Spectroscopic constants calculations

Table I. CCSD(T) spectroscopic constants calculated for the 11 state of YC using the new ECP-based cc-pVnZ-PP (V/tZ-PP) and all-electron cc- pVQZ (-NR and -DK) basis sets for Y and cc-pV/fZ for C...

Table II. CCSD(T) spectroscopic constants calculated for the X state of HgH using the new ECP-based cc-pVwZ-PP (VifZ-PP) and aug-cc-pViiZ (AV/fZ-PP) basis sets for Hg. The cc-pViiZ and aug-cc-pVwZ basis sets were...

Table IV. Spectroscopic constants calculated for the state of Hg2 at the CCSD(T) level of theory using...

The polarizability a is an important second-order molecular property. Its variation with internuclear separation has been investigated for H2 and Hs by Zeroka,58 using the method of Das and Bersohn. Spectroscopic constants calculated from the BO and adiabatic KW functions for H2 were also studied by Wu and Beckel.59... 

Ground State of CO. The CO molecule has been extensively studied, both experimentally and theoretically. Table 14 compares ground-state 02+) spectroscopic constants calculated by the Hartree-Fock method109 and by the density functional approach99 with experiment.104 In addition to these spectroscopic constants, the polar nature of the molecule provides a further measurable quantity, the dipole moment. Since the intensities of infrared vibration-rotation bands allow the dipole moment to be determined as a function of C-O separation this provides a useful comparison with the results of ab initio calculations. For example, the positive sign obtained from the equilibrium dipole moment by Hartree-Fock calculations was viewed as a reason to question the negative value found experimentally, whereas the current view is that the positive sign is a defect of the Hartree-Fock method. 

Due to the multi-configurational nature of TI2, a multi-reference treatment appears to be necessary to obtain quantitative spectroscopic constants, and spin-orbit interactions are essential even for a qualitative description of the bonding situation. For a system like TI2, the KRCI approach is a very useful tool for molecular calculations. From the larger spin-orbit splitting in element 113, the (113)2 bond is expected to be even weaker than that of TI2. A preliminary study on (113)2 indicates that the spectroscopic constants calculated at the REP-KRCCSD(T) level are 3.82 A, 17 cm and 0.05 eV with the corresponding spin-orbit effects of 0.56 A, -46 cm and -0.81 eV, confirming this expectation. 

For the vibrational frequencies, the CAS(2,2)CCSD method performs noticeably better than the CAS(2,2)CISD[+Q]. This can be seen by examining the standard deviations shown in Table 3.9. In Table 3.11 some selected spectroscopic constants calculated for FH in the ground eiectronic state (X S+) are shown. The results are compared with the experimental values taken from Huber and Herzberg [64], with the exception of the dissociation energy, Dg, which was taken from Lonardo and Douglas [74]. To calculate the spectroscopic constants we used the numerical differentiation formulas. As one can expect, the values of the spectroscopic constants... 

The At2 species and other species containing At atom have brought the attention mainly for testing the rehabiUty of relativistic quantum mechanical methods [9, 28, 29, 92, 96, 97]. It came out notably that SOC strongly affects the properties of the closed-sheU At2 species. Spectroscopic constants calculated at CCSD(T) level using either the 4c Dirac-Coulomb Hamiltonian or an X2C Hamiltonian [9, 98], are presented in Table 20.1. 

In Table 9 we report the spectroscopic constants calculated for hydrogen fluoride and molecular nitrogen with the cc-pV/iZ sets. As can be seen, the properties of both these species are nearly converged for the quadruple zeta basis sets - differences between the results obtained with the quadruple and sextuple basis sets are a few tenths of a kcal mol in De, a few thousandths of an angstrom in re, and a few wavenumbers in ct>c- In fact, the errors in the Hartree-Fock calculations are rather small even with the triple zeta basis sets. 

The molecule S12, like Se, is of Dsd symmetry but in the soHd state it occupies sites of the much lower C211 symmetry [163]. Due to the low solubihty and the thermal decomposition on melting only solid state vibrational spectra have been recorded [2,79]. However, from carbon disulfide the compound Si2-CS2 crystallizes in which the S12 molecules occupy sites of the high Sg symmetry which is close to 03a [163]. The spectroscopic investigation of this adduct has resulted in a revision [79] of the earher vibrational assignment [2] and therefore also of the earlier force constants calculation [164]. In Fig. 24 the low-temperature Raman spectra of S12 and Si2-CS2 are shown. 

The CPF approach gives quantitative reement with the experimental spectroscopic constants (24-25) for the ground state of Cu2 when large one-particle basis sets are used, provided that relativistic effects are included and the 3d electrons are correlated. In addition, CPF calculations have given (26) a potential surface for Cus that confirms the Jahn-Teller stabilization energy and pseudorotational barrier deduced (27-28) from the Cus fluorescence spectra (29). The CPF method has been used (9) to study clusters of up to six aluminum atoms. 

Many of these points are well illustrated by Cu2, which has become a benchmark for theoretical calculations owing to its relative simplicity and the availability of accurate experimental data. The theoretical spectroscopic constants are quite poor unless the 3d electrons are correlated, even though both Cu atoms nominally have a 3d °4s occupation. In fact, quantitative agreement with experiment is achieved only if both the 3d and 4s electrons are correlated, both higher excitations and relativistic effects are included, and large one-particle basis sets, including several sets of polarization functions, are used (24,25). This level of treatment is difficult to apply even to Cua, let alone larger Cu clusters. 

This chapter is restricted to a discussion of halogen-bonded complexes B XY that involve a homo- or hetero-dihalogen molecule XY as the electron acceptor and one of a series of simple Lewis bases B, which are chosen for their simplicity and to provide a range of electron-donating abilities. Moreover, we shall restrict attention to the gas phase so that the experimental properties determined refer to the isolated complex. Comparisons with the results of electronic structure calculations are then appropriate. All of the experimental properties of isolated complexes B- XY considered here result from interpreting spectroscopic constants obtained by analysis of rotational spectra. 

An analysis of the Fourier Transform i.r. spectrum of PF around 946 cm-1 gave rise to nine spectroscopic constants for the Vg band and five for the Vg + v -v band which allowed calculation of the wavenumbers of the Vg band with a precision of 1 x 10-3 cm-1.11... 

Terms representing these interactions essentially make up the difference between the traditional force fields of vibrational spectroscopy and those described here. They are therefore responsible for the fact that in many cases spectroscopic force constants cannot be transferred to the calculation of geometries and enthalpies (Section 2.3.). As an example, angle deformation potential constants derived for force fields which involve nonbonded interactions often deviate considerably from the respective spectroscopic constants (7, 7 9, 21, 22). Nonbonded interactions strongly influence molecular geometries, vibrational frequencies, and enthalpies. They are a decisive factor for the transferability of force fields between systems of different strain (Section 2.3.). 

Bartell and coworkers investigated the structures of a series of noncyclic alkanes by means of gas electron diffraction (14, 44, 45) and invoked for the interpretation of their results a simple force field which contained to a high extent vibrational spectroscopic constants of Snyder and Schachtschneider. This force field reproduces bond lengths and bond angles of acyclic hydrocarbons well, energies of isomerisation satisfactorily. As an example, Fig. 8 shows geometry parameters of tri-t-butylmethane as observed by electron diffraction and calculated with this force field (14). 

In this chapter, we therefore consider whether it is possible to eliminate spin-orbit coupling from four-component relativistic calculations. This is a situation quite different from that of more approximate relativistic methods where a considerable effort is required for the inclusion of spin-orbit coupling. We have previously shown that it is indeed possible to eliminate spin-orbit coupling from the calculation of spectroscopic constants [12,13]. In this chapter, we consider the extension of the previous result to the calculation of second-order electric and magnetic properties, i.e., linear response functions. Although the central question of this article may seem somewhat technical, it will be seen that its consideration throws considerable light on the fundamental interactions in molecular systems. We will even claim that four-component relativistic theory is the optimal framework for the understanding of such interactions since they are inherently relativistic. 

On matrix form the non-unitary transformations (27) and (30) of the previous section are easily extended to the complete Hamiltonian and have therefore allowed relativistic and non-relativistic spin-free calculations of spectroscopic constants and first-order properties at the four-component level (see, for instance. Refs. [45 7]). In this section, we consider the elimination of spin-orbit interaction in four-component calculations of second-order electric and magnetic properties. Formulas are restricted to the Hartree-Fock [48] or Kohn-Sham [49] level of theory, but are straightforwardly generalized. 

Table III. Spectroscopic constants of X L HgH from all-electron CCSD(T) calculations both with (DK) and without (NR) the approximate inclusion of scalar relativistic effects"...

Studies on the reactivity of benzofuran and its derivatives from the chemical and physical point of view (determination of constants, calculation of orbitals, spectrographic data). In most of the recent papers, structural determination and reaction mechanism interpretation has increasingly relied upon spectroscopic methods. This has produced a considerable amount of data, which cannot fully be covered within the scope of this survey. 

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