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Potentials curves

We will consider two problems in the framework of the conservation laws the potential curves principle and the theory of collisions in areas of science close to chemistry. [Pg.74]

In spite of the fact that curve U(f) reflects only the potential energy change, with its imaging we can also find the value of the kinetic energy in each interparticle point (at given total energy E). [Pg.74]

It describes the interaction between two resting charges depending on the intercharge distance r it is expressed by the formula [Pg.75]

More complex type of interaction is the interplay of molecules [Pg.76]

Without looking deeply into the nature of these interactions, we can say that both attraction and repulsion forces act simultaneously between molecules. Because attraction forces decrease with distance slower than repulsion forces, attraction forces dominate at longer distances and at shorter distances repulsion forces dominate. [Pg.76]


Moseley J T 1984 Determination of ion molecular potential curves using photodissociative processes Applied Atomic Collision Physics ed H S W Massey, E W McDaniel and B Bederson (New York Academic)... [Pg.822]

Figure Bl.1.1. (a) Potential curves for two states with little or no difference in the equilibrium position of tire upper and lower states. A ttansition of O2, witli displacement only 0.02 A, is shown as an example. Data taken from [11]. Most of the mtensity is in the 0-0 vibrational band with a small intensity in the 1-0 band, (b) Potential curves for two states with a large difference in the equilibrium position of the two states. A ttansition in I2, with a displacement of 0.36 A, is shown as an example. Many vibrational peaks are observed. Figure Bl.1.1. (a) Potential curves for two states with little or no difference in the equilibrium position of tire upper and lower states. A ttansition of O2, witli displacement only 0.02 A, is shown as an example. Data taken from [11]. Most of the mtensity is in the 0-0 vibrational band with a small intensity in the 1-0 band, (b) Potential curves for two states with a large difference in the equilibrium position of the two states. A ttansition in I2, with a displacement of 0.36 A, is shown as an example. Many vibrational peaks are observed.
Figure Bl.26.21. Potential energy curves for an electron near a metal surface. Image potential curve no applied field. Total potential curve applied external field = -E. ... Figure Bl.26.21. Potential energy curves for an electron near a metal surface. Image potential curve no applied field. Total potential curve applied external field = -E. ...
In the case of an irreversible electrode reaction, the current-potential curve will display a similar shape, with... [Pg.1935]

Figure B3.4.12. A schematic ID vibrational pre-dissociation potential curve (wide flill line) with a superimposed plot of the two bound fimctions and the resonance fimction. Note that the resonance wavefiinction is associated with a complex wavevector and is slowly increasing at very large values of R. In practice this increase is avoided by iismg absorbing potentials, complex scaling, or stabilization. Figure B3.4.12. A schematic ID vibrational pre-dissociation potential curve (wide flill line) with a superimposed plot of the two bound fimctions and the resonance fimction. Note that the resonance wavefiinction is associated with a complex wavevector and is slowly increasing at very large values of R. In practice this increase is avoided by iismg absorbing potentials, complex scaling, or stabilization.
Figure 4. Spin-orbit splitting in AT — 1 and 2 vibronic levels of the state of NCN. Solid lines connect the results of calculations thar employ ab initio computed potential curves [28], For comparison the results obtained by employing experimentally derived potential curves (dashed lines) [30,31] are also given. Full points represent energy differences between P — K — and P — K spin levels, and crosses are differences between P — K + I and P — K levels. Figure 4. Spin-orbit splitting in AT — 1 and 2 vibronic levels of the state of NCN. Solid lines connect the results of calculations thar employ ab initio computed potential curves [28], For comparison the results obtained by employing experimentally derived potential curves (dashed lines) [30,31] are also given. Full points represent energy differences between P — K — and P — K spin levels, and crosses are differences between P — K + I and P — K levels.
Figure 5, Low-eriergy vibronic spectrum in a electronic state of a linear triatomic molecule. The parameter c determines the magnitude of splitting of adiabatic bending potential curves, is the spin-orbit coupling constant, which is assumed to be positive. The zero on the... Figure 5, Low-eriergy vibronic spectrum in a electronic state of a linear triatomic molecule. The parameter c determines the magnitude of splitting of adiabatic bending potential curves, is the spin-orbit coupling constant, which is assumed to be positive. The zero on the...
Now, we discuss briefly the situation when one or both of the adiabatic electronic states has/have nonlinear equilibrium geometry. In Figures 6 and 7 we show two characteristic examples, the state of BH2 and NH2, respectively. The BH2 potential curves are the result of ab initio calculations of the present authors [33,34], and those for NH2 are taken from [25]. [Pg.498]

Figure 6. Bending potential curves for the X Ai, A B electronic system of BH2 [33,34], Full hotizontal lines K —Q vibronic levels dashed lines /f — I levels dash-dotted lines K — 2 levels dotted lines K — 3 levels. Vibronic levels of the lower electronic state are assigned in benf notation, those of the upper state in linear notation (see text). Zero on the energy scale corresponds to the energy of the lowest vibronic level. Figure 6. Bending potential curves for the X Ai, A B electronic system of BH2 [33,34], Full hotizontal lines K —Q vibronic levels dashed lines /f — I levels dash-dotted lines K — 2 levels dotted lines K — 3 levels. Vibronic levels of the lower electronic state are assigned in benf notation, those of the upper state in linear notation (see text). Zero on the energy scale corresponds to the energy of the lowest vibronic level.
Figire 7. Betiding potential curves for the A A electronic system of NH2 [25], Full... [Pg.499]

In his classical paper, Renner [7] first explained the physical background of the vibronic coupling in triatomic molecules. He concluded that the splitting of the bending potential curves at small distortions of linearity has to depend on p, being thus mostly pronounced in H electronic state. Renner developed the system of two coupled Schrbdinger equations and solved it for H states in the harmonic approximation by means of the perturbation theory. [Pg.507]

Vo + V2 and = Vo — 2 (actually, effective operators acting onto functions of p and < )), conesponding to the zeroth-order vibronic functions of the form cos(0 —4>) and sin(0 —(()), respectively. PL-H computed the vibronic spectrum of NH2 by carrying out some additional transformations (they found it to be convenient to take the unperturbed situation to be one in which the bending potential coincided with that of the upper electi onic state, which was supposed to be linear) and simplifications (the potential curve for the lower adiabatic electi onic state was assumed to be of quartic order in p, the vibronic wave functions for the upper electronic state were assumed to be represented by sums and differences of pairs of the basis functions with the same quantum number u and / = A) to keep the problem tiactable by means of simple perturbation... [Pg.509]

The present perturbative beatment is carried out in the framework of the minimal model we defined above. All effects that do not cincially influence the vibronic and fine (spin-orbit) stracture of spectra are neglected. The kinetic energy operator for infinitesimal vibrations [Eq. (49)] is employed and the bending potential curves are represented by the lowest order (quadratic) polynomial expansions in the bending coordinates. The spin-orbit operator is taken in the phenomenological form [Eq. (16)]. We employ as basis functions... [Pg.533]

FIGURE 6.2 Hannonic, cubic, and Morse potential curves used to describe the energy due to bond stretching in molecular mechanics force fields. [Pg.51]

This difference is shown in the next illustration which presents the qualitative form of a potential curve for a diatomic molecule for both a molecular mechanics method (like AMBER) or a semi-empirical method (like AMI). At large internuclear distances, the differences between the two methods are obvious. With AMI, the molecule properly dissociates into atoms, while the AMBERpoten-tial continues to rise. However, in explorations of the potential curve only around the minimum, results from the two methods might be rather similar. Indeed, it is quite possible that AMBER will give more accurate structural results than AMI. This is due to the closer link between experimental data and computed results of molecular mechanics calculations. [Pg.160]

The potential energy 0(z) depends not only on the distance z hut also on the position of the gas molecule in the xy plane parallel to the surface of the solid and distant z from it. For any given position, the adsorption energy will be equal to the value of 0 = 0o minimum of the potential curve (cf. Fig. 1.2), which of course represents the equilibrium position. [Pg.8]

Maloy, J. T. Factors Affecting the Shape of Current-Potential Curves, ... [Pg.540]

Owing to the effects of mechanical anharmonicity - to which we shall refer in future simply as anharmonicity since we encounter electrical anharmonicity much less frequently -the vibrational wave functions are also modified compared wifh fhose of a harmonic oscillator. Figure 6.6 shows some wave functions and probabilify densify functions (iA A ) for an anharmonic oscillator. The asymmefry in and (iA A ) 5 compared wifh fhe harmonic oscillator wave functions in Figure f.i3, increases fheir magnitude on the shallow side of the potential curve compared with the steep side. [Pg.146]

In the case where r > r" there is, when anharmonicity is taken into account, a relatively steep part of the excited state potential curve above v" = 0, giving a relatively broad... [Pg.249]

Section 6.13.2 and illustrated in Figure 6.5. The possible inaccuracies of the method were made clear and it was stressed that these are reduced by obtaining term values near to the dissociation limit. Whether this can be done depends very much on the relative dispositions of the various potential curves in a particular molecule and whether electronic transitions between them are allowed. How many ground state vibrational term values can be obtained from an emission spectrum is determined by the Franck-Condon principle. If r c r" then progressions in emission are very short and few term values result but if r is very different from r", as in the A U — system of carbon monoxide discussed in Section 7.2.5.4, long progressions are observed in emission and a more accurate value of Dq can be obtained. [Pg.252]


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See also in sourсe #XX -- [ Pg.77 , Pg.78 , Pg.111 , Pg.148 , Pg.149 , Pg.150 ]

See also in sourсe #XX -- [ Pg.48 ]

See also in sourсe #XX -- [ Pg.20 ]

See also in sourсe #XX -- [ Pg.48 ]

See also in sourсe #XX -- [ Pg.87 ]




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Ab initio potential curves

Absorbance-potential curve

Acceptors potential energy curve

Action potential curves

Adiabatic channel potential curves

Adiabatic potential curve minimum energy paths

Adiabatic potential curves

Alloys, anodic behavior current-potential curves

An example Fluctuating potential curves

Appearance potential curves

Aromaticity potential curves

Azobenzenes potential energy curves

Benzene potential curves

Bond breaking potential energy curves for

Born-Oppenheimer approximation potential curve

Bound potential curve

Capacitance-potential curve

Capacity-potential curves

Capacity-potential curves shape

Carbonyls potential energy curve

Cathode potential-current density curves

Cathodic polarization curve potential portions

Chemisorption potential energy curve

Chronopotentiometric potential-time curves

Configuration interaction potential energy curves

Coupled-cluster theory potential energy curves

Crossing of potential energy curves for diatomics

Current -potential curves for

Current density / potential curves, platinum electrodes

Current potential curves, irreversible

Current potential curves, irreversible reversible

Current vs. potential curves

Current-bias potential curves

Current-potential curves

Current-potential curves Additivity principle

Current-potential curves Butler-Volmer equation

Current-potential curves Evans diagram

Current-potential curves INDEX

Current-potential curves Wagner-Traud diagram

Current-potential curves accumulation region

Current-potential curves at semiconductor electrodes

Current-potential curves cathode

Current-potential curves characteristics

Current-potential curves characterized

Current-potential curves copper

Current-potential curves depletion region

Current-potential curves determination

Current-potential curves electroless deposition

Current-potential curves equilibrium

Current-potential curves nucleation process

Current-potential curves partial reactions

Current-potential curves recommendations

Current-potential curves response

Current-potential curves semiconductor

Current-potential curves surface

Current-potential curves transient

Current-potential curves usefulness

Current-potential curves, quantitative

Current-potential curves, quantitative behavior

Current-potential curves, steady state

Current-potential curves, steady state hydrogen oxidation

Current-potential curves, steady state oxygen reduction

Curve crossing, potential energy surfaces

Definitions and Approximations Associated with Different Types of Potential Energy Curves

Density-potential curve

Diabatic and adiabatic potential curves

Diabatic potential curves

Discrete quanta potential energy curves

Disk electrodes current-potential curves

Electrode potential curves

Electrolysis potential-current curves

Electromagnetic Field-Dressed Diabatic and Adiabatic Potential Energy Curves

Electron affinity potential energy curves

Electrostatic potential energy curve

Experimental Current—Potential Curves for Porous Electrodes

Field-dressed potential energy curves for Hj

Fluctuating potential energy curves

Full configuration interaction potential energy curves

Ground state potential curve

H2 potential curves

Harmonic oscillator potential curve

Harmonic potential curves

Hat-curved-cosine-squared potential composite

Instantaneous potential curves

Interatomic potential curve

Lines potential curves

Methane potential energy curves

Methanol current-potential curves

Molecular potential energy curve

Morse Potential Energy Curves Antibonding

Morse Potential Energy Curves Bonding

Morse Potential Energy Curves Cytosine, Thymine

Morse Potential Energy Curves for Thymine and Cytosine

Morse potential curve

Morse potential energy curve

Nitrogen potential energy curve

One-dimensional potential energy curves

Ozone potential energy curves

Parabolic potential curves

Passivating potential polarization curves related

Passivity current density potential curve

Photoisomerization potential energy curves

Physisorption potential energy curve

Polanyi potential theory characteristic curve

Polarization Curves With Included Ohmic Potential Drop

Polarization Curves Without Included Ohmic Potential Drop

Polarization curves active metal electrode, corrosion potential

Potassium ion channel Potential energy curves

Potential Curves and Large Amplitude Motions

Potential Curves of Diatomic Noble Gas Molecules

Potential Energy Curves from Electronic Band Spectra

Potential current density curves

Potential curve Subject

Potential curve for

Potential curves dissociative

Potential curves endothermic

Potential curves fluorine

Potential curves tungsten surface

Potential decay curves

Potential energy curve

Potential energy curve For diatomic molecule

Potential energy curve diatomic molecule

Potential energy curve harmonic oscillator

Potential energy curve hydrogen molecule

Potential energy curve of the O-H oscillator

Potential energy curve on the

Potential energy curve stilbenes

Potential energy curve surface

Potential energy curves adiabatic

Potential energy curves case /-complex

Potential energy curves computation

Potential energy curves diabatic

Potential energy curves dressed

Potential energy curves electron transfer

Potential energy curves electronic excitation

Potential energy curves for

Potential energy curves for doublezeta HF, N2, and

Potential energy curves for doublezeta HF, N2, and molecule

Potential energy curves for two electronic states

Potential energy curves harmonic

Potential energy curves in excited electronic states

Potential energy curves isomerization

Potential energy curves landscapes

Potential energy curves maxima

Potential energy curves mixed valence complexes

Potential energy curves of OH and Calculated photodissociation cross sections

Potential energy curves profiles

Potential energy curves relativistic density

Potential energy curves research

Potential energy curves rotational motion

Potential energy curves solutions

Potential energy curves state

Potential energy curves wave functions

Potential energy curves, coordination

Potential energy curves, electronic structure

Potential energy curves, ethylene

Potential energy-distance curves

Potential magnetic curves

Potential switching curves

Potential-charge curve

Potential-energy curve for molecules

Potential-energy curve, for hydrogen molecule

Potential-time curves, in constant-current

Potential/anodic current density curves, nickel alloys

Potential/time curves

Qualitative Description of Current-Potential Curves at Semiconductor Electrodes

Quantitative Derivation of Current-Potential Curves

Radiationless potential energy curves

Reaction current versus potential curve

Reaction potential energy curve

Recombination on a Repulsive Potential Curve

Reflectivity-potential curves

Relativistic effects potential energy curves

Relativistic potential curves

Representing ET reactions by the crossing of two potential-energy curves

Repulsive potential curve

Reversible waves, potential-time curves

Ring electrodes current-potential curves

Rotating disk electrode current-potential curves

Rotating ring-disk electrode current-potential curves

Sodium potential energy curves

Stilbene potential energy curve

Surface potentials force-distance curves

The Parabolic Coverage-Potential Curve

The Total-Interaction Potential Curve

The potential energy curve

The potential energy curve of a spherical ion pair

The potential energy curves of

The potential energy curves of CH

The potential energy curves of OH

Titanium potential-time curves

Torsional potential energy curves

Ultramicroelectrode current-potential curves

Vibrationally adiabatic potential curves

Working, curves potential

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