Ideas of Quantum Chemistry P35 pptx
Ideas of Quantum Chemistry P35 pptx
... correlation of motion of some atoms or
groups of atoms, i.e. the space correlation (“when this group of atoms is shifted to
correlation and
auto-correlation
the left, then another group is most often ... (1953)
1087.
314
7. Motion of Nuclei
(sometimes it takes months on the fastest computers of the world) and calculat-
ing statistics of the number of accepted conformations as...
Ideas of Quantum Chemistry P6 pptx
... is
mean value of measurements
Fig. 1.9. The results of measurements of a quantity A are the eigenvalues of the operator
ˆ
A: E
1
and E
2
.
Postulate V (spin angular momentum)
spin
Spin of elementary ... systems.
16
1. The Magic of Quantum Mechanics
moving along a single coordinate axis x (the mathematical foundations of quantum
mechanics are given in Appendix B on p. 895).
P...
Ideas of Quantum Chemistry P8 pptx
... and some of the inequalities they have to fulfil. The the-
orem pertains to the basic logic of the measurements and is valid independently
of the kind of particles and of the nature of their interaction. ... Copenhagen for quantum mechanics was like Rome for
catholics, and Bohr played the role of the president of the Quantum Faith Con-
gregation.
52
The picture of the wor...
Ideas of Quantum Chemistry P16 pptx
... abyss
of the sea without a bottom.
22
The presence of the Dirac sea makes the Dirac the-
ory, in fact, a theory of an infinite number of particles, whereas formally it was
only a theory of a single ... CALCULATION OF THE GROUND STATE OF THE
HYDROGEN-LIKE ATOM WITHIN DIRAC THEORY
Matrix form of the Dirac equation
We will use the Dirac equation (3.59). First, the basis set compos...
Ideas of Quantum Chemistry P25 pptx
... disposal all the necessary solutions of eq. (5.16). The eigenfunctions of
the
ˆ
H
(0)
operator appeared as a consequence of using them as the complete set of
functions (e.g., in expanding ψ
(1)
k
). ... ψ
k
(λ) are analytical functions
of λ (p. 205). In this mathematical aspect of the physical problem we may treat λ
as a complex number. Then the radius of convergence ρ of the...
Ideas of Quantum Chemistry P31 pptx
... has to be convex as a function of the positions of the nuclei.
6. Please choose the wrong answer. As a result of the rotational excitation J → (J +1) of a
molecule of length R:
a) the angular momentum ... func-
tion in the form of a product of an electronic function and a function describing the
motion of the nuclei; c) leads to the notion of the potential energy curve for t...
Ideas of Quantum Chemistry P34 pptx
... bond
One of the molecules is a donor, the other is an acceptor of a proton, Fig. 7.10.a.
A local minimum of smaller stability appears when one of the water molecules
serves as a donor of two protons, ... 7.10.a):
• stretchingofthehydrogenbondO–H O(thevibrationoftwowatermolecules
treated as entities): 183 cm
−1
• bendingofthehydrogenbondO–H Ointheplaneofthefigure:345cm
−1
• bendingoft...
Ideas of Quantum Chemistry P36 pptx
... professor of Mathe-
matics at Queen’s College in
Cork and a member of the
Royal Society. In 1854 Boole
wrote his Opus Magnum “
An
Investigation of the Laws of
Thought
”, creating a domain
of ... interval has to
be decreased by a factor of 10 (i.e. 0.1 fs instead of 1 fs), which allows us to reach
simulation times of the order of 10–100 picoseconds instead of (in classical...
Ideas of Quantum Chemistry P57 pptx
... sign, not of the strength of quantum chemistry, but of its weakness.
What are we going to do with such a function? We may load it back into the com-
puter and calculate all the properties of the ... results, we need to include a large number of determi-
nants, e.g., of the order of thousands, millions or even billions.
52
This means that
contemporary quantum chemistry has...
Ideas of Quantum Chemistry P80 pptx
... (born
1929), Canadian chemist of
Hungarian origin, son of Mic-
hael Polanyi (one of the pio-
neers in the field of chemical
reaction dynamics), professor
at the University of Toronto.
John was attracted ... powerful theoretical tool for determining the
approximate shape of molecules with numbers of atoms even of the order of hundreds of
thousands. To obtain more reliable in...