High-resolution infrared and ab initio investigation of CHD2 79Br: Ro-vibrational analysis of the ν6 fundamental and the 2ν6−ν6 hot band

The high-resolution infrared spectrum of CHD₂ ⁷⁹Br has been investigated by Fourier transform spectroscopy in the range 540–615?cm^?1 at an unapodised resolution of 0.0035?cm^?1. This spectral region is characterised by the ν₆ fundamental (584.8510?cm^?1), corresponding to C–Br stretching mode, and its hot band 2ν₆?ν₆ (578.4333?cm^?1). The spectral analysis resulted in the identification of 3430 transitions (J’?≤?73 and K'_a ?≤?18) for the ν₆ fundamental and 1212 transitions (J’?≤?49 and K'_a ?≤?11) for the hot band 2ν₆?ν₆. The assigned data have been fitted using the Watson’s S-reduced Hamiltonian in the I^r representation and new constants for the ground state from about 24,600 combination differences and sets of parameters for the v ₆?=?1 and 2 vibrational states have been obtained. From spectral simulations the intensity ratio between 2ν₆?ν₆ and ν₆ has been estimated to be 0.15?±?0.02. High-quality ab initio calculations have also been performed at the CCSD(T) level of theory in order to support the experimental investigation through the calculation of molecular parameters relevant to ro-vibrational spectroscopy.     

High-resolution infrared spectrum of CHD279Br: ro-vibrational analysis of the ν5 and ν9 fundamentals

ABSTRACT

The high-resolution infrared spectrum of CHD₂⁷⁹Br has been investigated by Fourier transform spectroscopy in the range 700–900?cm^?1 at an unapodized resolution of 0.0035?cm^?1. This spectral region is characterised by the absorptions of the ν₅ (814.5185?cm^?1) and ν₉ (716.9649?cm^?1) fundamental bands, corresponding to H–C–Br deformation and CD₂ rocking modes, respectively. The ν₅ vibration of symmetry species A^′ gives rise to an a-/c-hybrid band with a predominant a-type component, while the ν₉ mode of A^′′ symmetry produces a b-type envelope. The spectral analysis resulted in the identification of 5290 (J^′?≤?63 and K_a^′?≤?13) and 1657 (J^′?≤?53 and K_a^′?≤?12) transitions for ν₅ and ν₉ bands, respectively. The assigned data were fitted using the Watson’s S-reduced Hamiltonian in the I^r representation and the v₅?=?1 and v₉?=?1 state parameters up to the quartic centrifugal distortion terms have been obtained. From spectral simulations the dipole moment ratio |Δμ_a/Δμ_c| of the ν₅ band has been determined to be 1.4?±?0.1 while the intensity ratio between ν₅ and ν₉ fundamentals has been estimated to have a value of 4.3?±?0.5.     

Intramolecular cyclisation of isosorbide by dimethylcarbonate chemistry

In this work the synthesis of a tricyclic isosorbide derivative in moderate yield directly from the dicarboxymethyl isosorbide in a continuous-flow apparatus is reported. The tricyclic structure has been isolated as pure and fully characterized. This product confirms the potentiality of dimethylcarbonate (DMC) as dehydrating agent also for complicated structure and opens up further investigation and application of DMC chemistry on renewable starting materials.     

Exact methods for large-scale multi-period financial planning problems

A relevant financial planning problem is the periodical rebalance of a portfolio of assets such that the portfolio’s total value exhibits certain characteristics. This problem can be modelled using a transition graph G to represent the future state space evolution of the corresponding economy and mathematically formulated as a linear programming problem. We present two different mathematical formulations of the problem. The first considers explicitly the set of the possible scenarios (scenario-based approach), while the second considers implicitly the whole set of scenarios provided by the graph G (graph-based approach). Unfortunately, for both the formulations the size of the corresponding linear programs can be huge even for simple financial problems. However, the graph-based approach seems to be a more powerful model, since it allows to consider a huge number of scenarios in a very compact formulation. The purpose of this paper is to present both heuristic and exact methods for the solution of large-scale multi-period financial planning problems using the graph-based model. In particular, in this paper we propose lower and upper bounds and three exact methods based on column, row and column/row generation, respectively. Since the methods based on column/row generation exploits simultaneously both the primal and the dual structure of the problem we call it Criss-Cross generation method. Computational results are given to prove the effectiveness of the proposed methods.      

Exact algorithms for routing problems under vehicle capacity constraints

The solution of a vehicle routing problem calls for the determination of a set of routes, each performed by a single vehicle which starts and ends at its own depot, such that all the requirements of the customers are fulfilled and the global transportation cost is minimized. The routes have to satisfy several operational constraints which depend on the nature of the transported goods, on the quality of the service level, and on the characteristics of the customers and of the vehicles. One of the most common operational constraint addressed in the scientific literature is that the vehicle fleet is capacitated and the total load transported by a vehicle cannot exceed its capacity.     

Jet-cooled diode laser spectra of CF3Br in the 9.2 microm region and rovibrational analysis of symmetric CF3 stretching mode

Pulsed slit-jet high resolution (up to 0.0009 cm(-1) FWHM) infrared diode laser spectra of CF(3)Br, with natural isotopic abundance, were obtained in the region around 9.2 microm at the rotational temperature of about 50 K. In addition, diode laser spectra at reduced temperature (200 K) were recorded. We present here the rovibrational analysis of the nu(1) fundamental in the range 1075-1090 cm(-1). The fine structure of many P(J) and R(J) clusters has been well resolved for the first time. The assignment of rovibrational transitions has been accomplished up to K = 27, J = 63 for CFBr and K = 33, J = 62 for CFBr. A total of 636 (CFBr) and 880 (CFBr) lines were used in the final fit and a very accurate set of molecular constants, including the quartic centrifugal distortion coefficients for the v(1) = 1 state of both the bromine isotopologues, was obtained. In addition, spectral features belonging to the nu(1) + nu(6)-nu(6) hot band were unambiguously identified and a set of spectroscopic parameters were determined.     

High-Resolution Analysis of the nu(4) Absorption Band of CH(2)(79)BrF

The gas-phase infrared spectrum of the nu(4) fundamental band of CH(2)(79)BrF was recorded in the 1010-1116 cm(-1) wavenumber region using a TDL spectrometer. In this first high-resolution investigation of the synthesized (79)Br isotopic form, more than 10 200 transitions of this a/b-hybrid band centered at 1068.5385 cm(-1) were assigned and, using the Watson's A-reduced Hamiltonian in the I(r)-representation, a reliable set of molecular constants for the excited state v(4) = 1 was determined. From ground state combination differences having rotational quantum numbers J and K(a) up to 97 and 21, respectively, improved and extended ground state rotational and centrifugal distortion constants were calculated as well. Comparison between the observed and calculated band intensities in appropriate regions of the spectrum gave an estimate of the transition dipole-moment ratio along the a and b axes as ||Deltaμ(a)/Deltaμ(b) || = 2.0 +/- 0.2, in agreement with the predicted theoretical value of 1.99. Copyright 2000 Academic Press.     

High-resolution infrared spectroscopy of the interacting ν9, ν5 + ν6 and 3ν6 levels of CH2BrF

The high-resolution (0.0030 cm⁻¹) Fourier transform infrared spectrum of CH₂⁷⁹BrF has been studied in part of the atmospheric window between 910 and 980 cm⁻¹, the region of the ν₉ (935.847 cm⁻¹) and ν₅ + ν₆ (961.239 cm⁻¹) bands. The ν₉ fundamental consists of a pseudo a-type band induced by Coriolis coupling with ν₅ + ν₆, in turn exhibiting a predominant a-type structure. Several interactions connecting these levels and the dark state 3ν₆ have been assessed. The whole data set is treated using Watson’s A-reduced Hamiltonian in the I^r representation implemented with first order a- and b- and c-type Coriolis terms. A detailed analysis of the rotational structure yields a set of accurate upper-state parameters up to quartic distortion terms for ν₉ and ν₅ + ν₆. In addition, spectroscopic information about the dark ternary overtone of ν₆ has been obtained.     

Microwave, high-resolution infrared, and quantum chemical investigations of CHBrF2: ground and v4 = 1 states

A combined microwave, infrared, and computational investigation of CHBrF(2) is reported. For the vibrational ground state, measurements in the millimeter- and sub-millimeter-wave regions for CH(79)BrF(2) and CH(81)BrF(2) provided rotational and centrifugal-distortion constants up to the sextic terms as well as the hyperfine parameters (quadrupole-coupling and spin-rotation interaction constants) of the bromine nucleus. The determination of the latter was made possible by recording of spectra at sub-Doppler resolution, achieved by means of the Lamb-dip technique, and supporting the spectra analysis by high-level quantum chemical calculations at the coupled-cluster level. In this context, the importance of relativistic effects, which are of the order of 6.5% and included in the present work using second-order direct perturbation theory, needs to be emphasized for accurate predictions of the bromine quadrupole-coupling constants. The infrared measurements focused on the ν(4) fundamental band of CH(79)BrF(2). Fourier transform investigations using a synchrotron radiation source provided the necessary resolution for the observation and analysis of the rotational structure. The spectroscopic parameters of the v(4) = 1 state were found to be close to those of the vibrational ground state, indicating that the ν(4) band is essentially unaffected by perturbations.