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Groundwater and Intruder Radionuclide Screening

Solid Waste Management (SWM) operates the E-Area Low-Level Waste Facility (ELLWF) where low level on-site and off-site solid waste streams are buried. The facility has been in operation since late 1994 and is currently projected to remain in operation until 2065. This facility can accommodate a broad range of waste forms resulting from the six different types of disposal unit options (i.e., varying degrees of engineered barriers → trenches to concrete vaults). This facility is currently operating under a Performance Assessment (PA) issued back in 2008, along with several subsequent supporting Special Analyses (SA). The Savannah River National Laboratory (SRNL) developed the prior PAs and SAs and has been tasked to update the facility’s PA. For operating the E-Area facility, a Waste Inventory Tracking System (e.g., WITS) is actively employed by waste generators where every radionuclide entering the facility (to be buried in one of its many disposal units1) must be either directly or indirectly accounted for. Since there is a large number of radionuclides in existence (>3,000), the International Commission on Radiological Protection (ICRP-107) has provided guidance on the subset of radionuclides requiring further assessment in landfills such as the E-Area LLWF. The ICRP-107 publication provides critical radiological information on 1,252 radionuclides of 97 elements. This database is the critical starting point for developing a consistent inventory limit system. The explicit measurement and tracking of all 1,252 ICRP-107 radionuclides can be reduced when process knowledge, burial history, and radiological aspects are factored into conservative groundwater and intruder screening processes. Across the DOE complex these screening processes have been historically performed using the methodology suggested by the National Council on Radiation Protection and Measurements (NCRP) as presented in their original report (NCRP 1984) and then refined in a later report (NCRP 1996). In the recommended screening models employed within this report the traditional NCRP models are updated to better handle progeny and better reflect the known characteristics of E-Area. This improved screening process is referred to as the “NCRP-like” method. Various upgrades to the traditional NCRP methodology have been used by others (e.g., NRC funded effort by Kennedy and Strenge 1992). The more detailed models by Kennedy and Strenge (1992) were considered in this effort and are compared to the results from the more traditional NCRP-like models. The groundwater and inadvertent intruder screening analyses presented in this report start with this 1,252 radionuclide list and reduces it down to more manageable lists that are applicable to the various disposal unit types contained within E-Area. In order to reduce this starting list, some level of exposure risk must be considered acceptable. Historically, a dose (or concentration level) has been compared with a screening criterion set to 1% of a performance measure (e.g., a betagamma dose not to exceed the 4 mrem/yr beta-gamma performance measure x 0.01 = 0.04 mrem/yr). Thus, if a radionuclide produced a bounding or screening-level dose (or concentrations) less than the screening criterion, it could be safely removed from further consideration. Several tiers of screening and bounding level analyses have been considered in this report.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Process Anomaly Detection for Sparsely Labeled Events in Nuclear Power Plants

An essential aspect of online monitoring, subtle anomaly detection increases the detection lead time for equipment failure and enables a nuclear power plant (NPP) to mitigate unexpected partial or full outages, resulting in significant cost saving to the plant. Once an anomaly is detected by plant staff, its cause and severity are investigated. Because the vast majority of anomalies require some level of investigation, including some that require time-consuming examination, before they are passed over to the engineering organization for further analysis, plants are often equipped with tools to assist the staff in performing anomaly detection. Those tools operate as a black box and are often based on statistical methods that establish sensor correlations using preconfigured mathematical models and flag correlation deviations as anomalies. Due to the number of anomalies detected at a given NPP on a daily basis, a significant number of flagged anomalies usually await examination for days or weeks. A primary cause of this backlog is that the methods used by the tools generate many false positives. Though this is usually attributed to oversensitive model settings due to very narrow normal operation bands, it can also be associated with the model development being inadequate for the process being monitored, or with missing model inputs that could have explained misclassified positives. The performance of anomaly detection tools impacts their plant acceptance and utilization, especially when the effort to address false positives generated by the tool depletes the value or cost saved by using that tool. Thus, means to advance anomaly detection performance have been investigated by the Department of Energy’s Light Water Reactor Sustainability program. Previous and ongoing efforts have targeted unsupervised machine-learning (ML) methods, which do not require the labeling of any data fed into the ML model. By contrast, in supervised anomaly detection methods, every data point is labeled as either a normal or abnormal process condition, and the model is trained to replicate the classification process. Supervised methods usually outperform unsupervised methods, due to the added value in differentiating normal from anomalous states of the monitored process. An NPP’s corrective action program requires it to track and document, via a dedicated report, the resolution of any issues that occur within the plant. Once created, each report is reviewed by a plant screening committee, and several classifications and decisions are made. Recently, a collaborating NPP developed an artificial intelligence and ML-based classifier to categorize a condition report (CR) into classes that can serve to label the data as normal or anomalous. Applying CRs as labels represents a semi-supervised use case. Semi-supervised ML assumes that labels exist for some data points (i.e., labeled anomalies, in this case) but not for the rest. In this effort, semi-supervised ML methods were used to fuse data from CRs with anomaly detection methods in order to test the hypothesis that partially labeled anomalies would improve the accuracy of the anomaly detection methods. Specifically, two methods were used. The first is the deep Semi-supervised Anomaly Detection (deep SAD) method, which can handle labels ranging from fully unsupervised to fully supervised cases. The second is a newly designed ML method developed specifically for this effort and referred to as the high-order feature (HOF)-based method. To evaluate these two methods in controlled environments, synthetic data generators were developed and used. The first datasets used a spring-mass-damper (SMD) system simulator commonly found in mechanical engineering references. This was used to create two use cases: a one- and a three-mass system. Anomalies were introduced by changing the spring and damper coefficients while the system was actuated by random forces. The second datasets used the commercial Dymola-Modelica software to build a simplified nuclear reactor model. Anomalies were added in the form of corrupted sensor readings and/or control commands. The deep SAD method was tested using the SMD system, while the HOF method was tested using both datasets. Application of the deep SAD semi-supervised ML method demonstrated that labels can generate increased confidence in detecting true anomalies. This helped increase the number of true positives and decrease the number of false negatives—something that would aid in addressing the backlog of possible anomalies. Application of the HOF method demonstrated that labels can aid in down selecting from a candidate set of features to a more optimal subset in order to better differentiate between normal and anomalous conditions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Improving Bond Dissociations of Reactive Machine Learning Potentials through Physics-Constrained Data Augmentation

In the field of computational chemistry, predicting bond dissociation energies (BDEs) presents well-known challenges, particularly due to the multireference character of reactive systems. Many chemical reactions involve configurations where single-reference methods fall short, as the electronic structure can significantly change during bond breaking. As generating training data for partially broken bonds is a challenging task, even state-of-the-art reactive machine learning interatomic potentials (MLIPs) often fail to predict reliable BDEs and smooth dissociation curves. By contrast, simple and inexpensive physics-based models, such as the well-established Morse potential, do not suffer from any such limitations. This work leverages the Morse potential to improve reactive MLIPs by augmenting the training data set with inexpensive Morse data along the dissociation pathways. Further, this physics-constrained data augmentation (PCDA) approach results in MLIPs with smooth bond dissociation curves as well as near coupled-cluster level BDEs, all without requiring any expensive multireference quantum mechanical calculations. A case study for methane combustion demonstrates how the PCDA approach can improve an existing reactive MLIP, namely, ANI-1xnr. In conclusion, not only are the BDEs and bond dissociation curves for all radicals and molecules significantly improved compared to ANI-1xnr but the PCDA-trained MLIP retains the reliability of ANI-1xnr when performing reactive molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

LUMINOUS SATELLITES VERSUS DARK SUBHALOS: CLUSTERING IN THE MILKY WAY

The observed population of the Milky Way satellite galaxies offers a unique testing ground for galaxy formation theory on small scales. Our novel approach was to investigate the clustering of the known Milky Way satellite galaxies and to quantify the amount of substructure within their distribution using a two-point correlation function statistic in each of three spaces: configuration space, line-of-sight velocity space, and four-dimensional (4D) phase space. These results were compared to those for three sets of subhalos in the Via Lactea II cold dark matter (CDM) simulation defined to represent the luminous dwarfs. We found no evidence at a significance level above 2{sigma} of substructure within the distribution of the Milky Way satellite galaxies in any of the three spaces. The 'luminous' subhalo sets are more strongly clustered than are the Milky Way satellites in all three spaces and over a broader range of scales in 4D phase space. Each of the 'luminous' subhalo sets are clustered as a result of substructure within their line-of-sight velocity space distributions at greater than 3{sigma} significance, whereas the Milky Way satellite galaxies are randomly distributed in line-of-sight velocity space. While our comparison is with only one CDM simulation, the inconsistencies between the Milky Way satellite galaxies and the Via Lactea II subhalo sets for all clustering methods suggest a potential new 'small-scale' tension between CDM theory and the observed Milky Way satellites. Future work will obtain a more robust comparison between the observed Milky Way satellites and CDM theory by studying additional simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

Systematic Evaluation of Stochastic Methods in Power System Scheduling and Dispatch with Renewable Energy

As more wind power and other renewable resources are being integrated into the electric power grid, the forecast uncertainty brings operational challenges for the power system operators. In this report, different operational strategies for uncertainty management are presented and evaluated. A comprehensive and consistent simulation framework is developed to analyze the performance of different reserve policies and scheduling techniques under uncertainty in wind power. Numerical simulations are conducted on a modified version of the IEEE 118-bus system with a 20% wind penetration level, comparing deterministic, interval, and stochastic unit commitment strategies. The results show that stochastic unit commitment provides a reliable schedule without large increases in operational costs. Moreover, decomposition techniques, such as load shift factor and Benders decomposition, can help in overcoming the computational obstacles to stochastic unit commitment and enable the use of a larger scenario set to represent forecast uncertainty. In contrast, deterministic and interval unit commitment tend to give higher system costs as more reserves are being scheduled to address forecast uncertainty. However, these approaches require a much lower computational effort Choosing a proper lower bound for the forecast uncertainty is important for balancing reliability and system operational cost in deterministic and interval unit commitment. Finally, we find that the introduction of zonal reserve requirements improves reliability, but at the expense of higher operational costs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

An Explainable Machine-Learning Model for Compensatory Reserve Measurement: Methods for Feature Selection and the Effects of Subject Variability

Tracking vital signs accurately is critical for triaging a patient and ensuring timely therapeutic intervention. The patient’s status is often clouded by compensatory mechanisms that can mask injury severity. The compensatory reserve measurement (CRM) is a triaging tool derived from an arterial waveform that has been shown to allow for earlier detection of hemorrhagic shock. However, the deep-learning artificial neural networks developed for its estimation do not explain how specific arterial waveform elements lead to predicting CRM due to the large number of parameters needed to tune these models. Alternatively, we investigate how classical machine-learning models driven by specific features extracted from the arterial waveform can be used to estimate CRM. More than 50 features were extracted from human arterial blood pressure data sets collected during simulated hypovolemic shock resulting from exposure to progressive levels of lower body negative pressure. A bagged decision tree design using the ten most significant features was selected as optimal for CRM estimation. This resulted in an average root mean squared error in all test data of 0.171, similar to the error for a deep-learning CRM algorithm at 0.159. By separating the dataset into sub-groups based on the severity of simulated hypovolemic shock withstood, large subject variability was observed, and the key features identified for these sub-groups differed. This methodology could allow for the identification of unique features and machine-learning models to differentiate individuals with good compensatory mechanisms against hypovolemia from those that might be poor compensators, leading to improved triage of trauma patients and ultimately enhancing military and emergency medicine.

60 APPLIED LIFE SCIENCES↗

A mono-dimensional nuclear fuel performance analysis code, PUMA, development from a coupled approach

Multidimensional-multi-physical phenomena in nuclear fuels are treated as a set of mono-dimensional-coupled problems which encompass heat, displacement, fuel constituent redistribution, and fission gas release. Rather than uncoupling these coupled equations as in conventional fuel performance analysis codes, efforts are put into to obtain fully coupled solutions by relying on the recent advances of numerical analysis. Through this approach, a new SFR metal fuel performance analysis code, called PUMA (Performance of Uranium Metal fuel rod Analysis code) is under development. Although coupling between temperature and fuel constituent was made easily, the coupling between the mechanical equilibrium equation and a set of stiff kinetics equations for fission gas release is accomplished by introducing one-level Newton scheme through backward differentiation formula. Displacement equations from 1D finite element formulation of the mechanical equilibrium equation are solved simultaneously with stress equation, creep equation, swelling equation, and FGR equations. Calculations was made successfully such that the swelling and the hydrostatic pressure are interrelated each other. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Time-resolved spectroscopy using a chopper wheel as a fast shutter

Widely available, small form-factor, fiber-coupled spectrometers typically have a minimum exposure time measured in milliseconds, and thus cannot be used directly for time-resolved measurements at the microsecond level. Spectroscopy at these faster time scales is typically done with an intensified charge coupled device (CCD) system where the image intensifier acts as a “fast” electronic shutter for the slower CCD array. In this paper, we describe simple modifications to a commercially available chopper wheel system to allow it to be used as a “fast” mechanical shutter for gating a fiber-coupled spectrometer to achieve microsecond-scale time-resolved optical measurements of a periodically pulsed light source. With the chopper wheel synchronized to the pulsing of the light source, the time resolution can be set to a small fraction of the pulse period by using a chopper wheel with narrow slots separated by wide spokes. Different methods of synchronizing the chopper wheel and pulsing of the light sources are explored. The capability of the chopper wheel system is illustrated with time-resolved measurements of pulsed plasmas.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A 24 μm point source catalog of the galactic plane from Spitzer/MIPSGAL

In this contribution, we describe the applied methods to construct a 24 μm based point source catalog derived from the image data of the MIPSGAL 24 μm Galactic Plane Survey and the corresponding data products. The high quality catalog product contains 933,818 sources, with a total of 1,353,228 in the full archive catalog. The source tables include positional and photometric information derived from the 24 μm images, source quality and confusion flags, and counterpart photometry from matched 2MASS, GLIMPSE, and WISE point sources. Completeness decay data cubes are constructed at 1′ angular resolution that describe the varying background levels over the MIPSGAL field and the ability to extract sources of a given magnitude from this background. The completeness decay cubes are included in the set of data products. We present the results of our efforts to verify the astrometric and photometric calibration of the catalog, and present several analyses of minor anomalies in these measurements to justify adopted mitigation strategies.

79 ASTRONOMY AND ASTROPHYSICS↗

Network-Level Traffic Signal Cooperation: A Higher-Order Conflict Graph Approach

Traffic signal control and cooperation are extremely important to alleviate traffic congestion in a large traffic network. This study develops a higher-order conflict graph approach for network-wide traffic signal control and cooperation. A conflict graph is applied to model the traffic signal configurations, which identifies the conflict and unconflicted movements for each intersection. In conflict graph, the node represents each movement. The weight of each node can be defined as traffic volume, queue length, fuel consumption, or any weighted combinations of these measurements. The calculation of the optimal green light duration and green light sequence (for different movements) is equivalent to sequentially finding the maximum weight independent set (MWIS) in the conflict graph. The conflict graph also provides a uniform and efficient way to connect traffic signal operations among nearby intersections spatially. Then, we introduced the concept of the k -th order neighborhood to model the degree of connectivity between each movement to the movements at upstream or downstream intersections. The weight of each node in the higher-order conflict graph not only represents its own congestion level, but also relates to the traffic conditions of nearby intersections. Through this approach, the cooperation of multiple intersections can be realized by incorporating their spatial connectivity into conflict graph and solving the MWIS problem. A simulation network is built in SUMO to test the effectiveness of the proposed method. Results suggested that the proposed model outperformed other state-of-the-art signal control methods. Also, the scheme maintains good performance under varying traffic demands.

42 ENGINEERING↗

Trajectory analysis of the rotational dynamics of molecules

A method for analysis of the rotational dynamics of molecular systems has been proposed on the basis of the calculation of the set of exact classical vibrational–rotational trajectories. It has been proposed to compose and to numerically solve the complete system of dynamic equations consisting of Hamilton’s equations and generalized Euler equations for an arbitrary system. The computer algebra system can be applied to automatize the process of derivation and subsequent solution of dynamic equations. The variation of the picture of known bifurcation in the rotational dynamics of symmetric triatomic hydride molecules with an increase in vibrational excitation has been studied within the proposed approach. It has been shown that manifestations of bifurcation completely disappear at a quite high level of vibrational excitations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Measurements of $\sigma(V+D^{*})/\sigma(V)$ in $9.7$ fb$^{-1}$ at CDF Run II

The Standard Model of particle physics has been remarkably successful, but the non-perturbative features of quantum chromodynamics must be tested and modeled with data. There have been many such tests, focused primarily on the use of jet-based probes of heavy flavor (bottom and charm quark) production at hadron colliders. In this thesis, we propose and test a strategy for identifying heavy flavor in events containing a W or Z vector boson (a V boson); this technique probes a much lower energy regime than can be explored by jet-based methods. In a sample of W and Z events skimmed from 9.7 fb -1 of high- pT electron and muon data from CDF Run II p p collisions at center of mass energy √s = 1:96 GeV , we identify charm by fully reconstructing D* (2010) → D 0 (→ Kπ )π s decays at the track level. Using a binned fit of Δm=m(Kππ s ) m(Kπ ) to count reconstructed D* candidates, we then unfold these raw counts with acceptance values derived from Monte Carlo, and present measurements of σ(W + D* )/ σ(W) and σ(Z + D* )/ σ(Z) in the W/Z leptonic decay channels. All measurements are found to be in agreement with the predictions of Pythia 6.2 (PDF set CTEQ5L). These results include the first measurement of W/Z + c production in events with zero jet objects at the Tevatron, and the first measurement of W/Z +c production with p T (c) < 15 GeV at the Tevatron.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Excited-state uncertainties in lattice-QCD calculations of multi-hadron systems

Excited-state effects lead to hard-to-quantify systematic uncertainties in lattice quantum chromodynamics (LQCD) spectroscopy calculations when computationally accessible imaginary times are smaller than inverse excitation gaps, as often arises for multi-hadron systems with signal-to-noise problems. Lanczos residual bounds address this by providing two-sided constraints on energies that do not require assumptions beyond Hermiticity, but often give very conservative systematic uncertainty estimates. Here, a more-constraining set of gap bounds is introduced for hadron spectroscopy. These bounds provide tighter constraints whose validity requires an explicit assumption about an energy gap. Exactly solvable lattice field theory correlators are used to test the utility of residual and gap bounds at finite and infinite statistics. Two-sided bounds and other analysis methods are then applied to a high-statistics LQCD calculation of nucleon-nucleon scattering at $m_π\sim 800$ MeV. Generalized eigenvalue problem (GEVP) and Lanczos energy estimators are compatible when applied to the same correlator data, but analyses including different interpolating operators show statistically significant inconsistencies. However, two-sided bounds from all operators are consistent. Under the assumption that the number of energy levels below $NΔ$ and $ΔΔ$ thresholds is the same as for non-interacting nucleons, gap bounds are sufficient to constrain nucleon-nucleon scattering amplitudes at phenomenologically relevant precision. Lanczos methods further reveal that energy-eigenstate estimates from previously studied asymmetric correlators have not converged over accessible imaginary times. Nevertheless, data-driven examples demonstrate why assumptions are required to draw conclusions about the natures of two-nucleon ground states at these masses.

Detmold, William [MIT, Cambridge, CTP]↗

The {sup 18}O(d,p){sup 19}O reaction and the ANC method

The neutron capture rate {sup 18}O(n,γ){sup 19}O is important for analysis of nucleosynthesis in inhomogeneous Big Bang models and also for models of processes in massive red giant stars and AGB stars. Angular distributions of the {sup 18}O(d,p){sup 19}O reaction were measured at a deuteron energy of 16.3 MeV in NPI in Řež, Czech Republic, with the aim to determine Asymptotic Normalization Coefficients which can then be used for indirect determination of the direct contribution to the {sup 18}O(n,γ){sup 19}O process. In the experiment, the gas target with {sup 18}O isotope of high purity 99.9 % was used thus eliminating any contaminating reactions. Reaction products were measured by the set of 8 ΔE-E telescopes consisting of thin and thick silicon surface-barrier detectors. Angular distributions of proton transfers corresponding to 6 levels of {sup 19}O up to the 4.1093 MeV excitation energy were determined. The analysis of angular distributions in the angular range from 6 to 64 degree including also the angular distribution of elastically scattered deuterons was carried out by means of ECIS and DWUCK codes. From the determined ANCs the direct contribution to the radiative capture {sup 18}O(n,γ){sup 19}O was deduced and compared with existing direct measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

SU-G-TeP3-04: Evaluation of the Dose Enhancement with Gold Nanoparticle in Microdosimetry Level Using the Geant4-DNA Toolkit

Purpose: This study investigated the dose enhancement effect of using gold nanoparticles (GNP) as radiation sensitizers radiated by different photon beam energies. Microdosimetry of photon-irradiated GNP was determined by the Geant4-DNA process in the DNA scale. Methods: Monte Carlo simulation was conducted using the Geant4 toolkit (ver. 10.2). A GNP with different sizes (30, 50, and 100nm diameter sphere) and a DNA were placed in a water cube (1µm{sup 3}). The GNP was irradiated by photon beams with different energies (50, 100, and 150keV) and produced secondary electrons to increase the dose to the DNA. Energy depositions were calculated for both with and without GNP and to investigate the dose enhancement effect at the DNA. The distance between the GNP and DNA was varied to optimize the best GNP position to the DNA. The photon beam source was set to 200nm from the GNP in each simulation. Results: It is found that GNP had a dose enhancement effect on kV photon radiations. For Monte Carlo results on different GNP sizes, distances between the GNP and DNA, and photon beam energies, enhancement ratio was found increasing as GNP size increased. The distance between the GNP and DNA affected the result that as distance increased while the dose enhancement ratio decreased. However, the effect of changing distance was not as significant as varying the GNP size. In addition, increasing the photon beam energy also increased the dose enhancement ratio. The largest dose enhancement ratio was found to be 3.5, when the GNP (100nm diameter) irradiated by the 150keV photon beam was set to 80nm from the DNA. Conclusion: Dose enhancement was determined in the DNA with GNP in the microdosimetry scale. It is concluded that the dose enhancement varied with the photon beam energy, GNP size and distance between the GNP and DNA.

60 APPLIED LIFE SCIENCES↗

Operator-level quantum acceleration of non-logconcave sampling

Sampling from probability distributions of the form 𝝈 ∝ e −𝜷V , where V is a continuous potential, is a fundamental task across physics, chemistry, biology, computer science, and statistics. However, when V is nonconvex, the resulting distribution becomes non-logconcave, and classical methods such as Langevin dynamics often exhibit poor performance. We introduce a quantum algorithm that provably accelerates a broad class of continuous-time sampling dynamics. For Langevin dynamics, our method encodes the target Gibbs measure into the amplitudes of aquantum state, identified as the kernel of a block matrix derived from a factorization of the Witten Laplacian operator. This connection enables Gibbs sampling via singular value thresholding and yields up to a quartic quantum speedup over best-knownclassical Langevin-based methods in the non-logconcave setting. Building on this framework, we further develop the first quantum algorithm that accelerates replica exchange Langevin diffusion, a widely used method for sampling from complex, rugged energy landscapes.

97 MATHEMATICS AND COMPUTING↗

Theoretical spectroscopic investigations of HNS{sup q} and HSN{sup q} (q = 0, +1, −1) in the gas phase

We performed accurate ab initio investigations of the geometric parameters and the vibrational structure of neutral HNS/HSN triatomics and their singly charged anions and cations. We used standard and explicitly correlated coupled cluster approaches in connection with large basis sets. At the highest levels of description, we show that results nicely approach those obtained at the complete basis set limit. Moreover, we generated the three-dimensional potential energy surfaces (3D PESs) for these molecular entities at the coupled cluster level with singles and doubles and a perturbative treatment of triple excitations, along with a basis set of augmented quintuple-zeta quality (aug-cc-pV5Z). A full set of spectroscopic constants are deduced from these potentials by applying perturbation theory. In addition, these 3D PESs are incorporated into variational treatment of the nuclear motions. The pattern of the lowest vibrational levels and corresponding wavefunctions, up to around 4000 cm{sup −1} above the corresponding potential energy minimum, is presented for the first time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A theoretical study on 3-(4-methoxyphenyl)-1-(pyridin-2-Yl) prop-2-en-1-one

This study reports the geometric parameters, vibration frequencies, {sup 13}C and {sup 1}H NMR chemical shifts of 3-(4-Methoxyphenyl)-1-(pyridin-2-yl) prop-2-en-1-one (MPP) molecule calculated by B3LYP level of density functional theory (DFT) with 6-311++G(d,p) basis set. {sup 13}C and {sup 1}H NMR chemical shifts were calculated within GIAO approach which is one of the most common approaches. Additionally, 3D molecular surfaces such as molecular electrostatic potential (MEP) and electrostatic potential (ESP), were simulated by the same level. As a result, obtained theoretical results were found to be consistent with experimental ones. All of calculations were carried out Gaussian 09 package program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗