Despite not being a tangible substance, light is becoming an increasingly valuable tool in numerous areas of science and technology: the use of laser excitation of a fluorescent probe can generate incredibly detailed images of cellular structures without the need for large amounts of dissection; new types of solar cells are being produced using organic dyes to harvest light; computer data can be stored by inducing a chemical change in a compound through irradiation with light. However, before any of these materials can be applied in such a way, their properties must first be analyzed for them to be deemed viable. The focus of this dissertation is the photophysical characterization, linear and nonlinear, of a several novel organic compounds, and a europium complex, as well as using quantum chemical calculation techniques to understand some of the phenomena that are witnessed and begin to develop predictive capability. The nonlinear characterization of compounds utilizes wavelengths outside of their linear absorption range, where a focused beam can achieve the same excitation as one at half the wavelength, though this effect has a quadratic dependence on power. The potential for nonlinear excitation, or two-photon absorption (2PA), is becoming of increasing interest and importance for organic chromophores. Exciting only a small volume of material at a focal point makes it possible to nondestructively image samples in 3-dimensions, record data in multiple layers, and fabricate intricate structures through photopolymerization reactions. Lanthanides such as europium are known to exhibit sharp emission bands when excited, typically through an antenna effect due to the low probability of achieving direct excitation. This emission is long-lived, and through gating systems can readily be separated from background noise and autofluorescence (often observed in biological samples) that have much shorter lifetimes. Thus, one of the foci of this dissertation is the photophysical investigation of a series of novel lanthanide complexes, with particular attention to a europium complex.

Aqueous mineral oxide surfaces are ubiquitous in nature, where they play an important role in soil erosion, delta formation etc. Understanding the interfacial solvent environment at mineral oxide surfaces is important as many reactions, e.g., mineral dissolution, heterogeneous catalysis, and electrochemical water splitting occur at interfaces.Vibrational sum frequency generation (vSFG), a second-order nonlinear spectroscopic technique, inherently surface specific under the electric dipole approximation, serves as an excellent tool to study aqueous interfaces. vSFG is forbidden in centrosymmetric environments under the electric dipole approximation, making vSFG inherently specific to non-centrosymmetric environments such as surfaces, where the centrosymmetry is broken. vSFG is capable of measuring interfacial structure and dynamics without contributions from the bulk. Though vSFG has been extensively used to study aqueous interfaces yet there remain fundamental questions that need to be addressed. Is the interface capable of perturbing the environment of a centrosymmetric molecule to render it vSFG active? What higher order multipole terms contribute to vSFG? What are the vibrational energy relaxation pathways and mechanisms at oxide/water interfaces? In this dissertation, we have employed Stark active IR probe molecules (SCN-, N3-), that are sensitive to the local environment and whose frequency shifts depend on the localized electrostatic potential, to understand the interfacial solvent environment and measure the electrostatic potential associated with the charged sites at the aqueous Al2O3(0001) surface. The vibrational lifetime of IR probe molecules sheds information on solvent polarity, H-bonding network, and applied external electric fields. Hence, measuring the vibrational dynamics, whose timescales are comparable to the vibrational lifetime of the IR probe molecules, is a useful tool to understand vibrational energy relaxation (VER) pathways and mechanisms, specific solute-solvent interactions, and localized solvent environment. Though IR probe molecules have been employed to study bulk solvents, the literature for interfaces/surfaces is limited to reverse micelles, air/water interfaces and metal electrode surfaces. The VER rates of IR probe molecules (charged solutes) in bulk solvent and confined solvent environments are significantly different, which reflects the different local properties. The aim of this dissertation is to understand the localized solvent environment as well as the VER pathways and mechanisms of the IR probe molecule (SCN-) at the aqueous mineral oxide interfaces using IR pump-vSFG probe spectroscopy. Bulk H2O and D2O are similar in terms of H-bonding capability, static dielectric constant, and dipole moment. The FTIR spectra of the CN stretch of SCN- in bulk H2O and D2O share a similar central frequency, yet the measured vibrational lifetimes of SCN- reveal accelerated vibrational energy relaxation in bulk H2O vs. bulk D2O, indicating fundamental differences between the two solvent environments. This reflects distinct vibrational energy relaxation pathways. Probing the vibrational lifetime of the CN stretch of SCN- at the alumina(0001)/H2O and alumina(0001)/D2O interfaces enabled us to understand the effect of the interfacial solvent density of states on the solute-solvent vibrational coupling at interfaces. We observed three times faster vibrational energy relaxation (VER) for interfacial D2O (T1 ~7 ps) compared to bulk D2O (T1 ~22 ps). The lifetime of the CN stretch at the α-Al2O3(0001)/H2O interface (T1 ~3 ps) is, however, similar to the dynamics in bulk H2O (T1 ~ 2.7 ps) where effective coupling with the solvent combination band (water bending + librational modes) provides an efficient pathway for intermolecular vibrational energy transfer. Ab-initio simulations show that there is an increase in the vibrational density of states (VDOS) at the interface in the low-frequency region of the O-D stretch, resulting in greater overlap between SCN- and D2O vibrational modes compared to the bulk D2O. The VDOS is not the only factor determining VER. At the interface, there are likely enhanced solute-solvent interactions due to increased transition dipole – transition dipole coupling, as a result of reduced dielectric constant and more net oriented molecules. The two factors (a) availability of accessible energy-accepting states of the solvent and (b) increased solute-solvent coupling, cause acceleration in the vibrational relaxation at the alumina/D2O interface. This work provides insight into the vibrational relaxation pathways and coupling between solute and solvent vibrational modes, which is essential for understanding fundamental condensed phase phenomena in the bulk as well as at interfaces. Our research suggests that VER dynamics cannot be generalized for all interfaces as there are significant differences between how charged solutes behave within confined reverse micelles, at the air/water interface, and at solid/water interfaces. In this dissertation, the basic question of the origin of non-centrosymmetry is also addressed by studying the steady state vSFG response from the azido stretch of N3-, a centrosymmetric molecule, at the α-Al2O3 (0001)/H2O interface. We observed the azide asymmetric stretch peak at the aqueous alumina interface demonstrating that the interface sufficiently perturbs the centrosymmetric environment of the azide ion to make it vSFG active, thereby re-emphasizing the surface-specificity of the vSFG technique. DFT calculations revealed that the application of an external electric field (in the range 0.1 - 0.5 V/Å, similar to the ones typically observed at interfaces), 1-3 the centrosymmetry of the azide ion is broken, introducing Raman activity to the previously IR only active mode (asymmetry azide stretch) thereby making the mode vSFG active. Unlike metal surfaces, where the electrostatic potential is homogeneously distributed over the surface, mineral oxide surfaces have localized and spatially heterogeneous charged sites depending on the bulk pH solution, due to protonation/deprotonation of terminal hydroxyl groups. We employed the asymmetric stretching frequency of N3, an IR probe molecule, that is sensitive to the local solvent environment and applied electric potential to determine the localized interfacial electrostatic potential. Having demonstrated that the interface perturbs the centrosymmetry of N3-, shifts in the central frequency of its asymmetric stretch mode can be used to report on the interfacial localized surface potential of the Al2O3 surfaces. Our previous work using Stark active SCN- to probe the localized charged sites of the alumina (0001)/H2O interface led to the foundation of vSFG spectroscopy as a probe of the local electrostatic potential. Using the N3- Stark tuning rate, the localized electrostatic potential at the negatively charged Al-O- sites was measured to be -170 mV, similar to the one measured by SCN- (-154 mV). In this dissertation, we expand the library of nitrile groups that can be used to measure the interfacial electrostatic potential by using N3-, another Stark active IR molecule, while probing the origin of non-centrosymmetry in this centrosymmetric molecule at mineral oxide/water interfaces. / Chemistry

Práce se zabývá teorií nelineární spektroskopie a projevy kvantové koherentní dynamiky v nelineární spektroskopii. Poskytuje stručný přehled spektroskopických metod se zaměřením na metodu pump-probe. Dále rozví- jíme teorii nelineární odezvy, přičemž vycházíme z obecného N-wave mixing experimentu, a dospíváme ke tvaru odezvové funkce třetího řádu vyjádřené pomocí Liouvillových drah. Pro vybrané modelové systémy sledujeme koher- entní efekty, které se projevují v 2D a pump-probe spektrech, a provádíme jejich porovnání. D·raz je kladen na objasnění jev· relaxace a excitonové koherence mezi dvěma excitovanými stavy molekulárního dimeru. 1

Nesta tese estudamos a relação entre as propriedades de absorção de multi-fótons e a estrutura molecular de três classes distintas de compostos orgânicos π-conjugados: derivados de vitamina A, complexos de platina acetilada e compostos quirais. Materiais orgânicos emergiram nas últimas décadas como candidatos para aplicações em dispositivos fotônicos, principalmente aqueles envolvendo processos de absorção multifotônica, uma vez que suas propriedades podem ser facilmente otimizadas através de engenharia molecular. Devido às diferenças inerentes entre as estruturas químicas dos compostos aqui investigados, foi possível verificar individualmente a influência do comprimento de conjugação, da presença de grupos doadores e aceitadores de elétrons (estruturas push-pull), da planaridade molecular e de efeitos de comprimento de ligação sobre a seção de choque de absorção multifotônica. Para tanto, foram utilizadas as técnicas de Varredura-Z convencional e com contínuo de luz branca, espectroscopia de fluorescência por absorção de multi-fótons e fluorescência resolvida no tempo. Para correlacionar as propriedades moleculares com os espectros não-lineares, foram utilizados cálculos de química quântica em conjunto com o modelo de soma de estados essenciais. Através desse modelo foi possível associar aspectos puramente moleculares, como o momento de dipolo de transição, o momento de dipolo estático, a força do oscilador e a largura de linha dos estados eletrônicos com a estrutura molecular dos cromóforos, visando futuras aplicações tecnológicas. Resultados de espectroscopia de absorção de dois fótons revelaram que os derivados da vitamina A, como o trans-β-apo-8-carotenal e all-trans β-caroteno, possuem magnitudes da seção de choque extremamente elevadas (~5000 GM), indicando-os como materiais promissores para armazenamento óptico 3D. Os complexos de platina acetilada apresentaram características impares para aplicações em dispositivos de limitação de potência óptica baseados em processos de absorção de dois e três fótons como, elevadas absortividades não-lineares, boa transparência óptica, baixo limiar de limitação, alto intervalo dinâmico e rápido tempo de resposta. Por fim, os compostos quirais abriram possibilidades de explorar novos efeitos em óptica não-linear como, por exemplo, efeito de dipolo magnético e quadrupolo elétrico, apenas modificando o estado de polarização da luz. / In this thesis we studied the relationship between the multi-photon absorption properties and the molecular structure of three distinct classes of π-conjugated organic compounds: derivatives of vitamin A, platinum acetylide complexes and chiral compounds. Organic materials have emerged as potential candidates for applications involving multiphoton absorption, since their properties can be changed through molecular engineering. Because of the inherent differences between the molecular structures of the compounds investigated here, it was possible to verify the influence of conjugation length, electron donor and acceptors groups (push-pull structures), molecular planarity and effects of bond length alternation on the multi-photon absorption cross-section. To investigate such properties, we have employed the conventional and white-light continuum femtosecond Z-scan technique and multi-photon and time-resolved fluorescence spectroscopy. We have also employed quantum chemical calculation and the essential sum-over-states approach to correlate the impact of molecular properties on the nonlinear spectra. It was possible to link pure molecular features such as transition dipole moment, static dipole moment, oscillator strength and states linewidth with the chromophores structures, aiming at future applications. The two-photon absorption spectroscopy results revealed that the derivatives of vitamin A, such as trans-β-apo-8-carotenal and all-trans β-carotene, present cross-sections values extremely high (~ 5000 GM), indicating them as promising materials for 3D optical storage. The platinum acetylide complexes can be applied in optical power limiting devices based on the two- and three-photon absorption process, since they present unique features, such as high nonlinearity, good optical transparency, low threshold limit, high dynamic range and fast response time. Finally, the chiral compounds opened up new possibilities to be explored in nonlinear optics, such as the effect of magnetic dipole and electric quadrupole, only manipulating the polarization state of the light.

Neste trabalho foi utilizada Espectroscopia Vibracional por Geração de Soma de Freqüências, uma técnica óptica não-linear que é sensível à conformação molecular em interfaces e superfícies, para caracterizar o ordenamento molecular de filmes poliméricos automontados de polieletrólitos durante todos os passos do processo de fabricação, tendo como modelo o par de polieletrólitos PAH (poli(cloreto de alilamina)) / PSS (poli(estireno sulfonato de sódio)). Os espectros SFG permitiram verificar que durante o mergulho (in situ) do substrato na solução de polieletrólitos, estes adsorvem, mas se encontram numa configuração desordenada. Observou-se também que a secagem dos filmes pela ação de jato de nitrogênio produz filmes menos homogêneos do que por secagem espontânea, e às vezes até destruindo completamente o ordenamento molecular. Além disso, verificou-se também que camadas de polieletrólitos adsorvidas influenciam o ordenamento das camadas previamente adsorvidas. Com base nos resultados, modelos para a representação das estruturas desses filmes de polieletrólitos in situ e ex situ foram propostos. / In this work, Sum-Frequency Vibrational Spectroscopy, a nonlinear optical technique that is sensitive to molecular conformation at interfaces and surfaces, was used to characterize the molecular ordering of self-assembled films during all steps of self-assembly, having as model poly(allylamine hydrochloride) (PAH) / poly(styrene sulfonate) (PSS) polyelectrolyte assemble. SFG spectra showed that during immersion (in situ) of substrate in polyelectrolytes solutions, adsorption occurs but the molecules are in a disordered configuration. It was observed that the films drying by nitrogen flow are more inhomogeneous than those dried by spontaneous water evaporation. In some cases, dried films by nitrogen flow are quite disordered. Furthermore, it was observed that polyelectrolytes layers affect the ordering of the previously adsorbed layers. Based on our results, models were proposed to represent the structure of polyelectrolytes films in both: in situ and ex situ.

Nesta tese estudamos a relação entre as propriedades de absorção de multi-fótons e a estrutura molecular de três classes distintas de compostos orgânicos π-conjugados: derivados de vitamina A, complexos de platina acetilada e compostos quirais. Materiais orgânicos emergiram nas últimas décadas como candidatos para aplicações em dispositivos fotônicos, principalmente aqueles envolvendo processos de absorção multifotônica, uma vez que suas propriedades podem ser facilmente otimizadas através de engenharia molecular. Devido às diferenças inerentes entre as estruturas químicas dos compostos aqui investigados, foi possível verificar individualmente a influência do comprimento de conjugação, da presença de grupos doadores e aceitadores de elétrons (estruturas push-pull), da planaridade molecular e de efeitos de comprimento de ligação sobre a seção de choque de absorção multifotônica. Para tanto, foram utilizadas as técnicas de Varredura-Z convencional e com contínuo de luz branca, espectroscopia de fluorescência por absorção de multi-fótons e fluorescência resolvida no tempo. Para correlacionar as propriedades moleculares com os espectros não-lineares, foram utilizados cálculos de química quântica em conjunto com o modelo de soma de estados essenciais. Através desse modelo foi possível associar aspectos puramente moleculares, como o momento de dipolo de transição, o momento de dipolo estático, a força do oscilador e a largura de linha dos estados eletrônicos com a estrutura molecular dos cromóforos, visando futuras aplicações tecnológicas. Resultados de espectroscopia de absorção de dois fótons revelaram que os derivados da vitamina A, como o trans-β-apo-8-carotenal e all-trans β-caroteno, possuem magnitudes da seção de choque extremamente elevadas (~5000 GM), indicando-os como materiais promissores para armazenamento óptico 3D. Os complexos de platina acetilada apresentaram características impares para aplicações em dispositivos de limitação de potência óptica baseados em processos de absorção de dois e três fótons como, elevadas absortividades não-lineares, boa transparência óptica, baixo limiar de limitação, alto intervalo dinâmico e rápido tempo de resposta. Por fim, os compostos quirais abriram possibilidades de explorar novos efeitos em óptica não-linear como, por exemplo, efeito de dipolo magnético e quadrupolo elétrico, apenas modificando o estado de polarização da luz. / In this thesis we studied the relationship between the multi-photon absorption properties and the molecular structure of three distinct classes of π-conjugated organic compounds: derivatives of vitamin A, platinum acetylide complexes and chiral compounds. Organic materials have emerged as potential candidates for applications involving multiphoton absorption, since their properties can be changed through molecular engineering. Because of the inherent differences between the molecular structures of the compounds investigated here, it was possible to verify the influence of conjugation length, electron donor and acceptors groups (push-pull structures), molecular planarity and effects of bond length alternation on the multi-photon absorption cross-section. To investigate such properties, we have employed the conventional and white-light continuum femtosecond Z-scan technique and multi-photon and time-resolved fluorescence spectroscopy. We have also employed quantum chemical calculation and the essential sum-over-states approach to correlate the impact of molecular properties on the nonlinear spectra. It was possible to link pure molecular features such as transition dipole moment, static dipole moment, oscillator strength and states linewidth with the chromophores structures, aiming at future applications. The two-photon absorption spectroscopy results revealed that the derivatives of vitamin A, such as trans-β-apo-8-carotenal and all-trans β-carotene, present cross-sections values extremely high (~ 5000 GM), indicating them as promising materials for 3D optical storage. The platinum acetylide complexes can be applied in optical power limiting devices based on the two- and three-photon absorption process, since they present unique features, such as high nonlinearity, good optical transparency, low threshold limit, high dynamic range and fast response time. Finally, the chiral compounds opened up new possibilities to be explored in nonlinear optics, such as the effect of magnetic dipole and electric quadrupole, only manipulating the polarization state of the light.

The primary goal of spectroscopy is to obtain molecularly detailed information about the system under study. Sum frequency generation (SFG) vibrational spectroscopy is a nonlinear optical technique that is highly interface specific, and is therefore a powerful tool for understanding interfacial structure and dynamics. SFG is a second order, electronically nonresonant, polarization experiment and is consequently dipole forbidden in isotropic media such as a bulk liquid. Interfaces, however, serve to break the symmetry and produce a signal. Theoretical approximations to vibrational spectra of O-H stretching at aqueous interfaces are constructed using time correlation function (TCF) and instantaneous normal mode (INM) methods. Detailed comparisons of theoretical models and spectra are made with those obtained experimentally in an effort to establish that our molecular dynamics (MD) methods can reliably depict the system of interest. The computational results presented demonstrate the potential of these methods to accurately describe fundamentally important systems on a molecular level.

Neste trabalho foi utilizada Espectroscopia Vibracional por Geração de Soma de Freqüências, uma técnica óptica não-linear que é sensível à conformação molecular em interfaces e superfícies, para caracterizar o ordenamento molecular de filmes poliméricos automontados de polieletrólitos durante todos os passos do processo de fabricação, tendo como modelo o par de polieletrólitos PAH (poli(cloreto de alilamina)) / PSS (poli(estireno sulfonato de sódio)). Os espectros SFG permitiram verificar que durante o mergulho (in situ) do substrato na solução de polieletrólitos, estes adsorvem, mas se encontram numa configuração desordenada. Observou-se também que a secagem dos filmes pela ação de jato de nitrogênio produz filmes menos homogêneos do que por secagem espontânea, e às vezes até destruindo completamente o ordenamento molecular. Além disso, verificou-se também que camadas de polieletrólitos adsorvidas influenciam o ordenamento das camadas previamente adsorvidas. Com base nos resultados, modelos para a representação das estruturas desses filmes de polieletrólitos in situ e ex situ foram propostos. / In this work, Sum-Frequency Vibrational Spectroscopy, a nonlinear optical technique that is sensitive to molecular conformation at interfaces and surfaces, was used to characterize the molecular ordering of self-assembled films during all steps of self-assembly, having as model poly(allylamine hydrochloride) (PAH) / poly(styrene sulfonate) (PSS) polyelectrolyte assemble. SFG spectra showed that during immersion (in situ) of substrate in polyelectrolytes solutions, adsorption occurs but the molecules are in a disordered configuration. It was observed that the films drying by nitrogen flow are more inhomogeneous than those dried by spontaneous water evaporation. In some cases, dried films by nitrogen flow are quite disordered. Furthermore, it was observed that polyelectrolytes layers affect the ordering of the previously adsorbed layers. Based on our results, models were proposed to represent the structure of polyelectrolytes films in both: in situ and ex situ.

Important aspects of adhesion occur at interfaces, including structures that may be different from those in the bulk materials. However, probing the orientation of molecules in functional adhesives poses a significant challenge because adhesive molecules are always located at a buried interface. The limited penetration depth of surface-specific analysis prohibits the study of buried interfaces using those techniques. The large quantity of bulk molecules relative to the adhesive molecules interacting at the interface results in the bulk signal swamping out adhesive signal in bulk analysis techniques. An interface-specific technique is required to study functional adhesives. One such technique that has shown promise in recent years is Vibrational sum frequency generation (VSFG) spectroscopy. This technique is useful for studying interactions that occur at surfaces and interfaces because it selectively probes regions of broken inversion symmetry. Despite the ability of VSFG to isolate signal from a buried interface, a non-resonant signal that is produced simultaneously with the resonant signal corrupts the vibrational data of interest and greatly impedes reliable analysis of VSFG spectra. Over the last several years, researchers have experimentally removed non-resonant signal by delaying the upconverting pulse with respect to the initial excitation. Obtaining reliable results from VSFG data depends upon complete removal of non-resonant signal. However, complete removal of non-resonant signal presents a challenge because it can be present in spectra even when the indicators of non-resonant signal are absent. By taking advantage of polarization selection rules for VSFG and the differing symmetry of an azimuthally isotropic film and an azimuthally non-isotropic substrate, spectra containing non-resonant signal can be easily identified. These and other advances in VSFG methodology have enabled the study of surface and interfacial systems of interest. In a study of the effects of plasma treatment on polystyrene thin films, plasma exposure was found to affect not only the free surface but also portions of the sub-surface polymer, challenging previous assumptions that plasma effects are constrained to the free surfaces of materials. The next step is to use VSFG to study functional adhesives under known amounts of applied stress. An apparatus is in place to simultaneously collect VSFG spectra during mechanical testing of a functional adhesive, and in preliminary studies, an increase in VSFG non-resonant signal has been observed when a pulling force is applied to the adhesive bond.

Supercontinuum (SC) generation, oftentimes referred to as white-light continuum (WLC), has been a subject of interest for more than 40 years. From the first observation of WLC in condensed media in the early 1970s to the first observation of WLC in gases in the mid-1980s, much work has been devoted to developing a framework for understanding the complex nature of this phenomenon as well as discovering its utility in various applications. The main effort of this dissertation is to develop a WLC for the purpose of broadband nonlinear spectroscopy and use it in spectroscopic measurements. The ability to generate a high-quality, high-spectral-irradiance source of radiation confined in a single beam that spans the visible and near-infrared spectral regimes has great utility for nonlinear measurement methods such as the Z-scan technique. Using a broadband WLC instead of conventional tunable sources of radiation such as optical parametric generators/amplifiers has been shown to increase the efficiency of such measurements by nearly an order of magnitude. Although WLC generation has many complex processes involved, and complete models of the process involve highly complex numerical modeling, simple models can still guide us in the optimization of systems for WLC generation. In this dissertation the effects of two key mechanisms behind WLC generation in gaseous media are explored: self-phase modulation (SPM) and ionization leading to plasma production. The effects of SPM are largely dependent upon the third-order nonlinear refractive index, n2, of the gaseous medium whereas the effects of plasma production are dependent upon many parameters including the initial number density, ionization potential/energy, and the rate of ionization production. It is found that in order to generate a stable WLC suitable for nonlinear spectroscopy, the phase contributions from SPM and plasma production should be nearly equal. This guided our experiments in inert gases using mJ level, 150 fs-FWHM (full-width at half-maximum) pulses at 780 nm as well as 40 fs-FWHM pulses primarily at 1800 nm to create a stable, high-spectral-irradiance WLC. The generated WLC is shown to have sufficient spectral energy and spatial quality suitable for nonlinear spectroscopic measurements. In addition to extending the WLC bandwidth by using a long wavelength (1800 nm) pump source, it is found that by using a secondary weak seed pulse with a peak irradiance three orders of magnitude less than the main pulse, the spectral energy density is enhanced by more than a factor of 3 in Krypton gas for a WLC spectrum that spans over 2 octaves. Numerical simulations are presented which qualitatively describe the experimental results. The spectral enhancement of the WLC by seeding is also demonstrated for other inert gases and condensed media. Other efforts described in this dissertation include the development of the Dual-Arm Z-scan technique and its extension to measuring thin film nonlinearities in the presence of large substrate signals as well as predicting the n2 spectra of organic molecules (where we can approximate their behavior as if they were centrosymmetric) from knowledge of the one-photon and two-photon absorption spectra using a simplified sum-over-states quantum perturbative model by utilizing a quasi 3-level and quasi 4-level system.