Molecular Engineering of Dipolar and Octupolar Non-Linear Optical Materials for Next-Generation Telecommunications

In an age where next-generation all-optical circuitry and optical data storage are at the forefront of the telecommunications industry, the molecular engineering and design of new organic materials continues apace. Such materials are particularly attractive on account of their fast optical response times, and superior non-linear optical susceptibilities, relative to their traditional inorganic counterparts. While dipolar molecules dominate the field of organic non-linear optical (NLO) materials, octupolar molecules have the potential to produce far greater NLO effects; moreover, they have the capacity to produce 3-D sensitive NLO phenomena. This PhD explores new classes of dipolar organic and octupolar organometallic materials, where computations have predicted them to serve with superior NLO properties. To this end, concerted experimental and theoretical data are employed to characterise the electronic structure of these materials and elucidate their NLO properties. Data for electronic structures in this thesis were secured via in-house and synchrotron-based X-ray diffraction experiments (by proxy), which the author employed for charge density analyses. Multipolar modelling of experimental charge densities of the subject NLO materials forms an integral part of this thesis. Topological analysis is applied to these electronic structures, using the quantum theory of atoms in molecules (QTAIM), from which the structural and chemical origins of their NLO properties are assessed. Complementary theoretical methods were also used in this work, including calculations undertaken via density functional theory, as well as the relatively new technique of X-ray constrained wave-function refinement, which especially complements multipolar modelling methods, providing direct corroboratory topological analysis. An array of complementary experimental and computational methods is employed to evaluate the NLO properties of these materials in the gas-, solution-, and solid state-phase. The organometallic complexes presented in this thesis were also synthesised by the author. Chapter 1 of this work begins by presenting some of the main principles behind NLO phenomena, before providing a review of some of the most salient organic and organometallic NLO materials investigated, to date. Chapter 2 provides details pertaining to the experimental and computational methods used within this work to evaluate the molecular origins of the NLO properties of the materials investigated herein. Chapter 3 explores the molecular origins of the NLO properties of a new class of dipolar organic chromophores via structural analysis, experimental charge density analyses, hyper-Rayleigh scattering and density functional theory. Chapter 4 similarly investigates a new class of dipolar organic NLO chromophores via structural analysis, hyper-Rayleigh scattering and density functional theory. However, topological analysis herein was undertaken solely via the X-ray constrained wave-function fitting method, due to the absence of high-resolution X-ray diffraction data for experimental multipolar modelling. Chapter 5 investigates two ionic organic chromophores and the implications of their intermolecular interactions on their respective NLO responses by building up the ionic system using a ‘molecular lego’ approach. Chapters 6-7 detail investigations of newly identified octupolar NLO organometallic complexes, and feature several rare examples of charge-density studies of materials containing heavy elements, such as the transition metal, zinc, and bromine These heavy elements are particularly challenging even for state-of-the-art experimental and computational materials characterisation methods. Chapter 8 concludes this work, and identifies possible future directions for investigations of NLO materials for next-generation telecommunications.EPSR

Computational Studies of Dispersion Interactions in Coinage and Volatile Metal Clusters

Intermolecular interactions are ubiquitous, and their intricate network plays a decisive role in most of the phenomena encountered in our everyday lives. The focus of this thesis is on the London dispersion forces, a component present in all interactions between atoms and molecules, and often the most important one at long intermolecular distances. The quantum-mechanical origin of these forces can be traced to the correlated fluctuations of the molecular charge distributions, which however render the dispersion interactions challenging to calculate accurately, due to the high-level electronic structure methods required. The aim of the research presented in this thesis is to investigate the dispersion interactions, and to develop a viable method for modeling them. The systems studied in the accompanying research articles mainly encompass small clusters of coinage (Cu, Ag, and Au) and volatile (Zn, Cd, and Hg) metals. The long-range forces present in these clusters are calculated by means of highly correlated electronic structure methods, and the interaction potentials are used to develop a simple but effective model, capable of accurately describing the dispersion interactions in a variety of systems. Some original theoretical considerations are also elaborated. A novel formula is derived for the tensor describing all intermolecular interactions, and it is applied to investigate the long-range interaction potential of coinage metal hydrogen clusters. The method developed to account for the dispersion energy is a pair-potential model, where the total intermolecular London forces are calculated by means of atomic dispersion coefficients describing the magnitude and orientation dependence of the interaction. The coefficients are calculated based on small model systems, and they are used to compute the dispersion energy in larger clusters at no additional cost. Encouraging results are also obtained for the computed orientation averaged interaction potentials. All things considered, the publications included in this thesis indicate that the methods proposed and implemented to analyze the studied systems are capable of accurately modeling the non-covalent forces in a straightforward fashion.Molekyylien väliset voimat vaikuttavat kaikkialla elinympäristössämme ja ne ovat avainasemassa useimmissa päivittäin kohtaamissamme tuotteissa, materiaaleissa ja kemiallisissa prosesseissa. Tässä väitöskirjassa tarkastellaan erityisesti niin kutsuttua Londonin dispersiovoimaa, joka on osallisena kaikissa atomien ja molekyylien välisissä vuorovaikutuksissa. Tällä täysin kvanttimekaanisella ilmiöllä ei ole vastinetta klassisessa fysiikassa, mutta sen voidaan ajatella saavan alkunsa molekyylien varausjakaumien tahdistuneista heilahteluista. Pitkillä molekyylien välisillä etäisyyksillä dispersio on usein tärkein vuorovaikutusenergiaan vaikuttava tekijä, mutta sen tarkka laskennallinen mallintaminen on haastavaa. Tässä väitöskirjassa kehitetyllä laskennallisella menetelmällä dispersiovuorovaikutuksia voidaan tutkituissa systeemeissä kuvata yksinkertaisesti ja tarkasti. Tähän väitöskirjaan kuuluvissa tutkimusartikkeleissa keskitytään lähinnä pieniin metalliryppäisiin, jotka koostuvat rahametalleista (Cu, Ag ja Au) sekä sinkkiryhmän (Zn, Cd, Hg) metalleista. Molekyylien välinen vuorovaikutusenergia määritetään korkeatasoisten elektroniverholaskujen avulla, ja tuloksena saatavista energiakäyristä lasketaan parametreja, jotka kuvaavat dispersioenergiaa kvantitatiivisesti useissa eri systeemeissä. Tässä väitöskirjassa esitetään myös molekyylien välisten voimien matemaattista käsittelyä yksinkertaistavia teoreettisia tuloksia. Voimien orientaatioriippuvuutta kuvaavalle vuorovaikutustensorille johdetaan uudenlainen kaava, jota käytetään rahametalli- ja vetydimeerien välisten pitkän kantaman vuorovaikutusten tutkimiseen. Dispersiovoimien kuvaamiseen käytetyssä menetelmässä molekyylien välinen vuorovaikutusenergia voidaan laskea eri atomipareille määritetyistä kertoimista. Nämä kertoimet lasketaan pienten metalliryppäiden avulla ja niiden osoitetaan kuvaavan dispersioenergiaa myös suuremmissa systeemeissä ilman ylimääräisiä elektroniverholaskuja. Käytettyä mallia sovelletaan hyvin tuloksin myös orientaatiokeskiarvoistettujen dispersiopotentiaalien laskemiseen sinkkiryhmän metallidimeerien välillä. Kaiken kaikkiaan tähän väitöskirjaan sisältyvät tutkimusartikkelit osoittavat, että käytetyillä laskennallisilla malleilla ja menetelmillä voidaan pitkän kantaman vuorovaikutuksia mallintaa luotettavasti ja suoraviivaisesti tutkittujen molekyylien välillä

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

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.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

Accurate variational electronic structure calculations with the density matrix renormalization group

During the past fifteen years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low­-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many­-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. Whereas the MPS ansatz can only capture exponentially decaying correlation functions in the thermodynamic limit, and will therefore only yield an efficient description for noncritical one-dimensional systems, it can still be used as a variational ansatz for finite­-size systems. Rather large virtual dimensions are then required. The two most important aspects to reduce the corresponding computational cost are a proper choice and ordering of the active space orbitals, and the exploitation of the symmetry group of the Hamiltonian. By taking care of both aspects, DMRG becomes an efficient replacement for exact diagonalization in quantum chemistry. For hydrogen chains, accurate longitudinal static hyperpolarizabilities were obtained in the thermodynamic limit. In addition, the low-lying states of the carbon dimer were accurately resolved. DMRG and Hartree-­Fock theory have an analogous structure. The former can be interpreted as a self­-consistent mean­-field theory in the DMRG lattice sites, and the latter in the particles. It is possible to build upon this analogy to introduce post-­DMRG methods. Based on an approximate MPS, these methods provide improved ansätze for the ground state, as well as for excitations. Exponentiation of the single­-particle excitations for a Slater determinant leads to the Thouless theorem for Hartree-­Fock theory, an explicit nonredundant parameterization of the entire manifold of Slater determinants. For an MPS with open boundary conditions, exponentiation of the single-site excitations leads to the Thouless theorem for DMRG, an explicit nonredundant parameterization of the entire manifold of MPS wavefunctions. This gives rise to the configuration interaction expansion for DMRG. The Hubbard-­Stratonovich transformation lies at the basis of auxiliary field quantum Monte Carlo for Slater determinants. An analogous transformation for spin-­lattice Hamiltonians allows to formulate a promising variant for matrix product states

Accurate variational electronic structure calculations with the density matrix renormalization group

During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. The underlying matrix product state (MPS) ansatz is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS controls the size of the corner of the many-body Hilbert space that can be reached. Whereas the MPS ansatz will only yield an efficient description for noncritical one-dimensional systems, it can still be used as a variational ansatz for other finite-size systems. Rather large virtual dimensions are then required. The two most important aspects to reduce the corresponding computational cost are a proper choice and ordering of the active space orbitals, and the exploitation of the symmetry group of the Hamiltonian. By taking care of both aspects, DMRG becomes an efficient replacement for exact diagonalization in quantum chemistry. DMRG and Hartree-Fock theory have an analogous structure. The former can be interpreted as a self-consistent mean-field theory in the DMRG lattice sites, and the latter in the particles. It is possible to build upon this analogy to introduce post-DMRG methods. Based on an approximate MPS, these methods provide improved ans\"atze for the ground state, as well as for excitations. Exponentiation of the single-particle (single-site) excitations for a Slater determinant (an MPS with open boundary conditions) leads to the Thouless theorem for Hartree-Fock theory (DMRG), an explicit nonredundant parameterization of the entire manifold of Slater determinants (MPS wavefunctions). This gives rise to the configuration interaction expansion for DMRG. The Hubbard-Stratonovich transformation lies at the basis of auxiliary field quantum Monte Carlo for Slater determinants. An analogous transformation for spin-lattice Hamiltonians allows to formulate a promising variant for MPSs.Comment: PhD thesis (225 pages). PhD thesis, Ghent University (2014), ISBN 978946197194