State averaging


The nonrelativistic states are described at the first-order configuration interaction level using a six orbital, eight electron, active space with the oxygen Is orbital kept doubly occupied. The molecular orbitals were constructed from a state-averaged multiconfigurational self-consistent field procedure [31] using an extended atomic orbital basis on oxygen and hydrogen. The details of this description can be found in [30].  [c.465]

State averaging gives a wave function that describes the first few electronic states equally well. This is done by computing several states at once with the same orbitals. It also keeps the wave functions strictly orthogonal. This is necessary to accurately compute the transition dipole moments.  [c.220]

Because difiiaction methods lack the element specificity of EXAFS and because EXAFS lacks the power of molecular-crystal structure solution of diffraction, these two techniques provide complementary information. On the one hand, diffraction is sensitive to the stereochemical short- and long-range order of atoms in specific sites averaged over the different atoms occupying those sites. On the other hand, EXAFS is sensitive to the radial short-range order of atoms about a specific element averaged over its different sites. Under favorable circumstances, stereochemical details (i.e., bond angles) may be determined from the analysis of EXAFS for both oriented and unoriented samples. Furthermore, EXAFS is applicable to solutions and gases, whereas diffiaction is not. One drawback of EXAFS concerns the investigation of samples wherein the absorbing element is in multiple sites or multiple phases. In either case, the results obtained are for an average environment about all of the X-ray absorbing atoms due to the element-specific site averaging of structural information. Although not common, site-selective EXAFS is possible.  [c.223]

Run a final state-averaged calculation at the fuUy-optimized conical intersection using the 4-31G basis set and P to predict the energies of the two states and view the configuration coefficients. (This step will not be necessary if you chose to use P for the final conical intersection optimization job you ll find the relevant output in the CAS output for the final optimization step, preceding the table giving the stationary point geometry.)  [c.235]

The diesel engine operates, inherently by its concept, at variable fuel-air ratio. One easily sees that it is not possible to attain the stoichiometric ratio because the fuel never diffuses in an ideal manner into the air for an average equivalence ratio of 1.00, the combustion chamber will contain zones that are too rich leading to incomplete combustion accompanied by smoke and soot formation. Finally, at full load, the overall equivalence ratio  [c.212]

It would be unrealistic to represent the porosity of the sand as the arithmetic average of the measured values (0.20), since this would ignore the range of measured values, the volumes which each of the measurements may be assumed to represent, and the possibility that the porosity may move outside the range away from the control points. There appears to be a trend of decreasing porosity to the south-east, and the end points of the range may be 0.25 and 0.15, i.e. larger than the range of measurements made. An understanding of the geological environment of deposition and knowledge of any diagenetic effects would be required to support this hypothesis, but it could only be proven by further data gathering in the extremities of the field.  [c.159]

During the optical coat work stress examination method the upper plate of the head of some of the bolts was covered with an optical coat work (Fig. 4). On the head of some other bolts strain gauges were stuck which measured the plain biaxial stress state in the middle of the top surface of the head of the bolt (3.5 x 3 mm). The magnetic probe detected average stresses up to 0.1 mm depth in an area of 14 mm diameter in the middle of the head of the bolt.  [c.7]

Fig. 7 shows the torque necessary to obtain the specified body force under construction conditions and in tbe state when removed from the bridge. It can well be seen that the change of the friction coefficient causes a very big scattering, and the necessary torque is much bigger than specified. The distribution of the results of a measurement performed on 1,127 bolts is presented in Figure 8. An average of 80% of nominal body force was found by the new method. The traditional method found the nuts could be swivelled much further than specified on 42 bolts, these bolts were found to have 40 - 60 % body force by the new method.  [c.9]

Fig.2. Tomographic (a) and graphic (b, for depth 13 mm) images of relative change of Young s modulus 5E% (average on volume Eo=218,310 Pa) of material in section perpendicular to surface of thick-sheet sample (thickness 26 mm). Fig.2. Tomographic (a) and graphic (b, for depth 13 mm) images of relative change of Young s modulus 5E% (average on volume Eo=218,310 Pa) of material in section perpendicular to surface of thick-sheet sample (thickness 26 mm).
As the geometry of the sample is cylindrieal, the pump and the probe beams, foeused at the same side, are loeated on the generating line of the eylinder, as shown in figure 4. Thus, the control of the weld depths penetration and artifieial slots is achieved by seanning the laser system along this generating line. In faet, only the sample moves in one direction. Then, ultrasonic images such as B-scan views are obtained by this scanning, which is suitable for the evaluation of the defects. The analysis of the ultrasonic images, therefore the visualization of the lacks of weld penetration and slots, depends on several parameters linked to the operating system. First, in order to ensure a non-destructive testing, the incident energy deposited on the surface sample is very weak (about 1 mJ). So that, each measurement has to be averaged from few laser shots because of the signal to noise ratio induced by the laser system. The scanning step is optimized to obtain a sufficient spatial resolution of the ultrasonic image and an efficient flaw detection. Nevertheless, these parameters (average, scanning step and length) involve testing duration which have to be reduced within the field of industrial applications. We can also notice that all the following ultrasonic images are presented without any signal or image processing.  [c.697]

Fig. 7b shows the detailed view of fig. 7a but with averaging over four cycles. The random signals have largely disappeared, the signal over the segregation remains and is more clearly to be seen. At this point of the examination, the signal can be caused by a susceptibility variation or by a ferromagnetic inclusion which is not fully demagnetized. In order to distinguish between them, the disk was also measured from the flat side with the direction of rotation being changed in order to have the measuring plots better comparable. Fig. 7c shows the result. The sign of the signal, which is marked with the arrow is the same. If the origin would be ferromagnetic remanence, the sign would have changed. Comparing fig. 7b and c shows that the origin of the signal is a susceptibility variation, either paramagnetic or diamagnetic.  [c.991]

Identifying tube eccentricity versus uniform wastage along the side of the tube is usually a simple matter of averaging the minimum and maximum nominal wall measurements at or near the maximum insertion point of the transducer, typically 50-60 mm above the tube sheet. This location is above any distortions caused by rolling of the generator tube above the tube sheet. Figure 4 is a conceptual diagram of how the scan of an eccentric tube evolves. When the minimum and maximum thickness of the scan are averaged i.e.((4,7 + 3,7)/2 mm) it approximates the average wall thickness of 4,2 mm.  [c.1035]

In December 1997 the average age of the world fleet stood at 19 years, having risen steadily from 12.8 years in 1980. In three or more years time a large proportion of the 6,400 bulk dry or bulk dry/oil carriers in service will be within the critical 14 to 18 years age group. The life of any ship is finite. If the age of the world fleet continues to rise the quality of welding in new constructions and repaired ships together with the detection of corrosion and fatigue damage in existing ships will assume an even greater importance.  [c.1051]

The picture that emerges is that a quiescent liquid surface is actually in a state of violent agitation on the molecular scale with individual molecules passing rapidly back and forth between it and the bulk regions on either side. Under a microscope of suitable magnification, the surface region should appear as a fuzzy blur, with the average density varying in some continuous manner from that of the liquid phase to that of the vapor phase.  [c.57]

L. The liquid-expanded, L phase is a two-dimensionally isotropic arrangement of amphiphiles. This is in the smectic A class of liquidlike in-plane structure. There is a continuing debate on how best to formulate an equation of state of the liquid-expanded monolayer. Such monolayers are fluid and coherent, yet the average intermolecular distance is much greater than for bulk liquids. A typical bulk liquid is perhaps 10% less dense than its corresponding solid state.  [c.133]

If attractive forces are present, then according to an equation by Frenkel (see Ref. 2), the average time of stay t of the molecule on the surface will be  [c.602]

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states.  [c.646]

The variation in qj with 0 will not in general be the same as F(0), since some adsorption will be occurring on all portions of the surface so that the heat liberated on adsorption of dn moles will be a weighted average. There is one exception, however, namely adsorption at 0 K the adsorption will occur sequentially on portions of increasing Q value so that qd(Q) now gives F(0). This circumstance was used by Drain and Morrison [1], who determined qd(0) for argon, nitrogen, and oxygen on titanium dioxide at a series of temperatures and extrapolated to 0 K. The procedure is a difficult one and not without some approximations in the extrapolation. Clearly, it would be very desirable to find a way of solving the integral equation so that site or adsorption energy distributions could be obtained from data at customary temperatures.  [c.656]

There is a limit to the usefulness in elaborating on procedures for solving Eq. XVn-127 since in general there is no exactly correct solution. Experimental data have error, only arbitrarily improved by smoothing the assumed Q(Q, P, T) will not be exactly correct. There is one redeeming situation. In the case of a very heterogeneous surface, the site energy distribution obtained is relatively independent of what adsorption model is used—one may even use just a step function (sometimes known as the condensation approximation—see Refs. 158 and 159). A gross error in the assumed entropy of adsoiption (e.g., bo) can be detected in that the distribution will fail to be temperature independent, and if a model providing for lateral interactions is used, the distribution will be shifted along the Q scale by an amount corresponding to the average lateral interaction energy.  [c.658]

The MCSCF method then optimizes both the molecular orbitals, represented as usual in SCF calculations by linear combinations of atomic orbitals (LCAO), and the Cl expansion coefficients to obtain the variational wave function for one state. The optimization of the orbitals for a particular state, however, will not converge if a degeneracy, or a near degeneracy, of states is present, as the wave function will have problems following a single state. To overcome this, state-averaged orbitals (SA-MCSCF) must be used [231,232]. Rather than optimizing a single eigenvalue of the Flamiltonian matrix, an averaged energy function is used so that the orbitals describe all the states of interest simultaneously to the same accuracy.  [c.300]

The second system studied was the quenching of excited Li(2p) by collision with H2 [236], which is a simple system for the study of energy transfer. The electronic wave function was heated using configurations based on Hartree-Fock molecular orbitals. The orbitals were occupation averaged , which means that the lithium valence elechon was split between tbe ground-state HOMO and LUMO [ -- the Li (2s) and Li (2p)]. This is a simplified foim of the state averaging used in the SA-CASSCF methods mentioned above, used to prevent bias of the basis toward the ground state. The singly occupied HOMO and LUMO then provide the reference configurations. A basis set with all single excitations from the references were then used as a basis set for the wave function. As the reference orbitals were not reoptimized this is termed a CAS-CI rather than a full SA-CASSCF calculation.  [c.308]

Perform a series of state-averaged 4,4 CAS calculations on the ground state, using the active space you have selected. Normally, a CAS calculation optimizes the orbitals and hence the wavefimction for the state of interest (as specified by the NRoot option). However, in a state-averaged CAS, orbitals are optimi. ed to provide the best description of the specified group of states as a whole that is possible with a single set of orbitals  [c.233]

For a state-averaged CAS calculation, you must specify the states to be averaged by selecting the highest state of interest with the NRoot option. All states between that one and the ground state will be averaged. You must also provide the weights for each state to be averaged in a separate input section, in format nFlO.8.  [c.233]

We are interested in the three lowest states, and we want each state to be treated equally, so we will specify NRooi=3 and all three weights as 0.3333333. We will run a series of state-averaged CAS(4,4) calculations (the option is StoleAveroge) on the ground state structure, using this sequence of basis sets 3-21G, 4-31G, 6-31G(d) and 6-31+G(d,p). Begin the first computation using the wavefimction computed in the RHF calculation.  [c.233]

Build up to a good CAS description of this structure by running two state-averaged 4,4 CAS calculations beginning with the wavefunction from the first step (since we will be looking for a conical intersection, we will average the lowest two states using equal weights of 0.5). Use the STO-3G basis set for the first job, along with the UNO and NoFullDiag options to the CASSCF keyword use the 4-3IG basis set for the second job. Include the NoSymm keyword on both jobs.  [c.234]

C=C stretch 80 C-13 chemical shifts 22, 53 C60 31,32 C60O isomers 54 carbon dioxide 120, 182 carbon monoxide 175,191 carbonyl series 84 carbonyl stretch 84, 220 in solution 244 Carmichael 136 Carpenter 152, 196 Cartesian coordinates 52, 286, 287 CASSCF keyword 228 CASSCF method 228,229,230,231, 232,233, 234,235 state-averaged 233  [c.297]

A more balanced description requires MCSCF based methods where the orbitals are optimized for each particular state, or optimized for a suitable average of the desired states (state averaged MCSCF). It should be noted that such excited state MCSCF solutions correspond to saddle points in the parameter space for the wave function, and second-order optimization techniques are therefore almost mandatory. In order to obtain accurate excitation energies it is normally necessarily to also include dynamical Correlation, for example by using the CASPT2 method.  [c.147]

Although gas chromatography can give the concentration of each component in a petroleum gas or gasoline sample, the same cannot be said for heavier cuts and one has to be satisfied with analyses by chemical family, by carbon atom distribution, or by representing the sample as a whole by an average molecule.  [c.44]

Within the same geographicai region, the crude specific gravity varies from one reservoir to another, in Saudi Arabia, for example, the crude from the Ghawar field has an average standard specific gravity on the order of 0.850 (34° API) while the specific gravity of the crude from the nearby Safaniyah field is 0.893 (27° API).  [c.316]

A flowing bottom hole pressure survey (FBHP) is useful in determining the pressure drawdown in a well (the difference between the average reservoir pressure and the flowing bottom hole pressure, Pwf) from which the productivity index is calculated. By measuring the FBHP with time for a constant production rate, it is possible to determine the parameters of permeability and skin, and possibly the presence of a nearby fault, by using the radial inflow equation introduced in Section 9.2. Also, by measuring the response of the bottom hole pressure against time when the well is then shut in, these parameters can be calculated.  [c.222]

The features needed for the training of the neuronal networks are obtained for both kind of ROIs by a very similar procedure. First all local maxima and minima are determined in a y-scan. Afterwards the largest difference between two adjacent local mini- and maxima is determined. Then the corresponding surrounding of one local minimum in the middle and another two local minima on the sides of the local maxima is interpreted as the representation of the crack in the scan. From this representation several features are determined. Starting with the half-power width of the signal, the average depth of the central minimum, the depths and the width of the side minima etc. These features are averaged in y-direction. The denoising effect of the wavelet transform allows to detect the minimum in a scan according to the flaw with a precision of nearly 100% if there is any. Returning with this special information to the non denoised ROI and detecting the flaw in the noise of the original ROI heads to further features.  [c.463]

The basic part of the system is the radiation cabinet housing the X-ray unit, a high frequency, state of the art SMART 160 with a small focal spot of 0.4 mm and the Tru-Vision 300-M-CCD-12" real time imaging chain. Tn between the X-ray tubehead and the imaging chain a conveyor based manipulator is positioned. The frozen fish block is presented on its side so that the average thickness will always be 63 mm and the scanning will be along the length of the block giving the best utilization of the imaging system.  [c.591]

Because of the large acoustic impedance mismatch between air and solid materials the through-transmission teclmique with separate transmitter and receiver transducers on opposite sides of the component is used [3]. However, many applications require a one side access, therefore experiences with a normal incidence echo technique were carried out. A CFRP fabric sandwich laminate with Nomex cores (100x350 mm% total thickness 16 mm) was used. The transducer C 95-137 (IzfP) with a centre frequency of 825 kHz enables a focal length of 40 mm in air. The DLR ultrasonic imaging system HFUS 2000 [4] used for this purpose had to be adapted with a special designed pulser/preamplifier to the air-coupled transducer. The rectangular pulser with an optimized pulse width provides a higher acoustic energy than a common spike pulser. The specially designed preamplifier with a band-pass filter (800-850 kHz, - 3dB) enables a very low-noise amplification so that no signal averaging was necessary for the C-scan recording.  [c.842]

It follows from the foregoing discussion that the essence of the problem is that of estimating the rate of formation of nuclei of critical size, and a semirig-orous treatment has been given by Becker and Doring (see Refs. 4-6). The simplifying device that was employed, which made the treatment possible, was to consider the case of a steady-state situation such that the average number of nuclei consisting of 2, 3, 4,. .., W molecules, although different in each case, did not change with time. A detailed balancing of evaporation and condensation rates was then set up for each size of nucleus, and by a clever integration procedure, the flux /, or the rate of formation of nuclei containing n molecules  [c.330]

Various aspects of the experimental approach to the chemisorption bond are illustrated in the preceding sections. Modem spectroscopic and surface diffraction techniques provide a wealth of information about the chemisorbed state. Analysis of LEED intensity data permits the estimation of adsorbate-adsorbent bond lengths [147], usually 5-10% longer than in molecules having a similar bond. Bond lengths may also be obtained from XPD and SEXAFS data (see Table VIII-1) [148]. A bond energy can be obtained from temperature-programmed desorption data if coupled with knowledge of the activation energy for adsorption (Eq. XVIII-21) see Ref. 149 for the case of a heterogeneous surface. The traditional approach to obtaining bond energies is, of course, through isosteric heats of adsorption, although complications are that equilibrium may be difficult to reach and/or the surface may be heterogeneous. Some literature data compiled by Shustorovich, Baetzold, and Muetterties [ISO] are shown in Table XVIII-2. For hydrogen atom-metal bonds Q averages about 62 kcal/mol, corresponding to about 20 kcal/mol for desorption as H2. Bond energies for CO and NO run somewhat higher. Values can vary depending on the surface preparation and, of course, on the crystal plane involved if the surface is a well-defined one. Older compilations may be found in Refs. 81 and 84, and more recent ones, in Somoijai [13].  [c.712]


See pages that mention the term State averaging : [c.220]    [c.657]    [c.234]    [c.301]    [c.536]    [c.536]    [c.228]    [c.441]    [c.14]    [c.582]    [c.14]   
See chapters in:

Computational chemistry  -> State averaging


Computational chemistry (2001) -- [ c.220 ]