A multiscale approach to coupled nuclear and electronic dynamics. I. Quantum-stochastic Liouville equation in natural internal coordinates

Multiscalemethodsarepowerfultoolstodescribelargeandcomplexsystems.Theyarebasedonahierarchicalpartitioningofthedegrees offreedom(d.o.f.)ofthesystem,allowingonetotreateachsetofd.o.f.inthemostcomputationallyefficientway.Inthecontextofcoupled nuclearandelectronicdynamics,amultiscaleapproachwouldoffertheopportunitytoovercomethecomputationallimitsthat,atpresent, donotallowonetotreatacomplexsystem(suchasabiologicalmacromoleculeinexplicitsolvent)fullyatthequantummechanicallevel. BasedonthepioneeringworkofKapralandCiccotti[R.KapralandG.Ciccotti,J.Chem.Phys.110,8919(1999)],thisworkisintendedto presentanonadiabatictheorythatdescribestheevolutionofelectronicpopulationscoupledwiththedynamicsofthenucleiofamoleculein adissipativeenvironment(condensedphases).Thetwoelementsofnoveltythatarehereintroducedare(i)thecastingofthetheoryinthe natural,internalcoordinates,thatarebondlengths,bondangles,anddihedralangles;(ii)theprojectionofthosenucleard.o.f.thatcanbe consideredatthelevelofathermalbath,thereforeleadingtoaquantum-stochasticLiouvilleequation.Usingnaturalcoordinatesallowsthe descriptionofstructureanddynamicsinthewaychemistsareusedtodescribemoleculargeometryanditschanges.Theprojectionofbath coordinatesprovidesanimportantreductionofcomplexityandallowsustoformulatetheapproachthatcanbeuseddirectlyinthestatistical thermodynamicsdescriptionofchemicalsystems.