Thermal Effects in Atomic and Molecular Polarizabilities with Path Integral Monte Carlo

Juha Tiihonen

Thermal Effects in Atomic and Molecular Polarizabilities with Path Integral Monte Carlo

Juha Tiihonen

Fysiikka

Tutkimustuotos: Väitöskirja › Collection of Articles

152 Lataukset (Pure)

Abstrakti

Väitöskirja käsittelee polarisoituvuutta ja erilaisia keinoja sen laskemiseksi polkuintegraali–Monte Carlo -menetelmällä (PIMC). Polarisoituvuus on kvanttimekaaninen suure, joka vastaa sähköistä suskeptibiliteettiä: se kuvaa atomien ja molekyylien vastetta sähkökenttään. Staattiset ja dynaamiset multipoli-polarisoituvuudet ovatkin yksiä tärkeimmistä elektronien vasteominaisuuksista ja näin ollen monikäyttöisiä parametrejä fysikaalisessa mallinnuksessa. Polarisoituvuuksien äärimmäisen tarkka laskeminen on kuitenkin haasteellista. Väitöskirjassa keskitytään siksi muutamaan erityiseen ongelmaan: tarkkaan monen kappaleen korrelaatiokuvaukseen, ei-adiabaattisiin efekteihin sekä lämpötilan vaikutuksiin.

Tässä työssä polarisoituvuuksien laskemista tarkastellaan ei-relativistisesti Feynmanin polkuintegraalien ja termisten tiheysmatriisien avulla. Sähkökentän ja sähköisten multipolien välinen vuorovaikutus kytketään kausaalisiin korrelaatiofunktioihin sekä epälineaarisen vasteen teoriaan. Uusi tieteellinen ansio muodostuu muutamasta erilaisesta keinosta määrittää polarisoituvuus PIMC-laskuista: äärellisen kentän simulointi, staattiset kenttä-derivaatan estimaattorit, sekä imaginääriajan korrelaatiofunktioiden analyyttinen jatkaminen. Vaadittu Matsubara-taajuuksien analyyttinen jatkaminen on yleisesti esiintyvä mutta huonosti määritelty numeerinen ongelma, jota lähestytään tässä työssä maksimientropiamenetelmällä.

Tärkeimmät laskennalliset tulokset ovat seuraavien yhden tai kahden elektronin systeemien polarisoituvuudet ja hyperpolarisoituvuudet: H, H2+, H2, H3+, HD+, He, He+, HeH+, Li+, Be2+, Ps, PsH, ja Ps2. Born–Oppenheimer-approksimaatiossa (BO) lasketut referenssitulokset vastaavat tunnettuja kirjallisuuden arvoja ja monessa tapauksessa myös täydentävät niitä. BO-approksimaation ulkopuolelta voidaan osoittaa mm. rovibraatiosta johtuvia heikkoja sekä voimakkaita lämpötilaefektejä. Muut tulokset käsittävät multipoli-spektrejä, dynaamisia polarisoituvuuksia sekä van der Waals-vakioita. Simulaatioiden kvanttimekaaninen kuvaus monen kappaleen korrelaatioista sekä elektronien ja ytimien ei-ediabaattisesta kytkennästä on poikkeuksellisen tarkka.

Alkuperäiskieli	Englanti
Kustantaja	Tampere University
Sivumäärä	120
Vuosikerta	35
ISBN (elektroninen)	978-952-03-1009-7
ISBN (painettu)	978-952-03-1008-0
Tila	Julkaistu - 5 huhtik. 2019
OKM-julkaisutyyppi	G5 Artikkeliväitöskirja

Julkaisusarja

Nimi	Tampere University Dissertations
Vuosikerta	35
ISSN (painettu)	2489-9860
ISSN (elektroninen)	2490-0028

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-03-1009-7

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title = "Thermal Effects in Atomic and Molecular Polarizabilities with Path Integral Monte Carlo",

abstract = "This Thesis is a review of polarizability and different means to estimate it from pathintegral Monte Carlo (PIMC) simulations. Polarizability is the quantum mechanical equivalent of electric susceptibility: it describes the electric ﬁeld response of atoms and molecules. The static and dynamic multipole polarizabilies are, arguably, the most important electronic response properties and multipurpose parameters for physical modeling. Computing them from ﬁrst principles is challenging in many ways, and in this Thesis we focus on a few particular aspects: exact many-body correlations, nonadiabatic effects and thermal coupling.The Thesis contains an introduction to polarizability in the framework of nonrelativistic Feynman path integrals and thermal density matrices. The electric ﬁeld interactions due to electric multipoles is associated with causal time-correlation functions and nonlinear response theory. The original scientiﬁc contribution manifests in various strategies to obtain the polarizabilities from PIMC simulations: we demonstrate ﬁnite-ﬁeld simulations, static ﬁeld-derivative estimators, and analytic continuation of imaginarytime correlation functions. The required analytic continuation of Matsubara frequencies is a common but ill-posed numerical challenge, which we approach with the Maximum Entropy method.For data, we provide the most important polarizabilities and hyperpolarizabilities of several one- or two-electron systems: H, H2+, H2, H3+, HD+, He, He+, HeH+, Li+, Be2+, Ps, PsH, and Ps2. Our benchmark simulations within the Born–Oppenheimer approximation (BO) agree with the available literature and complement it in many cases. Beyond BO, we are able to demonstrate weak and strong thermal effects due to, e.g., rovibrational coupling. We also estimate the ﬁrst-order multipole spectra, dynamic polarizabilities and van der Waals coefﬁcients. The simulations show unprecedented accuracy in terms of exact many-body correlations and fully nonadiabatic coupling of the electronic and nuclear quantum effects.",

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year = "2019",

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AU - Tiihonen, Juha

PY - 2019/4/5

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N2 - This Thesis is a review of polarizability and different means to estimate it from pathintegral Monte Carlo (PIMC) simulations. Polarizability is the quantum mechanical equivalent of electric susceptibility: it describes the electric ﬁeld response of atoms and molecules. The static and dynamic multipole polarizabilies are, arguably, the most important electronic response properties and multipurpose parameters for physical modeling. Computing them from ﬁrst principles is challenging in many ways, and in this Thesis we focus on a few particular aspects: exact many-body correlations, nonadiabatic effects and thermal coupling.The Thesis contains an introduction to polarizability in the framework of nonrelativistic Feynman path integrals and thermal density matrices. The electric ﬁeld interactions due to electric multipoles is associated with causal time-correlation functions and nonlinear response theory. The original scientiﬁc contribution manifests in various strategies to obtain the polarizabilities from PIMC simulations: we demonstrate ﬁnite-ﬁeld simulations, static ﬁeld-derivative estimators, and analytic continuation of imaginarytime correlation functions. The required analytic continuation of Matsubara frequencies is a common but ill-posed numerical challenge, which we approach with the Maximum Entropy method.For data, we provide the most important polarizabilities and hyperpolarizabilities of several one- or two-electron systems: H, H2+, H2, H3+, HD+, He, He+, HeH+, Li+, Be2+, Ps, PsH, and Ps2. Our benchmark simulations within the Born–Oppenheimer approximation (BO) agree with the available literature and complement it in many cases. Beyond BO, we are able to demonstrate weak and strong thermal effects due to, e.g., rovibrational coupling. We also estimate the ﬁrst-order multipole spectra, dynamic polarizabilities and van der Waals coefﬁcients. The simulations show unprecedented accuracy in terms of exact many-body correlations and fully nonadiabatic coupling of the electronic and nuclear quantum effects.

AB - This Thesis is a review of polarizability and different means to estimate it from pathintegral Monte Carlo (PIMC) simulations. Polarizability is the quantum mechanical equivalent of electric susceptibility: it describes the electric ﬁeld response of atoms and molecules. The static and dynamic multipole polarizabilies are, arguably, the most important electronic response properties and multipurpose parameters for physical modeling. Computing them from ﬁrst principles is challenging in many ways, and in this Thesis we focus on a few particular aspects: exact many-body correlations, nonadiabatic effects and thermal coupling.The Thesis contains an introduction to polarizability in the framework of nonrelativistic Feynman path integrals and thermal density matrices. The electric ﬁeld interactions due to electric multipoles is associated with causal time-correlation functions and nonlinear response theory. The original scientiﬁc contribution manifests in various strategies to obtain the polarizabilities from PIMC simulations: we demonstrate ﬁnite-ﬁeld simulations, static ﬁeld-derivative estimators, and analytic continuation of imaginarytime correlation functions. The required analytic continuation of Matsubara frequencies is a common but ill-posed numerical challenge, which we approach with the Maximum Entropy method.For data, we provide the most important polarizabilities and hyperpolarizabilities of several one- or two-electron systems: H, H2+, H2, H3+, HD+, He, He+, HeH+, Li+, Be2+, Ps, PsH, and Ps2. Our benchmark simulations within the Born–Oppenheimer approximation (BO) agree with the available literature and complement it in many cases. Beyond BO, we are able to demonstrate weak and strong thermal effects due to, e.g., rovibrational coupling. We also estimate the ﬁrst-order multipole spectra, dynamic polarizabilities and van der Waals coefﬁcients. The simulations show unprecedented accuracy in terms of exact many-body correlations and fully nonadiabatic coupling of the electronic and nuclear quantum effects.

M3 - Doctoral thesis

SN - 978-952-03-1008-0

VL - 35

T3 - Tampere University Dissertations

BT - Thermal Effects in Atomic and Molecular Polarizabilities with Path Integral Monte Carlo

PB - Tampere University

ER -

Thermal Effects in Atomic and Molecular Polarizabilities with Path Integral Monte Carlo

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