Wave number units

Here G(vj, v2, v3) is the level energy in wave number units (as far as possible we follow the notation of Herzberg, 1950) and the constants in Equation (0.1) are given in Table 0.1. As usual the vs are the vibrational quantum numbers of S02 and rather high (above 10) values can be reached using the SEP technique. Equation (0.1) provides a fit to the observed levels to within an error below 10 cm 1, which is almost the experimental accuracy. We need, however, to be able to relate the parameters in this expansion directly to a Hamiltonian. The familiar way of doing this proceeds in two steps. First, the electronic problem is solved in the Bom-Oppenheimer approximation, leading to the potential for the... 

Av Avc Rayleigh resolution in wave-number units half-width yc/4rc observed when collision broadening dominates (given in hertz)... 

Frequencies in the electromagnetic spectrum can be seen from Figure 9-7 generally to be large. As a result, it is common to use wave numbers instead of Hz or MHz (megahertz). The frequency in wave number is simply the frequency v in Hz divided by c, the velocity of light in cm. Wave-number units are cm-1 and we can think of the wave number v as being the number of wave crests per centimeter. 

There is a close analogy between the nephelauxetic series and the series of optical electronegativities in both cases, the oxidizing character of the central ion and the reducing character of the ligands are involved. Another fact of importance for the internal transitions in the partly filled shell of complexes with centre of inversion, such as Oh, is that their intensity is inversely proportional to the square of the distance in wave-number units between the Laporte-aMovted electron transfer band and the La or/e-forbiddcn transition considered. The complexes have been arranged in a hyperchromic series with respect to this variation of intensities. 

Here, and T" are the electronic contributions to the term values (energy divided by he), and the second terms are the potential energy terms expressed in wave number units (m ). r is the internuclear distance, and is its equilibrium value, k is the force constant, related to the molecular constant n>e by... 

Absorption band positions are given in wave number units (v), which are expressed as cm , or alternatively in wavelength units (A), in microns (fi) (also called micrometers, jum). The true unit of frequency (v) is measured in reciprocal seconds (sec ). The relations of these units to each other are v [cm ]= 1/A[cm] = 10,000/A [ji] V = c/A thus, 2000 cm = 5.00 ju, and 1250 cm = 8.00ju. The reader is referred to Appendix 2 for a Table of Reciprocals, which is useful in converting wavelengths to wave numbers, and vice versa. 

Electromagnetic radiation can be characterized by its wavelength A, its frequency v, or its wave number v. In the IR region the unit used for wavelength is the micrometer (/xm). The frequency unit is cycles per second or hertz (Hz). The wave number unit is cycles per centimeter or reciprocal centimeters (cm ). The wave number (cm ) is the number of waves in a continuous wave sequence 1 cm long. The relationship between the units is given in Eq. (1) ... 

In current practice, rationalized units are not used in IR the absorption bands have long been identified in terms of wavelengths, i. e., in micrometers. The general trend now is to express energy by a scale proportional to the frequency the wave number designated by v is defined as (... 

For infrared spectra, both microns and wave numbers (cm. ) are convenient units. For electronic spectra (ultraviolet and visible), the milb-micron is largely used the wave numbers, (cm. i) may range between 13,000 and 50,000 and consequently many authors employ cm.X 10 . ... 

Frequency (Section 13 1) Number of waves per unit time Although often expressed in hertz (Hz) or cycles per sec ond the SI unit for frequency is s ... 

Wave-height-concentration plot 604 Wave height measurement of, 605 Wavelengths approximate of colours, 646 limits of various types of radiation, 647 units for, 647 Wave numbers 646... 

Note that the energy (written as e) is expressed in cm-1 (wave numbers), an energy unit often used by spectroscopists. The ratio hc/k has a value of 1.43877 x 10 2 m-K or 1.43876 cm-K. The latter value is the one to use when energy is expressed in cm-1. 

The magnitude of k corresponds to a wave number 2n/X and therefore is measured with a unit of reciprocal length. For this reason k is said to be a vector in a reciprocal space or k space . This is a space in a mathematical sense, i.e. it is concerned with vectors in a coordinate system, the axes of which serve to plot kx, ky and kz. The directions of the axes run perpendicular to the delimiting faces of the unit cell of the crystal. 

An absorption spectrum is a plot that shows how well dilferent frequencies of light couple to excitations in the sample. It is conventional to convert the units for frequency (v) from Hertz to wave numbers (cm-1) by dividing v by the speed of light (c). IR frequencies are characteristic of certain bonds in molecules and can thus be used to identify species on surfaces. Correlation charts are available which permit assignments of particular molecular species to certain IR frequencies. 

A sensitive probe of electrostatic interactions in the distal pocket is provided by the structural and vibrational properties of the Fe-CO unit [9], The bound CO ligand exhibits three main infrared (IR) absorption bands, denoted Ao, A, and A3, with vibrational frequencies 1965 cm-1, 1949 cm, and 1933 cm, respectively. These bands, which change relative intensity and wave-number depending on temperature, pressure, pH, or solvent [10], are used to identify functionally different conformational substrates of MbCO, denoted taxonomic substates [11], Nevertheless the relationship between the A states and specific structural features of the protein has not yet been clarified. 

The IR spectrum is the name given to a band of frequencies between 4000 and 650 cm-1 beyond the red end of the visible spectrum. The units are called wave numbers or reciprocal centimeters (that s what cm-1 means). This range is also expressed as wavelengths from 2.5 to 15 micrometers (/im). 

Since NIR was developed by the USDA for food products, the first (commercial) mode developed was diffuse reflection. The earliest work was performed on instruments which had, in essence, NIR as an extra. The UV/Vis hardware (e.g., Cary model 10) had an additional detector and could be used through the NIR. This one fact explains why so much literature uses nanometers for units instead of wave numbers. 

When a wave, such as that on the sea, travels in a particular direction, we can characterize it by a number of parameters - the velocity of travel, its amplitude (the height of the waves), its wavelength (distance between adjacent peaks), and its frequency (the number of waves per unit time). The simplest form of wave to consider is a sine wave, the equation for... 

In some literature accounts, the term wave number (v) is used. This is the number of wavelengths per centimetre, and consequently wave number has units of reciprocal centimetres (cm4). 

In this book we deal mainly with stationary states, their energies, and matrix elements. Unless otherwise stated, we use the wave number (cm-1) as a measure of the energy. The conversion factors with other units are shown in Table 0.2. 

---