Mental picture

The HF method determines the best one-determinant trial wave function (within the given basis set). It is therefore clear that in order to improve on HF results, the starting point must be a trial wave function which contains more than one Slater Determinant (SD). This also means that the mental picture of electrons residing in orbitals has to be abandoned, and the more fundamental property, the electron density, should be considered. As the HF solution usually gives 99% of the correct answer, electron correlation methods normally use the HF wave function as a starting point for improvements. 

The lADC Drill Bits Subcommittee began work on a new classification method in 1985. It was determined from the outset that (1) a completely new approach was required, (2) the method must be simple enough to gain widespread acceptance and uniform application, yet provide sufficient detail to be useful, (3) emphasis should be placed on describing the form of the bit, i.e., paint a mental picture of the design , (4) no attempt should be made to describe the function of the bit, i.e., do not link the bit to a particular formation type or drilling technique since relatively little is certain yet about such factors for fixed cutter bits, (5) every bit should have a unique lADC code, and (6) the classification system should be so versatile that it will not be readily obsolete. 

Fig. 3.8 Drawings produced by different students about their mental picture of 2NaOH (p. 235)...

The sub-micro level is real, but is not visible and so it can be difficult to comprehend. As Kozma and Russell (1997) point out, understanding chemistry relies on making sense of the invisible and the untouchable (p. 949). Explaining chemical reactions demands that a mental picture is developed to represent the sub-micro particles in the substances being observed. Chemical diagrams are one form of representation that contributes to a mental model. It is not yet possible to see how the atoms interact, thus the chemist relies on the atomic theory of matter on which the sub-micro level is based. This is presented diagrammatically in Fig. 8.2. The links from the sub-micro level to the theory and representational level is shown with the dotted line. 

This first case vividly illustrates the importance of the boundary condition. Indeed, Poisson s equation or the system of field equations have an infinite number of solutions corresponding to different distributions of masses located outside the volume. Certainly, we can mentally picture unlimited variants of mass distribution and expect an infinite number of different fields within the volume V. In other words, Poisson s equation, or more precisely, the given density inside the volume V, allows us to find the potential due to these masses, while the boundary condition (1.83) is equivalent to knowledge of masses situated outside this volume. It is clear that if masses are absent in the volume V, the potential C7 is a harmonic function and it is uniquely defined by Dirichlet s condition. 

To be more exact, every bond is a multi-center bond with contributions of the wave functions of all atoms. However, due to the charge concentration in the region between two atoms and because of the inferior contributions %H2, Xm> and Xh4> the bond can be taken to a good approximation to be a two-center-two-electron bond (2c2e bond) between the atoms C and HI. From the mathematical point of view the hybridization is not necessary for the calculation, and in the usual molecular orbital calculations it is not performed. It is, however, a helpful mathematical trick for adapting the wave functions to a chemist s mental picture. 

It is perhaps useful to mentally picture the microwaves to travel through the waveguide like a water stream through a pipe. In reality, however, the transport is an electric phenomenon that occurs in a very thin layer of the waveguide s inside. The thickness of this layer is characterized by the skin depth parameter, 8, which depends on the used material and the frequency. For example, for the material copper and a frequency of 10 GHz the skin depth is 8 0.66 pm. While at the surface the amplitude of the electric field of the wave is maximal, at a depth of 8 the E is reduced by a factor e 1 0.37, and at a depth of a few 8 becomes negligibly small. Transmission of microwaves through a waveguide is essentially a surface phenomenon. 

In this article, we shall always be concerned with permutations of ligands among sites belonging to a molecular skeleton. No real generality will be lost if we think of permutations in this way from the outset indeed, this differs only in the mental picture invoked from formulations commonly used by mathematicians, as when Weyl 14> speaks of permuting men among "fields on a checkerboard. 

Much of science is abstract. While much of the study of polymers is abstract, it is easier to conceptualize, make mind pictures, of what a polymer is and how it should behave than many areas of science. For linear polymers, think of a string or rope. Long ropes get entangled with themselves and other ropes. In the same way, polymer chains entangle with themselves and with chains of other polymers that are brought into contact with them. Therefore, create mental pictures of the polymer molecules as you study them. 

Lavoisier had formed a clear, consistent, and suggestive mental picture of chemical changes. He thought of a chemical reaction as always the same under the same conditions, as an action between a fixed and measurable quantity of one substance, having definite and definable properties, with fixed and measurable quantities of other substances, the properties of each of which were definite and definable. 

Because of the "resonating character of bonds, it is usually difficult to form a mental picture of them. In this trigonal case which we have been discussing, we may imagine the p. orbital of the central atom to interact in turn with the pt orbitals of the external atoms. If the orbitals d , and dm are available, these may be combined with pn in the same way that and py can be combined with s, to form three directed... 

Chemistry is an experimental science concerned with the composition and properties of matter. The relation of the observed facts to one another forms the basis for the construction of generalized mental pictures, concepts, or models of matter into theories, which ideally should be as simple as possible, so that one can talk conveniently about the multitude of specific facts in a logical manner. Theories can be used to predict the outcome of new experiments. The test of any theory, however, lies in how well these predictions agree with the observed facts. 

This is the mental picture we get when we think of plastics. 

The five basic atomic theories are discussed those of Dalton, Thomson, Rutherford, Bohr, and Schrodinger. You should have a mental picture of an atom as described in each atomic theory. 

If there is a problem, finding out how it came about and how it may be resolved can only be determined from assessing the facts. So the crucial skill in the assessment is asking questions and building up a mental picture of the issues. As discussed before in the section on negotiation in Chapter 7, gathering information into a mind map can assist the process. It can also help to communicate the problem to others, especially those who would like to step-in and take charge for their own reasons. 

As Roylance [25] pointed out, in contrast to the instantaneous nature of the energetically controlles elasticity, the conformational or entropic changes are processed whose rates are sensitive to the local molecular mobility. This mobility is influenced by a variety of physical and chemical factors, such as molecular architecture, temperature, or the presence of absorbed fluids which may swell the polymer. Often a simple mental picture of free volume - roughly, the space available for molecular segments to act cooperatively so as to carry out the motion or reaction in question-is useful in intuiting these rates. 

A theory also serves as a scientific model. A model can be a physical model made of wood or plastic, a computer program that simulates events in nature, a mathematical model or simply a mental picture of an idea. A model illustrates a theory and explains nature. In your chemistry course, you will develop a mental (and maybe a physical) model of the atom and its behavior. Outside of science, the word theory is often used to describe someone s unproven notion about something. In science, theory means much more. It is a thoroughly tested explanation of things and events observed in nature. 

As demonstrated in the previous section, it is advantageous to obtain a deeper understanding of how to perform projections and cuts for multicomponent reactive systems. A single projection or cut captures only part of the system under consideration. However, the user can form a mental picture of the phase diagram in its entirety by making a sequence of such projections and cuts [6],... 

Success in chemistry has been linked to the ability to see things in your mind s eye. As you work your way through this self-instruction course, you will find activities designed to allow you to do this. Just as the letters of the alphabet can be used to form every word in our language, the elements of the periodic table can be used to form every substance in the world. Atoms of these elements join together to form the molecules and compounds that make up foods, furniture, automobiles, people, trees—all the matter that there is. In this unit, you will examine the ideas behind elements, atoms, molecules, and compounds. By the end of the unit you will have a mental picture of each of these ideas that will help you navigate through the concepts of chemistry. 

As you teach yourself about gases in this unit, develop a mental picture of how the molecules of a gas behave. The model for the action of gas molecules in a confined space is called kinetic molecular theory. Because kinetic means moving, the theory describes how molecules behave as a result of their motion. The speed of molecules is related to their temperature, in that the hotter they are, the faster they move. In an enclosed space, molecules randomly strike each other and collide with the walls of the container as they travel (Figure 6.1). 

AH, AS, and AG may help to elucidate a mental picture of events, the thermodynamic status of most polysaccharide dispersions depends on the processes it underwent to achieve a desired end-product or use. 

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