Approximation breakdown

In order to calculate q (Q) all possible quantum states are needed. It is usually assumed that the energy of a molecule can be approximated as a sum of terms involving translational, rotational, vibrational and electronical states. Except for a few cases this is a good approximation. For linear, floppy (soft bending potential), molecules the separation of the rotational and vibrational modes may be problematic. If two energy surfaces come close together (avoided crossing), the separability of the electronic and vibrational modes may be a poor approximation (breakdown of the Bom-Oppenheimer approximation. Section 3.1). 

Also at times, political factors enter into the choosing of a particular feedstock for ammonia production. Table 2 shows the approximate breakdown of the current world ammonia capacity according to the feedstocks used. The data were derived from SRI s "World Nitrogen" report. CiL)... 

An approximate breakdown showing the various sources of new capital for large corporations typical of the chemical industry is presented in Table 9. 

TABLE 17.5 Approximate Breakdown of Products on the Delayed Coking of Bitumen Recovered from the Alberta Tar Sands by Hot Water Extraction"... 

Figure 4 (a) Distribution of all of the Pseudopterogorgia elisabethae diterpenoid variants by carbon skeletal class (total = 109 compounds), (b) Approximate breakdown of all the rearranged diterpenoids from P. elisabethae by skeletal type. 

An approximate breakdown of 1987 Bioenergy Conversion R D expenditures in general technology areas is as follows ... 

The three basic polystyrene (PS) plastics are crystal (or general-purpose), high-impact (HIPS) and expandable beads. In 2004, the annual world consumption was 15.2 million tonnes, with the following approximate breakdown 45% crystal, 42% HIPS and 13% expandable beads. At present, the largest end use for crystal PS and HIPS is in the packaging industry, which accounts for about 30% of the world consumption. PS polymers and other styrene (S) copolymers such as acrylonitrile-butadiene-styrene (ABS) are... 

This section provides correlation charts and operational information for the design and interpretation of ultraviolet-visible spectrophotometric (UV-Vis) measurements. While UV-Vis is perhaps not as information-rich as infrared or nuclear magnetic resonance, it nonetheless has value in structure determination and sample identification. Moreover, it is extremely valuable in quantitative work. Typical UV-Vis instruments cover not only the UV and visible spectrum, but the near-infrared as well. Although there is overlap among the ranges, the approximate breakdown is ... 

Overall, the approximate breakdown of the commercial applications of chloro-sulfonic acid is as follows detergents 40% pharmaceuticals 20% dyes 15% pesticides 10% and miscellaneous uses, e.g. plasticizers, ion-exchange resins, etc. 15%. 

Unsaturated polyester resins are used alone, in conjunction with glass reinforcement or compounded with fillers and glass strands to prepare moulding materials. Table 10 gives an approximate breakdown of polyester consumption in the UK. 

The approximate breakdowns of railway-related fatalities versus number of accidents occurring during the period 1830-2007 in the United Kingdom are presented in Table 7.1 [17]. 

Approximate Breakdowns of Fatalities versus Number of Railway Accidents in the United Kingdom, 1830-2007... 

The approximate breakdown of surfactant consumption by class is shown in Figure 1.2. Six major surfactant types accounted for 60% of the total consumption. The big six are soaps, linear alkylbenzene sulfonates (LABS), alcohol ethoxylates (AE), alkylphenol ethoxylates (APE), alcohol ether sulfates (AES), and alcohol sulfates (AS). 

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