From First Principles - No

This similarity among species, in rather fundamental functional properties, has no doubt led to the development and use of earth system models that have little diversity content, but rather use the 

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This strategy is absolute in the sense that it employs symmetry properties of perfectly corresponding pairs rather than approximate models based on extrapolation, analogy, homology, or calculations from first principles. No other method is available in chemistry to provide such strong proof of internal consistency. Any measurable... 

Emphasis on Solving Problems The emphasis is on the solution of problems, and the text contains many example problems, questions for discussion, and appendices. Very few derivations and proofs are required of the student. The approach to problem-solving is to start each new problem from first principles. No attempt is made to train the student to use pre-prepared charts and graphs. 

When there is no specular reflectance, the third term in the denominator drops out, in agreement with Eqs. (5-134) and (5-135). When the reflectance is exclusively specular, the denominator becomes 1/Ai i -I- p g/Aifl — P59), easily derivable from first principles. 

At the other end of the spectrum are the ab initio ( from first principles ) methods, such as the calculations already discussed for H2 in Chapter 4. I am not trying to imply that these calculations are correct in any strict sense, although we would hope that the results would bear some relation to reality. An ab initio HF calculation of the potential energy curve for a diatomic Aj will generally give incorrect dissociation products, and so cannot possibly be right in the absolute sense. The phrase ab initio simply means that we have started with a certain Hamiltonian and a set of basis functions, and then done all the intermediate calculations with full rigour and no appeal to experiment. 

The concept of dipole hardness permit to explore the relation between polarizability and reactivity from first principles. The physical idea is that an atom is more reactive if it is less stable relative to a perturbation (here the external electric field). The atomic stability is measured by the amount of energy we need to induce a dipole. For very small dipoles, this energy is quadratic (first term in Equation 24.19). There is no linear term in Equation 24.19 because the energy is minimum relative to the dipole in the ground state (variational principle). The curvature hi of E(p) is a first measure of the stability and is equal exactly to the inverse of the polarizability. Within the quadratic approximation of E(p), one deduces that a low polarizable atom is expected to be more stable or less reactive as it does in practice. But if the dipole is larger, it might be useful to consider the next perturbation order ... 

The problem, as Woolley addressed it, is that quantum mechanical calculations employ the fixed, or "clamped," nucleus approximation (the Born-Oppenheimer approximation) in which nuclei are treated as classical particles confined to "equilibrium" positions. Woolley claims that a quantum mechanical calculation carried out completely from first principles, without such an approximation, yields no recognizable molecular structure and that the maintenance of "molecular structure" must therefore be a product not of an isolated molecule but of the action of the molecule functioning over time in its environment.47... 

As is evident from these examples, computational quantum mechanics, semiempirical and ab initio methods alike, represent important new tools for the estimation of rate parameters from first principles. Our ability to estimate activation energies is particularly significant because until the advent of these techniques, no fundamentally based methods were available for the determination of this important rate parameter. It must be recognized, however, that these theoretical approaches still are at their early stages of development that is to say, computational quantum chemical methods should only be used with considerable care and in conjunction with conventional methods of estimation discussed earlier in this article, as well with experiments. 

The Latin term "ab initio" means "from the beginning" or "from first principles." Ab initio calculations involve no experimental (empirical) data they are derived solely from theory. (Note that ab initio should not be italicized or used with quotation marks.)... 

The question these correlations ask is why does the entrainment rate decrease for smaller particles for some systems whereas in other systems, the entrainment rate correlates with the particle terminal velocity or particle drag. Baeyens infers that particles may be clnstering due to an interparticle adhesion force that becomes dominant at some critical particle diameter. However, no evidence of particle clnsters was reported. Baeyens assnmption was based on fitting their data. Therefore, the role of particle clnstering on entrainment rates was difficult to establish from first principles. 

There is no doubt that a giant step forward has been made in crystal structure prediction by coupling sound theoretical means with massive computer power, but the inherent uncertainties related to randomness and to handling of temperature remain - see above improvement in force fields and in computational procedures, as results demonstrate, are very welcome but are neither indispensable nor sufficient. And there is no hope that this barrier may fall in the future, as it stems from first principles. The next step forward is the inclusion of kinetic energies and temperature in the model. This is already possible, although with great limitations, as described in Sect. 6. 

For the case of the non-Fourier microscope there is no mathematical formula available, derived from first principles, to calculate its resolution limit. Nevertheless, one knows the practical experimental resolution, which will certainly be smaller than the theoretical limit. For the microscope under consideration, experiments have demonstrated that the resolution is of the order of... 

Table 3.7 also lists ternary spectral moments for a few systems other than H2-H2-H2. For the H2-He-He system, the pairwise-additive dipole moments are also known from first principles. The measured spectral moments are substantially greater than the ones calculated with the assumption of pairwise additivity - just as this was seen in pure hydrogen. For the other systems listed in the Table, no ab initio dipole surfaces are known and a comparison with theory must therefore be based on the approximate, classical multipole model. 

The rototranslational and fundamental absorption spectra of the H2-H complex have been obtained from first principles, for temperatures from 200 to 2500 K [21, 103]. Close-coupled and isotropic interaction approximation calculations give nearly identical values at frequencies from 0 to 6000 cm-1. No laboratory measurements exist for comparison with the calculations. The H2-H system is of considerable interest in stellar environments at such temperatures. 

In the realni of classical thermodynamics, equations of state arc assumed given. They can be derived from first principles only by the methods of statistical mechanics and quantum mechanics These rely on the adoption of suitable molecular models for substances, and so far no universal, generally applicable model has heen discovered even for narrow classes of subslunces such as gases. 

Ab initio methods calculate all quantities needed from first principles and use no experimentally determined parameters. The computations require more machine time and are therefore more expensive than semi-empirical ones. Good energies can now be obtained for small molecules by these techniques. The reader is referred to specialized treatments for further information/... 

Both A(3> and B(3> are longitudinally directed and are nonzero in the vacuum. Both A(3> and B(3> are phaseless, but propagate with the radiation [47-62] and with their (1) and (2) counterparts. The radiated vector potential A<3 does not give rise to a photon on the low-energy scale, because it has no phase with which to construct annihilation and creation operators. On the high-energy scale, there is a superheavy photon [44] present from electroweak theory with an SU(2)x SU(2) symmetry. The existence of such a superheavy photon has been inferred empirically [44], However, the radiated vector potential A<3) is not zero in 0(3) electrodynamics from first principles, which, as shown in this section, are supported empirically with precision. 

It is difficult theoretically to calculate a tunnelling barrier of Gamow type (not the same as activation barrier) from first principles. This paper summarizes methods that employ molecular orbital (MO) approaches to calculate the "electronic factor" which accounts for the transmittance in the forbidden region. The electronic factor will be structure dependent and there is no reason why it should be isotropic in space. 

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