# Lyman series

Table 3-4 Spectral Wavenumbers v for the Lyman Series of Hydrogen |

Other methods for analyzing combustion products can be substituted for chromatography. Gravimetry can be used, for example, after a series of absorption on different beds, as in the case of water absorption in magnesium perchlorate or CO2 in soda lime infra-red spectrometry can be used for the detection of CO2 and water. [c.29]

From the above plot, it can be seen that the recovery factor for gas reservoirs depends upon how low an abandonment pressure can be achieved. To produce at a specified delivery pressure, the reservoir pressure has to overcome a series of pressure drops the drawdown pressure (refer to Figure 9.2), and the pressure drops in the tubing, processing facility and export pipeline (refer to Figure 9.12). To improve recovery of gas, compression facilities are often provided on surface to boost the pressure to overcome the pressure drops in the export line and meet the delivery pressure specified. [c.198]

The method implies injection of a mixture of 3 radioactive tracers each being distributed into one of the 3 phases. The tracers must show such differences in the emitting y-radiation energy spectra that they can be simultaneously detected by on line y-spectrometry. Candidate tracers are Br-82 as bromobenzene for oil, Na-24 or La-140 for water, and Kr-85 for gas. The tracers are injected simultaneously at a constant rate into the flow in the pressurised pipe, and the concentration is detected as series of instantaneous measurements taken downstream as illustrated in figure 2. [c.1056]

[c.1141]

In this series of results, we encounter a somewhat unexpected result, namely, when the circle surrounds two conical intersections the value of the line integral is zero. This does not contradict any statements made regarding the general theory (which asserts that in such a case the value of the line integral is either a multiple of 2tu or zero) but it is still somewhat unexpected, because it implies that the two conical intersections behave like vectors and that they arrange themselves in such a way as to reduce the effect of the non-adiabatic coupling terms. This result has important consequences regarding the cases where a pair of electronic states are coupled by more than one conical intersection. [c.706]

Guner O F (Editor) 2000. Pharmacophore Perception, Development, and Use in Drug Design. International University Line Biotechnology Series, 2. [c.735]

Lyman series See Balmer series, lyogels See xerogels. [c.243]

Procedure. Use Mathcad, QLLSQ, or TableCurve (or, preferably, all three) to determine a value of the ionization energy of hydrogen from the wave numbers in Table 3-4 taken from spectroscopic studies of the Lyman series of the hydrogen spectrum where ni = 1. [c.76]

Bafmer series Frequencies of certain lines in the spectrum of hydrogen are simply related to each other, and can be expressed by a general formula. One group of lines is termed the Balmer series. Other series were later discovered in the spectrum of hydrogen by Lyman, Paschen, Brackett and Pfund. [c.50]

Hammen equation A correlation between the structure and reactivity in the side chain derivatives of aromatic compounds. Its derivation follows from many comparisons between rate constants for various reactions and the equilibrium constants for other reactions, or other functions of molecules which can be measured (e g. the i.r. carbonyl group stretching frequency). For example the dissociation constants of a series of para substituted (O2N —, MeO —, Cl —, etc.) benzoic acids correlate with the rate constant k for the alkaline hydrolysis of para substituted benzyl chlorides. If log Kq is plotted against log k, the data fall on a straight line. Similar results are obtained for meta substituted derivatives but not for orthosubstituted derivatives. [c.199]

Figure 1. Phase delay of Licrilite E202 cell, thickness 9.47)im, X 5l4nm. The solid line shows a power series best fit for the cell average data. |

Iiifomiation about the behaviour of the 3D Ising ferromagnet near the critical point was first obtained from high- and low-temperatnre expansions. The expansion parameter in the high-temperatnre series is tanli K, and the corresponding parameter in the low-temperatnre expansion is exp(-2A ). A 2D square lattice is self-dual in the sense that the bisectors of the line joining the lattice points also fomi a square lattice and the coefficients of the two expansions, for the 2D square lattice system, are identical to within a factor of two. The singularity occurs when [c.539]

The phase separation shown in figure A2.5.6 can also be illustrated by the entirely equivalent procedure of plotting the molar Helmlioltz free energy A(T, V ) as a fimction of the molar volume Vfor a series of constant temperatures, shown in figure A2.5.7. At constant temperature and volume, themiodynamic equilibrium requires that the Helmlioltz free energy must be minimized. It is evident for temperatures below the critical point that for certain values of the molar volume the molar free energy A(T, V) can be lowered by separation into two phases. The exact position of the phase separation is found by finding a straight line that is simultaneously tangent to the curve at two points the slope at any point of the curve is (5 A/ d V) = -p so the pressures are equal at the two tangent points. Similarly the chemical potential ).= A + p V is tire same at the two points. That the dashed and dotted parts of the curve are metastable or unstable is clear because they represent higher values of z than the correspondmg points on the two-phase line. (The metastable region is separated from the completely unstable region by a point of inflection on the curve.) [c.618]

At the critical pohit (and anywhere in the two-phase region because of the horizontal tie-line) the compressibility is infinite. However the compressibility of each conjugate phase can be obtained as a series expansion by evaluating the derivative (as a fiuictioii of p. ) for a particular value of T, and then substituting the values of p. for the ends of the coexistence curve. The final result is [c.622]

From 1965 on there was an extensive effort to calculate, or rather to estunate, the exponents for the Ising model. Initially this usually took the fonn of trying to obtain a low-temperature expansion (i.e. in powers of T) or a high-temperature expansion (i.e. in powers of 1/7) of the partition fiinction, in the hope of obtaining infomiation about the ultimate fonn of tlie series, and hence to leam about the singularities at the critical point. Frequently this effort took the fonn of convertmg the finite series (sometimes with as many as 25 tenns) into a Fade approximant, the ratio of two finite series. From this procedure, estimates of the various critical exponents (nonnally as the ratio of two integers) could be obtained. For the two-dimensional Ising model these estimates agreed with the values deduced by Onsager and Yang, which encouraged the belief that those for the three-dimensional model might be nearly conect. Indeed the

*[c.650]*

Such a sequence of snapshots, calculated in intervals of 4 fs, is shown as a series of double contour line plots on the left-hand side of figure A3.13.11 (tire outennost row shows the evolution of I equation (A3.13.68), the imremiost row is I I equation (A3.13.67), at the same time steps). This is the wave packet motion in CHD for excitation with a linearly polarized field along tlie the v-axis at 1300 cm and 10 TW cm after 50 fs of excitation. At this point a more detailed discussion regarding tlie orientational dynamics of the molecule is necessary. Clearly, the polarization axis is defined in a laboratory fixed coordinate system, while the bending axes are fixed to the molecular frame. Thus, exciting internal degrees of freedom along specific axes in the internal coordinate system requires two assumptions the molecule must be oriented or aligned with respect to the external polarization axis, and this state should be stationary, at least during the relevant time scale for the excitation process. It is possible to prepare oriented states [112. 114. 115] in the gas phase, and such a state can generally be represented as a superposition of a large number of rotational eigenstates. Two questions become important then How fast does such a rotational superposition state evolve How well does a purely vibrational wave packet calculation simulate a more realistic calculation which includes rotational degrees of freedom, i.e. with an initially oriented rotational wave packet The second question was studied recently by frill dimensional quantum dynamical calculations of the wave packet motion of a diatomic molecule during excitation in an intense infrared field [175], and it was verified that rotational degrees of freedom may be neglected whenever vibrational-rotational couplings are not important for intramolecular rotational-vibrational redistribution (IVRR) [ ]. Regarding the first question, because of the large rotational constant of methane, the time scales on which an initially oriented state of the free molecule is maintained are likely to be comparatively short and it would also be desirable to carry out calculations that include rotational states explicitly. Such calculations were done, for instance, for ozone at modest excitations [116. 117], but they would be quite difficult for the methane isotopomers at the high excitations considered in the present example. [c.1075]

X-rays for diffraction are generated in two ways. The most conunon is to bombard a metallic anode in a vacuum tube with electrons emitted thennionically from a hot cathode, thereby exciting the characteristic radiation from the anode material, which is usually copper or molybdenum, altliough some other metals are used for special purposes. If the accelerating voltage in the tube is well above that required to eject a K shell electron from an atom of the anode material, most of the x-radiation emitted will be in the characteristic lines of the K series on top of a continuous, Bremsstrahlung spectrum. Kp and higher energy lines may be filtered out using a suitable metallic filter, or the characteristic line may be selected by reflection from a monocluomator crystal. [c.1378]

Even if eehoes are used, there are still diffieiilties in reeording eomplete broad speetral lines with pulsed exeitation. Several approaehes have been adopted to overeome these diffieiilties based on the philosophy that although the line is broad it ean be reeorded using a series of narrow-banded experiments. One of these approaehes is to earry out a spin-eeho experiment using relatively weak RF pulses, reeording only the intensity of the on-resonanee magnetization and repeating the experiment at many freqiieneies to map out the [c.1477]

DOR provides significantly higher resolution than MAS [37, 39]. At 11.7 T a series of relatively narrow resonances and accompanying sidebands are observed under DOR ( figrne Bl.12.14(a)). The relatively slow spiiming speed of the outer rotor results in numerous sidebands and the isotropic line is identified by collecting spectra at several different spiiming speeds. If the isotropic position is then collected as a fiinction of the quadnipole interaction parameters can then be deduced. MQ MAS provides an alternative approach for producing high resolution [38, 40], with the whole 2D data set shown at 9.4 T along with the isotropic projections at 11.7 and 18.8 T ( figure B1.12.14(T)))) [38]. All tln-ee isotropic triple quantum (3Q) projections show only tlnee resolved lines as the NMR parameters from the two sites (Al, A4) with the largest Cq means that their resonances are superimposed at all fields. This is confmned by the 9.4 T 3Q data where an RF field of 280 kFIz was employed making the data more quantitative the tlnee resonances witli isotropic shifts of 43.0, 21.1 and 8.0 ppm had intensities of 2.1 1.1 1.0 respectively. At 11.7 and 18.8 T the MQ MAS NMR spectra collected are not quantitative since the RF fields to excite the 3Q transitions were not strong enough. For / = Sthe isotropic shifts are of the value compared to direct MAS at the same field, so MQ data [c.1493]

Vacha M, Liu Y, Nakatsuka FI and Tani T 1997 Inhomogeneous and single molecule line broadening of terryiene in a series of crystalline n-alkanes J. Phys. Chem 106 8324-31 [c.2507]

It is interesting to note the similarity of the expression in Eq. (48) with the result obtained through a WKB or eikonal type of argument [37,38], The eikonal approximation resorts to straight-line trajectories, while the END application of the Schiff approximation uses fully dynamical trajectories. Schiff [36] demonstrates that the scattering wave function obtained through his procedure of summing the Bom series contains an additional term, which is essential for the correct treatment of the scattering and is not present in the eikonal or WKB approaches to the problem. This fomiula of the scattering amplitude [Eq. (48)] is also considered to be in principle valid for all scattering angles (see [38], p. 604). [c.236]

On this occasion, we want also to refer to an incorrect statement that we made more than once [72], namely, that the (1,2) conical intersection results indicate that for any value of ri and r2 the two states under consideration form an isolated two-state sub-Hilbert space. We now know that in fact they do not form an isolated system because the second state is coupled to the thud state via a conical intersection as will be discussed next. Still, the fact that the series of topological angles, as calculated for the various values of r and r2, are either multiples of it or zero indicates that we can form, for this adiabatic two-state system, single-valued diabatic potentials. Thus if for some numerical heatment only the two lowest adiabatic states are required, the results obtained here suggest that it is possible to foiTn from these two adiabatic surfaces singlevalued diabatic potentials employing the line-integral approach. Indeed, recently Billing et al. [104] carried out such a photodissociation study based on the two lowest adiabatic states as obtained from ab initio calculations. The complete justification for such a study was presented in Section XI. [c.706]

Reference [73] presents the first line-integral study between two excited states, namely, between the second and the third states in this series of states. Here, like before, the calculations are done for a fixed value of ri (results are reported for ri = 1.251 A) but in contrast to the previous study the origin of the system of coordinates is located at the point of this particulai conical intersection, that is, the (2,3) conical intersection. Accordingly, the two polar coordinates (

Such a sequence of snapshots, calculated in intervals of 4 fs, is shown as a series of double contour line plots on the left-hand side of figure A3.13.11 (tire outennost row shows the evolution of I equation (A3.13.68), the imremiost row is I I equation (A3.13.67), at the same time steps). This is the wave packet motion in CHD for excitation with a linearly polarized field along tlie the v-axis at 1300 cm and 10 TW cm after 50 fs of excitation. At this point a more detailed discussion regarding tlie orientational dynamics of the molecule is necessary. Clearly, the polarization axis is defined in a laboratory fixed coordinate system, while the bending axes are fixed to the molecular frame. Thus, exciting internal degrees of freedom along specific axes in the internal coordinate system requires two assumptions the molecule must be oriented or aligned with respect to the external polarization axis, and this state should be stationary, at least during the relevant time scale for the excitation process. It is possible to prepare oriented states [112. 114. 115] in the gas phase, and such a state can generally be represented as a superposition of a large number of rotational eigenstates. Two questions become important then How fast does such a rotational superposition state evolve How well does a purely vibrational wave packet calculation simulate a more realistic calculation which includes rotational degrees of freedom, i.e. with an initially oriented rotational wave packet The second question was studied recently by frill dimensional quantum dynamical calculations of the wave packet motion of a diatomic molecule during excitation in an intense infrared field [175], and it was verified that rotational degrees of freedom may be neglected whenever vibrational-rotational couplings are not important for intramolecular rotational-vibrational redistribution (IVRR) [ ]. Regarding the first question, because of the large rotational constant of methane, the time scales on which an initially oriented state of the free molecule is maintained are likely to be comparatively short and it would also be desirable to carry out calculations that include rotational states explicitly. Such calculations were done, for instance, for ozone at modest excitations [116. 117], but they would be quite difficult for the methane isotopomers at the high excitations considered in the present example. [c.1075]

X-rays for diffraction are generated in two ways. The most conunon is to bombard a metallic anode in a vacuum tube with electrons emitted thennionically from a hot cathode, thereby exciting the characteristic radiation from the anode material, which is usually copper or molybdenum, altliough some other metals are used for special purposes. If the accelerating voltage in the tube is well above that required to eject a K shell electron from an atom of the anode material, most of the x-radiation emitted will be in the characteristic lines of the K series on top of a continuous, Bremsstrahlung spectrum. Kp and higher energy lines may be filtered out using a suitable metallic filter, or the characteristic line may be selected by reflection from a monocluomator crystal. [c.1378]

Even if eehoes are used, there are still diffieiilties in reeording eomplete broad speetral lines with pulsed exeitation. Several approaehes have been adopted to overeome these diffieiilties based on the philosophy that although the line is broad it ean be reeorded using a series of narrow-banded experiments. One of these approaehes is to earry out a spin-eeho experiment using relatively weak RF pulses, reeording only the intensity of the on-resonanee magnetization and repeating the experiment at many freqiieneies to map out the [c.1477]

DOR provides significantly higher resolution than MAS [37, 39]. At 11.7 T a series of relatively narrow resonances and accompanying sidebands are observed under DOR ( figrne Bl.12.14(a)). The relatively slow spiiming speed of the outer rotor results in numerous sidebands and the isotropic line is identified by collecting spectra at several different spiiming speeds. If the isotropic position is then collected as a fiinction of the quadnipole interaction parameters can then be deduced. MQ MAS provides an alternative approach for producing high resolution [38, 40], with the whole 2D data set shown at 9.4 T along with the isotropic projections at 11.7 and 18.8 T ( figure B1.12.14(T)))) [38]. All tln-ee isotropic triple quantum (3Q) projections show only tlnee resolved lines as the NMR parameters from the two sites (Al, A4) with the largest Cq means that their resonances are superimposed at all fields. This is confmned by the 9.4 T 3Q data where an RF field of 280 kFIz was employed making the data more quantitative the tlnee resonances witli isotropic shifts of 43.0, 21.1 and 8.0 ppm had intensities of 2.1 1.1 1.0 respectively. At 11.7 and 18.8 T the MQ MAS NMR spectra collected are not quantitative since the RF fields to excite the 3Q transitions were not strong enough. For / = Sthe isotropic shifts are of the value compared to direct MAS at the same field, so MQ data [c.1493]

Vacha M, Liu Y, Nakatsuka FI and Tani T 1997 Inhomogeneous and single molecule line broadening of terryiene in a series of crystalline n-alkanes J. Phys. Chem 106 8324-31 [c.2507]

It is interesting to note the similarity of the expression in Eq. (48) with the result obtained through a WKB or eikonal type of argument [37,38], The eikonal approximation resorts to straight-line trajectories, while the END application of the Schiff approximation uses fully dynamical trajectories. Schiff [36] demonstrates that the scattering wave function obtained through his procedure of summing the Bom series contains an additional term, which is essential for the correct treatment of the scattering and is not present in the eikonal or WKB approaches to the problem. This fomiula of the scattering amplitude [Eq. (48)] is also considered to be in principle valid for all scattering angles (see [38], p. 604). [c.236]

On this occasion, we want also to refer to an incorrect statement that we made more than once [72], namely, that the (1,2) conical intersection results indicate that for any value of ri and r2 the two states under consideration form an isolated two-state sub-Hilbert space. We now know that in fact they do not form an isolated system because the second state is coupled to the thud state via a conical intersection as will be discussed next. Still, the fact that the series of topological angles, as calculated for the various values of r and r2, are either multiples of it or zero indicates that we can form, for this adiabatic two-state system, single-valued diabatic potentials. Thus if for some numerical heatment only the two lowest adiabatic states are required, the results obtained here suggest that it is possible to foiTn from these two adiabatic surfaces singlevalued diabatic potentials employing the line-integral approach. Indeed, recently Billing et al. [104] carried out such a photodissociation study based on the two lowest adiabatic states as obtained from ab initio calculations. The complete justification for such a study was presented in Section XI. [c.706]

Reference [73] presents the first line-integral study between two excited states, namely, between the second and the third states in this series of states. Here, like before, the calculations are done for a fixed value of ri (results are reported for ri = 1.251 A) but in contrast to the previous study the origin of the system of coordinates is located at the point of this particulai conical intersection, that is, the (2,3) conical intersection. Accordingly, the two polar coordinates (

(,2/ )) again employing chain rules for the transformation
[c.706]

SMD simulations require selection of a path, i.e., a series of directions of the applied force. In some cases a straight line path is sufficient, e.g., for avidin-biotin (Fig. 2), actin (Fig. 4), lipids in membranes (Fig. 6), or the unfolding of titin immunoglobulin domains (Fig. 8). Other biomolecular systems involve a ligand positioned at the bottom of a convoluted binding cleft, e.g., bacteriorhodopsin (Fig. 3), prostaglandin H2 synthase (Fig. 7), and nuclear hormone receptors (Fig. 5). In the latter cases the forced unbinding of the ligand requires the direction of the force to be changed during the simulation to avoid distortion of the surrounding protein. The direction of the force can be chosen randomly (Liidemann et al., 1997) or by guessing a direction on the basis of structural information. A force is then applied to the ligand in the chosen direction, and this direction is accepted or rejected based on factors such as conservation of secondary structure of the protein, deformation of the protein, the magnitude of the force applied, the average velocity of the ligand along the unbinding pathway, etc. (Isralewitz et al., 1997 Liidemann et al., 1997). One possible protocol for selecting force directions in SMD defines a conical region of space around a preferred direction and selects new directions randomly within this region. A small cone angle strongly biases the chosen directions to the initial guess, whereas a large cone angle leads to exploration of more directions.
[c.42]

AGact in turn is composed of the enthalpy and entropy of activation, quantities which can in principle he calculated using other methods, such as those discussed above. The concentration of the jumping species is also predicted to vary in an exponential manner. It is thus expected that transport coefficients will follow an Arrhenius-like behaviour, and plotting the logarithm of fhe diffusion coefficient or the conductivity against 1/T will give a straight line (in fact, in the case of conductivity it is usual to plot log(crT) against 1/T in accordance with the Nernst-Einstein relationship). It is indeed quite common to observe a series of linear regions, each corresponding to different types of defect population. Some typical activation energies are 0.66 eV (cation vacancy migration in NaCl), 0.35 eV (aiaion vacancy migration in CaF2) and 2.0 eV (cation vacancy migration in MgO). [c.644]

See pages that mention the term

**Lyman series**:

**[c.50] [c.217] [c.88] [c.237] [c.240] [c.808] [c.1341] [c.1539] [c.1973] [c.1988] [c.2414] [c.160] [c.185] [c.247] [c.307] [c.605] [c.631] [c.157]**

Computational chemistry using the PC (2003) -- [ c.76 ]