Computational Chemistry

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Chapter 4 Introduction to Quantum Mechanics in Computational Chemistry It is by logic that we prove, but by intuition that we di ...

the role of quantum mechanics in computational chemistry. The wordquantum comes from Latin (quantus, “how much?”, pluralquanta) ...

4.2 The Development of Quantum Mechanics. The Schr€odinger Equation 4.2.1 The Origins of Quantum Theory: Blackbody Radiation and ...

wavelength rangeDl. The total area of all the rectangles is the total flux emitted over its whole wavelength range by the blackb ...

that fit the facts, and then tried to interpret the equation theoretically. To do this he had to make two assumptions: The tota ...

The first inkling of this phenomenon was due to Hertz,^3 who in 1888 noticed that the potential needed to elicit a spark across ...

Eparticle¼hv v¼frequency of the light (4.4) These particles became known as photons (the word was coined by Gilbert Lewis, ca. 1 ...

chlorine or bromine (see below) and because, strictly speaking, the Schr€odinger equation, the fundamental equation of quantum c ...

theory of gases and it was not until 1908, when Perrin’s^10 experiments confirmed Einstein’s atomistic analysis of Brownian moti ...

experiments in which alpha particles from a radioactive sample were shot through very thin gold foil. Most of the time the parti ...

A way out of this dilemma was suggested by Bohr^15 in 1913 [ 9 , 10 ]. He retained the classical picture of electrons orbiting t ...

So from Eq.4.8 Et¼ 1 2 mv^2 "mv^2 ¼" 1 2 mv^2 (4.11) From Eqs.4.7and4.10: v¼ Ze^2 2 e 0 nh (4.12) So from Eqs.4.11and4.12: Et¼" ...

many deficiencies for other atoms, which is to say, almost all atoms of interest other than hydrogen. The problems with the Bohr ...

equation was published, Heisenberg^17 published his matrix mechanics approach to calculating atomic (and in principle molecular) ...

and because the product of mass and velocity is momentum, Eq.4.18can be written pp¼h=l (4.19) relating the momentum of a photon ...

E¼total energy of the particle andV¼potential energy (the usual symbol), i.e. 1 2 mv^2 ¼E"V (4.25) Substituting Eq.4.25formv^2 i ...

The probability of finding the particle in an infinitesimal cube of sidesdx,dy,dz isc^2 dxdydz, and the probability of finding t ...

electron spin is taken into account. The time-independent equation is the one most widely-used in computational chemistry, but t ...

nonplanar systems [ 22 ]. Because of the importance of the concept of hybridization in the simple H€uckel method a brief discuss ...