009) Relaxation-assisted two-dimensional infrared spectroscopy (RA 2DIR) method: accessing distances over 10 Ã… and measuring bond connectivity patterns. Acc Chem Res 42:1385–1394

    Article  Google Scholar 

  • Rubtsova NI, Rubtsov IV (2015) Vibrational energy transport in molecules studied by relaxation-assisted two-dimensional infrared spectroscopy. Annu Rev Phys Chem 66:717–738

    Article  ADS  Google Scholar 

  • Segal D, Agarwalla BK (2016) Vibrational heat transport in molecular junctions. Annu Rev Phys Chem 67:185–209

    Article  ADS  Google Scholar 

  • Segal D, Nitzan A et al (2003) Thermal conductance through molecular wires. J Chem Phys 119:6840–6855

    Article  ADS  Google Scholar 

  • Sibert EL III, Gruebele M (2006) Molecular vibrational energy flow and dilution factors in an anharmonic state space. J Chem Phys 124:024317

    Article  ADS  Google Scholar 

  • Stocker KM, Gezelter JD (2013) Simulations of heat conduction at thiolate-capped gold surfaces: the role of chain length and solvent penetration. J Phys Chem C 117:7605–7612

    Article  Google Scholar 

  • Stocker KM, Neidhart SM et al (2016) Interfacial thermal conductance of thiolate-protected gold nanospheres. J Appl Phys 119:025106

    Article  ADS  Google Scholar 

  • Stuchebrukhov AA (1986) On the theory of intramolecular vibrational relaxation of polyatomic molecules. Sov Phys JETP 64(6):1195–1204

    Google Scholar 

  • Stuchebrukhov AA, Marcus RA (1993) Theoretical study of intramolecular vibrational relaxation of acetylenic CH vibration for v=1 and 2 in large polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si. J Chem Phys 98(8):6044–6061

    Article  ADS  Google Scholar 

  • Swartz ET, Pohl RO (1989) Thermal boundary resistance. Rev Mod Phys 61:605–668

    Article  ADS  Google Scholar 

  • Uzer T (1991) Theories of intramolecular vibrational energy transfer. Phys Rep 199(2):73–146

    Article  ADS  Google Scholar 

  • Wang JS, Wang J et al (2008) Quantum thermal transport in nanostructures. Eur Phys J B 62:381–404

    Article  ADS  Google Scholar 

  • Wilkinson M, Feingold M et al (1991) Localization and spectral statistics in a banded random matrix ensemble. J Phys A: Math Gen 24:175–181

    Article  ADS  Google Scholar 

  • Wu X, Varshney V et al (2017) How to characterize thermal transport capability of 2D materials fairly? – sheet thermal conductance and the choice of thickness. Chem Phys Lett 669:233–237

    Article  ADS  Google Scholar 

  • Xu Y, Leitner DM (2014) Vibrational energy flow through the green fluorescent protein-water interface: communication maps and thermal boundary conductance. J Phys Chem B 118:7818–7826

    Article  Google Scholar 

  • Xu Y, Gnanasekaran R et al (2013) The dielectric response to photoexcitation of GFP: a molecular dynamics study. Chem Phys Lett 564:78–82

    Article  ADS  Google Scholar 

  • Yu X, Leitner DM (2003a) Anomalous diffusion of vibrational energy in proteins. J Chem Phys 119:12673–12679

    Article  ADS  Google Scholar 

  • Yu X, Leitner DM (2003b) Vibrational energy transfer and heat conduction in a protein. J Phys Chem B 107:1698–1707

    Article  Google Scholar 

  • Yu X, Leitner DM (2005) Heat flow in proteins: computation of thermal transport coefficients. J Chem Phys 122:054902

    Article  ADS  Google Scholar 

Download references

Acknowledgments

Support from NSF grant CHE-1361776 is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Chemistry, University of Nevada, Reno, NV, USA

    David M. Leitner

Authors
  1. David M. Leitner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David M. Leitner .

Editor information

Editors and Affiliations

  1. Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Wanda Andreoni

  2. Department of Nuclear Science & Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Sidney Yip

Section Editor information

  1. University of California, Davis, Davis, USA

    Davide Donadio

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Leitner, D.M. (2018). Energy Relaxation and Thermal Transport in Molecules. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling. Springer, Cham. https://doi.org/10.1007/978-3-319-50257-1_14-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-50257-1_14-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-50257-1

  • Online ISBN: 978-3-319-50257-1

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

Publish with us

Policies and ethics

Search

Navigation