Mass defect

The deviation of exact mass from nominal mass can be to either side, higher or lower, depending on the isotopes encountered. While the matter itself can be easily understood, existing terminology here is somewhat unfortunate. The term mass defect, mdefect, defined as the difference between integer mass, nominal, and exact mass, ntexact, is used to describe this deviation [6]. 

Application of this concept leads to positive and negative mass defects. The hydrogen atom, for example, has a negative mass defect, mdefectn =-7.825 x 10 u. In addition, the association of something being defective with certain isotopic masses can be misleading. The mass defect was unveiled by Aston [2,3] who already had discovered 212 of the total 287 stable isotopes. 

The term mass deficiency better describes the fact that the exact mass of an isotope or a complete molecule is lower than the corresponding nominal mass. In case of 0, for example, the isotopic mass is 15.994915 u, being 5.085 x 10 u deficient as compared to the nominal value (Wdefecto = 5.085 x 10 u). Most isotopes are more or less mass deficient with a tendency towards larger mass defect for the heavier isotopes, e.g., M35C1 = 34.96885 u (-3.115 x 10 u) and = 129.90447 u (-9.553 x W u). 

Note The use of nominal mass is limited to the low mass range. Above about 500 u the first decimal of isotopic mass can be larger than. 5 causing it to be rounded up to 501 u instead of the expected value of 500 u. This will in turn lead to severe misinterpretation of a mass spectrum (Chap. 6). 

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Unlike semiempirical methods that are formulated to completely neglect the core electrons, ah initio methods must represent all the electrons in some manner. However, for heavy atoms it is desirable to reduce the amount of computation necessary. This is done by replacing the core electrons and their basis functions in the wave function by a potential term in the Hamiltonian. These are called core potentials, elfective core potentials (ECP), or relativistic effective core potentials (RECP). Core potentials must be used along with a valence basis set that was created to accompany them. As well as reducing the computation time, core potentials can include the effects of the relativistic mass defect and spin coupling terms that are significant near the nuclei of heavy atoms. This is often the method of choice for heavy atoms, Rb and up. 

The methods listed thus far can be used for the reliable prediction of NMR chemical shifts for small organic compounds in the gas phase, which are often reasonably close to the liquid-phase results. Heavy elements, such as transition metals and lanthanides, present a much more dilficult problem. Mass defect and spin-coupling terms have been found to be significant for the description of the NMR shielding tensors for these elements. Since NMR is a nuclear effect, core potentials should not be used. 

The most common description of relativistic quantum mechanics for Fermion systems, such as molecules, is the Dirac equation. The Dirac equation is a one-electron equation. In formulating this equation, the terms that arise are intrinsic electron spin, mass defect, spin couplings, and the Darwin term. The Darwin term can be viewed as the effect of an electron making a high-frequency oscillation around its mean position. 

High-mass resolution is needed to separate mass interferences of molecular and atom ions. Because of the mass defect of the binding energy of the nucleus, atomic ions have a slightly smaller mass than the corresponding molecular ions. To observe this typical mass resolutions between 5000 and 10000 are necessary. 

The quantity just calculated is referred to as the mass defect. The corresponding energy difference is... 

Beta radiation Electron emission from unstable nuclei, 26,30,528 Binary molecular compound, 41-42,190 Binding energy Energy equivalent of the mass defect measure of nuclear stability, 522,523 Bismuth (m) sulfide, 540 Blassie, Michael, 629 Blind staggers, 574 Blister copper, 539 Blood alcohol concentrations, 43t Body-centered cubic cell (BCC) A cubic unit cell with an atom at each comer and one at the center, 246 Bohrmodd Model of the hydrogen atom... 

Molecular ion The presence of sulfur can be detected by the 34S isotope (4.4%) and the large mass defect of sulfur in accurate mass measurements. In primary aliphatic thiols, the molecular ion intensities range from 5-100% of the base peak. 

Because an increase in resolution causes a decrease in sensitivity, it is best to operate at the lowest resolution commensurate with good results. Some instrument data systems will allow calibration with an external reference material such as perfluorokerosene and then use of a secondary reference material for the internal mass reference. Tetraiodothiophene, vaporized using the solids probe inlet, is recommended as the secondary reference. The accurate masses are 79.9721, 127.9045, 162.9045, 206.8765, 253.8090, 293.7950, 333.7810, 460.6855, and 587.5900. For a higher mass standard, use hexaiodobenzene. Because the mass defect for these internal reference ions are so large, a resolution of 2000 is ample to separate these ions from almost any sample ions encountered in GC/MS. 

The mass defect is the difference between the total mass of all products and the total mass of all reactants ... 

The isotopic molar masses are precise to five or more significant figures, so we are tempted to express the result with five significant figures. The mass defect is determined by addition and subtraction, however, and two of the isotopic molar masses are known to just three decimal places, so the mass defect is precise to three decimal places, and the... 

Mass defect plots utilized by Jones and coworkers44 highlight impossible mass defects for the compounds considered and suggest chemical com-... 

Figure 13.2 Theoretical mass defect plot for six common classes of phospholipids.

Figure 13.5 Mass defect plot of a 9.4 T MALDI-FTMS spectrum of Saccharomyces cerevisiae.

The results for bacterial whole-cell analysis described here establish the utility of MALDI-FTMS for mass spectral analysis of whole-cell bacteria and (potentially) more complex single-celled organisms. The use of MALDI-measured accurate mass values combined with mass defect plots is rapid, accurate, and simpler in sample preparation then conventional liquid chromatographic methods for bacterial lipid analysis. Intact cell MALDI-FTMS bacterial lipid characterization complements the use of proteomics profiling by mass spectrometry because it relies on accurate mass measurements of chemical species that are not subject to posttranslational modification or proteolytic degradation. 

Flughey, C. A. Hendrickson, C. L. Rodgers, R. R Marshall, A. G. Kendrick mass defect spectrum A compact visual analysis for ultrahigh-resolution broadband mass spectra. Anal. Chem. 2001, 73,4676-4681. 

When atoms are considered to be composed of their constituent particles, it is found that the atoms have lower masses than the sum of the masses of the particles. For example, 42He contains two electrons, two protons, and two neutrons. These particles have masses of 0.0005486, 1.00728, and 1.00866 amu, respectively, which gives a total mass of 4.03298amu for the particles. However, the actual mass of 42He is 4.00260 amu, so there is a mass defect of 0.030377 amu. That "disappearance" of mass occurs because the particles are held together with an energy that can be expressed in terms of the Einstein equation,... 

Nuclear fusion processes derive energy from the formation of low-mass nuclei, which have a different binding energy. Fusion of two nuclear particles produces a new nucleus that is lighter in mass than the masses of the two fusing particles. This mass defect is then interchangeable in energy via Einstein s equation E = me2. Specifically, the formation of an He nucleus from two protons and two neutrons would be expected to have mass ... 

Energy associated with a mass defect in the fusion of low-mass nuclei and the fission of high-mass nuclei... 

The left-hand sides of Eqs. (A 1.69) and (A 1.70) are of the same form, which enables the perturbed GF with the mass defect Am to be readily expressed in terms of the unperturbed one ... 

Until recently the only satisfactory way to separate these molecular interferences has been on the basis of nuclear mass defects, i.e., the mass of molecules having the same mass number differs from that of the atoms of the same mass number. Figure 2 shows the resolution that is needed to resolve the molecular impurities present in the previous example. Clearly, an unambiguous identification can be made, and all molecular fragments can only be eliminated for an instrument with resolution M/AM approximately 20,000. Once again, the need for high resolution will cause the transmission efficiency to be low. 

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