Period determination in the food-entrainable and methamphetamine-sensitive circadian oscillator(s)

Daily rhythmic processes are coordinated by circadian clocks, which are present in numerous central and peripheral tissues. In mammals, two circadian clocks, the food-entrainable oscillator (FEO) and methamphetamine-sensitive circadian oscillator (MASCO), are "black box" mysteries because their anatomical loci are unknown and their outputs are not expressed under normal physiological conditions. In the current study, the investigation of the timekeeping mechanisms of the FEO and MASCO in mice with disruption of all three paralogs of the canonical clock gene, Period, revealed unique and convergent findings. We found that both the MASCO and FEO in Per1(-/-)/Per2(-/-)/Per3(-/-) mice are circadian oscillators with unusually short (similar to 21 h) periods. These data demonstrate that the canonical Period genes are involved in period determination in the FEO and MASCO, and computational modeling supports the hypothesis that the FEO and MASCO use the same timekeeping mechanism or are the same circadian oscillator. Finally, these studies identify Per1(-/-)/Per2(-/-)/Per3(-/-) mice as a unique tool critical to the search for the elusive anatomical location(s) of the FEO and MASCO.

Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations

An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.

Intrinsic organization of the suprachiasmatic nucleus in the capuchin monkey

The suprachiasmatic nucleus (SCN), which is the main circadian biological clock in mammals, is composed of multiple cells that function individually as independent oscillators to express the self-sustained mRNA and protein rhythms of the so-called clock genes. Knowledge regarding the presence and localization of the proteins and neuroactive substances of the SCN are essential for understanding this nucleus and for its successful manipulation. Although there have been advances in the investigation of the intrinsic organization of the SCN in rodents, little information is available in diurnal species, especially in primates. This study, which explores the pattern of expression and localization of PER2 protein in the SCN of capuchin monkey, evaluates aspects of the circadian system that are common to both primates and rodents. Here, we showed that PER2 protein immunoreactivity is higher during the light phase. Additionally, the complex organization of cells that express vasopressin, vasoactive intestinal polypeptide, neuron-specific nuclear protein, calbindin and calretinin in the SCN, as demonstrated by their immunoreactivity, reveals an intricate network that may be related to the similarities and differences reported between rodents and primates in the literature.

Universal behavior of the Shannon mutual information of critical quantum chains

We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its finite-size behavior yields the conformal anomaly c of the underlying conformal field theory governing the long-distance physics of the quantum chain. We study analytically a chain of coupled harmonic oscillators and numerically the Q-state Potts models (Q = 2, 3, and 4), the XXZ quantum chain, and the spin-1 Fateev-Zamolodchikov model. The Shannon mutual information is a quantity easily computed, and our results indicate that for relatively small lattice sizes, its finite-size behavior already detects the universality class of quantum critical behavior.

Mathematical models of cognitive processes

The research activity carried out during the PhD course was focused on the development of mathematical models of some cognitive processes and their validation by means of data present in literature, with a double aim: i) to achieve a better interpretation and explanation of the great amount of data obtained on these processes from different methodologies (electrophysiological recordings on animals, neuropsychological, psychophysical and neuroimaging studies in humans), ii) to exploit model predictions and results to guide future research and experiments. In particular, the research activity has been focused on two different projects: 1) the first one concerns the development of neural oscillators networks, in order to investigate the mechanisms of synchronization of the neural oscillatory activity during cognitive processes, such as object recognition, memory, language, attention; 2) the second one concerns the mathematical modelling of multisensory integration processes (e.g. visual-acoustic), which occur in several cortical and subcortical regions (in particular in a subcortical structure named Superior Colliculus (SC)), and which are fundamental for orienting motor and attentive responses to external world stimuli. This activity has been realized in collaboration with the Center for Studies and Researches in Cognitive Neuroscience of the University of Bologna (in Cesena) and the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA). PART 1. Objects representation in a number of cognitive functions, like perception and recognition, foresees distribute processes in different cortical areas. One of the main neurophysiological question concerns how the correlation between these disparate areas is realized, in order to succeed in grouping together the characteristics of the same object (binding problem) and in maintaining segregated the properties belonging to different objects simultaneously present (segmentation problem). Different theories have been proposed to address these questions (Barlow, 1972). One of the most influential theory is the so called “assembly coding”, postulated by Singer (2003), according to which 1) an object is well described by a few fundamental properties, processing in different and distributed cortical areas; 2) the recognition of the object would be realized by means of the simultaneously activation of the cortical areas representing its different features; 3) groups of properties belonging to different objects would be kept separated in the time domain. In Chapter 1.1 and in Chapter 1.2 we present two neural network models for object recognition, based on the “assembly coding” hypothesis. These models are networks of Wilson-Cowan oscillators which exploit: i) two high-level “Gestalt Rules” (the similarity and previous knowledge rules), to realize the functional link between elements of different cortical areas representing properties of the same object (binding problem); 2) the synchronization of the neural oscillatory activity in the γ-band (30-100Hz), to segregate in time the representations of different objects simultaneously present (segmentation problem). These models are able to recognize and reconstruct multiple simultaneous external objects, even in difficult case (some wrong or lacking features, shared features, superimposed noise). In Chapter 1.3 the previous models are extended to realize a semantic memory, in which sensory-motor representations of objects are linked with words. To this aim, the network, previously developed, devoted to the representation of objects as a collection of sensory-motor features, is reciprocally linked with a second network devoted to the representation of words (lexical network) Synapses linking the two networks are trained via a time-dependent Hebbian rule, during a training period in which individual objects are presented together with the corresponding words. Simulation results demonstrate that, during the retrieval phase, the network can deal with the simultaneous presence of objects (from sensory-motor inputs) and words (from linguistic inputs), can correctly associate objects with words and segment objects even in the presence of incomplete information. Moreover, the network can realize some semantic links among words representing objects with some shared features. These results support the idea that semantic memory can be described as an integrated process, whose content is retrieved by the co-activation of different multimodal regions. In perspective, extended versions of this model may be used to test conceptual theories, and to provide a quantitative assessment of existing data (for instance concerning patients with neural deficits). PART 2. The ability of the brain to integrate information from different sensory channels is fundamental to perception of the external world (Stein et al, 1993). It is well documented that a number of extraprimary areas have neurons capable of such a task; one of the best known of these is the superior colliculus (SC). This midbrain structure receives auditory, visual and somatosensory inputs from different subcortical and cortical areas, and is involved in the control of orientation to external events (Wallace et al, 1993). SC neurons respond to each of these sensory inputs separately, but is also capable of integrating them (Stein et al, 1993) so that the response to the combined multisensory stimuli is greater than that to the individual component stimuli (enhancement). This enhancement is proportionately greater if the modality-specific paired stimuli are weaker (the principle of inverse effectiveness). Several studies have shown that the capability of SC neurons to engage in multisensory integration requires inputs from cortex; primarily the anterior ectosylvian sulcus (AES), but also the rostral lateral suprasylvian sulcus (rLS). If these cortical inputs are deactivated the response of SC neurons to cross-modal stimulation is no different from that evoked by the most effective of its individual component stimuli (Jiang et al 2001). This phenomenon can be better understood through mathematical models. The use of mathematical models and neural networks can place the mass of data that has been accumulated about this phenomenon and its underlying circuitry into a coherent theoretical structure. In Chapter 2.1 a simple neural network model of this structure is presented; this model is able to reproduce a large number of SC behaviours like multisensory enhancement, multisensory and unisensory depression, inverse effectiveness. In Chapter 2.2 this model was improved by incorporating more neurophysiological knowledge about the neural circuitry underlying SC multisensory integration, in order to suggest possible physiological mechanisms through which it is effected. This endeavour was realized in collaboration with Professor B.E. Stein and Doctor B. Rowland during the 6 months-period spent at the Department of Neurobiology and Anatomy of the Wake Forest University School of Medicine (NC, USA), within the Marco Polo Project. The model includes four distinct unisensory areas that are devoted to a topological representation of external stimuli. Two of them represent subregions of the AES (i.e., FAES, an auditory area, and AEV, a visual area) and send descending inputs to the ipsilateral SC; the other two represent subcortical areas (one auditory and one visual) projecting ascending inputs to the same SC. Different competitive mechanisms, realized by means of population of interneurons, are used in the model to reproduce the different behaviour of SC neurons in conditions of cortical activation and deactivation. The model, with a single set of parameters, is able to mimic the behaviour of SC multisensory neurons in response to very different stimulus conditions (multisensory enhancement, inverse effectiveness, within- and cross-modal suppression of spatially disparate stimuli), with cortex functional and cortex deactivated, and with a particular type of membrane receptors (NMDA receptors) active or inhibited. All these results agree with the data reported in Jiang et al. (2001) and in Binns and Salt (1996). The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain the fundamental aspects of multisensory integration, and provides a biologically plausible hypothesis about the underlying circuitry.

Dynamical measurements with quartz resonators

Dynamische Messungen mit Quarzresonatoren Die Resonanzfrequenz von Quarzoszillatoren liegt im MHz-Bereich. Die Resonanzen haben hohe Gueten und sind somit empfindlich auf kleine Aenderungen an der Resonatoroberflaeche. 1. Es wurde ein Aufbau entwickelt, um Reibung bei hohen Oberflaechengeschwindigkeiten zu messen (v = 1 m/s). Bei Annaeherung einer Kugel steigen Resonanzfrequenz sowie -breite des Schwingquarzes an. Für groeßere Normalkraefte entsteht ein elastischer Kontakt, der die Frequenzerhoehung erklaert. Kurz vor Eintreten dieses Kontaktes durchlaeuft die Daempfung ein Maximum, das charakteristisch ist für das Auftreten von Reibung. Bei Erhoehung der Schichtdicke (0,4-2,5 nm) einer Schmiermittelbeschichtung (Perfluoropolyether) verringern sich sowohl die Hoehe als auch die Breite dieses Maximums. Es verschwindet mit vollstaendiger Belegung mit einer Monolage (ca. 2 nm). Dies wird durch einen intermittierenden Kontakt der beiden Oberflaechen erklaert. 2. Die Schwingquarzoberfläche wurde mit Polymerbuersten verschiedener Schichtdicken (12-230 nm) beschichtet. Der Loesungsmittelgehalt in diesen Filmen variiert mit dem Dampfdruck der umgebenden Toluolatmosphaere. Bei Trocknung durchlaufen die Filme einen loesungsmittelinduzierten Glasuebergang. Die Sorptionskurven (Loesungsmittelgehalt gegen Dampfdruck) zeigen eine Knick beim Glasuebergang, ihre Ableitungen dagegen eine Stufe. Fuer duenner werdende Schichten verschiebt sich diese Stufe zu niedrigerem Dampfdruck sowie geringerem Loesungsmittelgehalt. Außerdem wird sie breiter und ihre Hoehe nimmt ab.

Systematische Untersuchung von Instabilitäten an lasergekühlten 40 Ca + - Ionen in einer linearen Paulfalle

In linearen Paulfallen gespeicherte und lasergekühlte Ionen stellen in weiten Bereichen der Physik ideale Objekte hinsichtlich störungsfreier und präziser Messungen atomarer Übergangsfrequenzen und der gezielten Manipulation von Quantenzuständen dar. Eine Einschränkung dieser optimalen Bedingungen erfolgt durch Heizmechanismen, die aus Abweichungen des Speicherpotentials von der idealen Quadrupolform resultieren. Höhere Potentialordnungen führen zu einer Kopplung der radialen Bewegungsmoden und bei bestimmten Speicherparametern zu nichtlinearen Resonanzen. Hierbei werden die Ionenbahnen durch eine Energieaufnahme aus dem Speicherfeld destabilisiert. Dieses kann zu Linienverbreiterungen, einer Limitierung der Kohärenzzeiten und unter Umständen zu einem Ionenverlust führen. Die systematische Untersuchung dieser Instabilitäten in einer linearen Paulfalle erfolgt durch Spektroskopie an einer kleinen Anzahl lasergekühlter ^40Ca^+ - Ionen. Der experimentell zugängliche Speicherbereich wird mit hoher Auflösung abgetastet. Durch eine eingehende Quantifizierung der Falleneigenschaften werden die nichtlinearen Resonanzen eindeutig den erzeugenden Potentialtermen zugeordnet. Die Resonanzlinien zeigen eine charakteristische Aufspaltung, deren Größe vom angelegten Axialpotential bestimmt wird. Diese zusätzliche Kopplung der Radialbewegung an die Axialbewegung führt zu einer modifizierten Resonanzbedingung. Nichtlineare Resonanzen treten massenspezifisch auf. Da eine präzise Kontrolle der Axialpotentiale sehr einfach ist, könnten die beobachteten radial-axial koppelnden Resonanzen eine Anwendung in der Massenspektrometrie finden.

Advanced signal and receiver design for next generation OFDM systems

This thesis deal with the design of advanced OFDM systems. Both waveform and receiver design have been treated. The main scope of the Thesis is to study, create, and propose, ideas and novel design solutions able to cope with the weaknesses and crucial aspects of modern OFDM systems. Starting from the the transmitter side, the problem represented by low resilience to non-linear distortion has been assessed. A novel technique that considerably reduces the Peak-to-Average Power Ratio (PAPR) yielding a quasi constant signal envelope in the time domain (PAPR close to 1 dB) has been proposed.The proposed technique, named Rotation Invariant Subcarrier Mapping (RISM),is a novel scheme for subcarriers data mapping,where the symbols belonging to the modulation alphabet are not anchored, but maintain some degrees of freedom. In other words, a bit tuple is not mapped on a single point, rather it is mapped onto a geometrical locus, which is totally or partially rotation invariant. The final positions of the transmitted complex symbols are chosen by an iterative optimization process in order to minimize the PAPR of the resulting OFDM symbol. Numerical results confirm that RISM makes OFDM usable even in severe non-linear channels. Another well known problem which has been tackled is the vulnerability to synchronization errors. Indeed in OFDM system an accurate recovery of carrier frequency and symbol timing is crucial for the proper demodulation of the received packets. In general, timing and frequency synchronization is performed in two separate phases called PRE-FFT and POST-FFT synchronization. Regarding the PRE-FFT phase, a novel joint symbol timing and carrier frequency synchronization algorithm has been presented. The proposed algorithm is characterized by a very low hardware complexity, and, at the same time, it guarantees very good performance in in both AWGN and multipath channels. Regarding the POST-FFT phase, a novel approach for both pilot structure and receiver design has been presented. In particular, a novel pilot pattern has been introduced in order to minimize the occurrence of overlaps between two pattern shifted replicas. This allows to replace conventional pilots with nulls in the frequency domain, introducing the so called Silent Pilots. As a result, the optimal receiver turns out to be very robust against severe Rayleigh fading multipath and characterized by low complexity. Performance of this approach has been analytically and numerically evaluated. Comparing the proposed approach with state of the art alternatives, in both AWGN and multipath fading channels, considerable performance improvements have been obtained. The crucial problem of channel estimation has been thoroughly investigated, with particular emphasis on the decimation of the Channel Impulse Response (CIR) through the selection of the Most Significant Samples (MSSs). In this contest our contribution is twofold, from the theoretical side, we derived lower bounds on the estimation mean-square error (MSE) performance for any MSS selection strategy,from the receiver design we proposed novel MSS selection strategies which have been shown to approach these MSE lower bounds, and outperformed the state-of-the-art alternatives. Finally, the possibility of using of Single Carrier Frequency Division Multiple Access (SC-FDMA) in the Broadband Satellite Return Channel has been assessed. Notably, SC-FDMA is able to improve the physical layer spectral efficiency with respect to single carrier systems, which have been used so far in the Return Channel Satellite (RCS) standards. However, it requires a strict synchronization and it is also sensitive to phase noise of local radio frequency oscillators. For this reason, an effective pilot tone arrangement within the SC-FDMA frame, and a novel Joint Multi-User (JMU) estimation method for the SC-FDMA, has been proposed. As shown by numerical results, the proposed scheme manages to satisfy strict synchronization requirements and to guarantee a proper demodulation of the received signal.

Study of molecules of astrochemical, astrophysical and atmospheric interest by means of High - Resolution Infrared Spectroscopy

The spectroscopic investigation of the gas-phase molecules relevant for the chemistry of the atmosphere and of the interstellar medium has been performed. Two types of molecules have been studied, linear and symmetric top. Several experimental high-resolution techniques have been adopted, exploiting the spectrometers available in Bologna, Venezia, Brussels and Wuppertal: Fourier-Transform-Infrared Spectroscopy, Cavity-Ring-Down Spectroscopy, Cavity-Enhanced-Absorption Spectroscopy, Tunable-Diode-Laser Spectroscopy. Concerning linear molecules, the spectra of a number of isotopologues of acetylene, 12C2D2, H12C13CD, H13C12CD, 13C12CD2, of DCCF and monodeuterodiacetylene DC4H, have been studied, from 320 to 6800 cm-1. This interval covers bending, stretching, overtone and combination bands, the focus on specific ranges depending on the molecule. In particular, the analysis of the bending modes has been performed for 12C2D2 (450-2200 cm-1), 13C12CD2 (450-1700 cm-1), DCCF (320-850cm-1) and DC4H (450-1100 cm-1), of the stretching-bending system for 12C2D2 (450-5500 cm-1) and of the 2nu1 and combination bands up to four quanta of excitation for H12C13CD, H13C12CD and 13C12CD2 (6130-6800 cm-1). In case of symmetric top molecules, CH3CCH has been investigated in the 2nu1 region (6200-6700 cm-1), which is particularly congested due to the huge network of states affected by Coriolis and anharmonic interactions. The bending fundamentals of 15ND3 (450-2700 cm-1) have been studied for the first time, characterizing completely the bending states, v2 = 1 and v4 = 1, whereas the analysis of the stretching modes, which evidenced the presence of several perturbations, has been started. Finally, the fundamental band nu4 of CF3Br in the 1190-1220 cm-1 region has been investigated. Transitions belonging to the CF379Br and CF381Br molecules have been identified since the spectra were recorded using a sample containing the two isotopologues in natural abundance. This allowed the characterization of the v4 = 1 state for both isotopologues and the evaluation of the bromine isotopic splitting.

Interacting quantum-dissipative tunnelling systems

Die Untersuchung von dissipativen Quantensystemen erm¨oglicht es, Quantenph¨anomene auch auf makroskopischen L¨angenskalen zu beobachten. Das in dieser Dissertation gew¨ahlte mikroskopische Modell erlaubt es, den bisher nur ph¨anomenologisch zug¨anglichen Effekt der Quantendissipation mathematisch und physikalisch herzuleiten und zu untersuchen. Bei dem betrachteten mikroskopischen Modell handelt es sich um eine 1-dimensionale Kette von harmonischen Freiheitsgraden, die sowohl untereinander als auch an r anharmonische Freiheitsgrade gekoppelt sind. Die F¨alle einer, respektive zwei anharmonischer Bindungen werden in dieser Arbeit explizit betrachtet. Hierf¨ur wird eine analytische Trennung der harmonischen von den anharmonischen Freiheitsgraden auf zwei verschiedenen Wegen durchgef¨uhrt. Das anharmonische Potential wird als symmetrisches Doppelmuldenpotential gew¨ahlt, welches mit Hilfe der Wick Rotation die Berechnung der ¨Uberg¨ange zwischen beiden Minima erlaubt. Das Eliminieren der harmonischen Freiheitsgrade erfolgt mit Hilfe des wohlbekannten Feynman-Vernon Pfadintegral-Formalismus [21]. In dieser Arbeit wird zuerst die Positionsabh¨angigkeit einer anharmonischen Bindung im Tunnelverhalten untersucht. F¨ur den Fall einer fernab von den R¨andern lokalisierten anharmonischen Bindung wird ein Ohmsches dissipatives Tunneln gefunden, was bei der Temperatur T = 0 zu einem Phasen¨ubergang in Abh¨angigkeit einer kritischen Kopplungskonstanten Ccrit f¨uhrt. Dieser Phasen¨ubergang wurde bereits in rein ph¨anomenologisches Modellen mit Ohmscher Dissipation durch das Abbilden des Systems auf das Ising-Modell [26] erkl¨art. Wenn die anharmonische Bindung jedoch an einem der R¨ander der makroskopisch grossen Kette liegt, tritt nach einer vom Abstand der beiden anharmonischen Bindungen abh¨angigen Zeit tD ein ¨Ubergang von Ohmscher zu super- Ohmscher Dissipation auf, welche im Kern KM(τ ) klar sichtbar ist. F¨ur zwei anharmonische Bindungen spielt deren indirekteWechselwirkung eine entscheidende Rolle. Es wird gezeigt, dass der Abstand D beider Bindungen und die Wahl des Anfangs- und Endzustandes die Dissipation bestimmt. Unter der Annahme, dass beide anharmonischen Bindung gleichzeitig tunneln, wird eine Tunnelwahrscheinlichkeit p(t) analog zu [14], jedoch f¨ur zwei anharmonische Bindungen, berechnet. Als Resultat erhalten wir entweder Ohmsche Dissipation f¨ur den Fall, dass beide anharmonischen Bindungen ihre Gesamtl¨ange ¨andern, oder super-Ohmsche Dissipation, wenn beide anharmonischen Bindungen durch das Tunneln ihre Gesamtl¨ange nicht ¨andern.

Self-sufficient control of urate homeostasis in mice by a synthetic circuit

Synthetic biology has shown that the metabolic behavior of mammalian cells can be altered by genetic devices such as epigenetic and hysteretic switches, timers and oscillators, biocomputers, hormone systems and heterologous metabolic shunts. To explore the potential of such devices for therapeutic strategies, we designed a synthetic mammalian circuit to maintain uric acid homeostasis in the bloodstream, disturbance of which is associated with tumor lysis syndrome and gout. This synthetic device consists of a modified Deinococcus radiodurans-derived protein that senses uric acids levels and triggers dose-dependent derepression of a secretion-engineered Aspergillus flavus urate oxidase that eliminates uric acid. In urate oxidase-deficient mice, which develop acute hyperuricemia, the synthetic circuit decreased blood urate concentration to stable sub-pathologic levels in a dose-dependent manner and reduced uric acid crystal deposits in the kidney. Synthetic gene-network devices providing self-sufficient control of pathologic metabolites represent molecular prostheses, which may foster advances in future gene- and cell-based therapies.

The Role of Anharmonicity in Hydrogen-Bonded Systems: The Case of Water Clusters

The nature of vibrational anharmonicity has been examined for the case of small water clusters using second-order vibrational perturbation theory (VPT2) applied on second-order Møller–Plesset perturbation theory (MP2) potential energy surfaces. Using a training set of 16 water clusters (H2O)n=2–6,8,9 with a total of 723 vibrational modes, we determined scaling factors that map the harmonic frequencies onto anharmonic ones. The intermolecular modes were found to be substantially more anharmonic than intramolecular bending and stretching modes. Due to the varying levels of anharmonicity of the intermolecular and intramolecular modes, different frequency scaling factors for each region were necessary to achieve the highest accuracy. Furthermore, new scaling factors for zero-point vibrational energies (ZPVE) and vibrational corrections to the enthalpy (ΔHvib) and the entropy (Svib) have been determined. All the scaling factors reported in this study are different from previous works in that they are intended for hydrogen-bonded systems, while others were built using experimental frequencies of covalently bonded systems. An application of our scaling factors to the vibrational frequencies of water dimer and thermodynamic functions of 11 larger water clusters highlights the importance of anharmonic effects in hydrogen-bonded systems.

Benchmark Structures and Binding Energies of Small Water Clusters with Anharmonicity Corrections

For (H2O)n where n = 1–10, we used a scheme combining molecular dynamics sampling with high level ab initio calculations to locate the global and many low lying local minima for each cluster. For each isomer, we extrapolated the RI-MP2 energies to their complete basis set limit, included a CCSD(T) correction using a smaller basis set and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled and unscaled harmonic vibrational frequencies. The vibrational scaling factors were determined specifically for water clusters by comparing harmonic frequencies with VPT2 fundamental frequencies. We find the CCSD(T) correction to the RI-MP2 binding energy to be small (<1%) but still important in determining accurate conformational energies. Anharmonic corrections are found to be non-negligble; they do not alter the energetic ordering of isomers, but they do lower the free energies of formation of the water clusters by as much as 4 kcal/mol at 298.15 K.

In search of CS2(H2O)n = 1–4 clusters

Gaussian-3 and MP2/aug-cc-pVnZ methods have been used to calculate geometries and thermochemistry of CS2(H2O)n, where n = 1–4. An extensive molecular dynamics search followed by optimization using these two methods located two dimers, six trimers, six tetramers, and two pentamers. The MP2/aug-cc-pVDZ structure matched best with the experimental result for the CS2(H2O) dimer, showing that diffuse functions are necessary to model the interactions found in this complex. For larger CS2(H2O)n clusters, the MP2/aug-cc-pVDZ minima are significantly different from the MP2(full)/6-31G* structures, revealing that the G3 model chemistry is not suitable for investigation of sulfur containing van der Waals complexes. Based on the MP2/aug-cc-pVTZ free energies, the concentration of saturated water in the atmosphere and the average amount of CS2 in the atmosphere, the concentrations of these clusters are predicted to be on the order of 105CS2(H2O) clusters∙cm−3 and 102 CS2(H2O)2 clusters∙cm−3 at 298.15 K. The MP2/aug-cc-pVDZ scaled harmonic and anharmonic frequencies of the most abundant dimer cluster at 298 K are presented, along with the MP2/aug-cc-pVDZ scaled harmonic frequencies for the CS2(H2O)n structures predicted to be present in a low-temperature molecular beam experiment.

The Role of Anharmonicity in Hydrogen-Bonded Systems: The Case of Water Clusters

The nature of vibrational anharmonicity has been examined for the case of small water clusters using second-order vibrational perturbation theory (VPT2) applied on second-order Møller–Plesset perturbation theory (MP2) potential energy surfaces. Using a training set of 16 water clusters (H2O)n=2–6,8,9 with a total of 723 vibrational modes, we determined scaling factors that map the harmonic frequencies onto anharmonic ones. The intermolecular modes were found to be substantially more anharmonic than intramolecular bending and stretching modes. Due to the varying levels of anharmonicity of the intermolecular and intramolecular modes, different frequency scaling factors for each region were necessary to achieve the highest accuracy. Furthermore, new scaling factors for zero-point vibrational energies (ZPVE) and vibrational corrections to the enthalpy (ΔHvib) and the entropy (Svib) have been determined. All the scaling factors reported in this study are different from previous works in that they are intended for hydrogen-bonded systems, while others were built using experimental frequencies of covalently bonded systems. An application of our scaling factors to the vibrational frequencies of water dimer and thermodynamic functions of 11 larger water clusters highlights the importance of anharmonic effects in hydrogen-bonded systems.