... MAGIC OF
QUANTUM MECHANICS
Where are we?
We are at the beginning of all the paths, at the base of the TREE.
An example
Since 1911 we have known that atoms and molecules are built of two kinds of ... surfaces of dielectrics.
by quantum mechanics using what is known as the wave function. The axioms of quantum
mechanics provide the rules for the derivation of this function...
... quantum cleanness” in favour
of exposing the inter-relationships of problems. In this respect, any division be-
tween physics and chemistry, organic chemistry and quantum chemistry, quantum
chemistry ... vary-
ing levels of knowledge in quantum chemistry as well as for those whose goals and
interests differ from those of traditional quantum chemistry.
This book is a...
... simply multiplication by
¯
h.
From axioms of quantum mechanics one can prove that a product of errors
(in the sense of standard deviation) of measurements of two mechanical
quantities is greater ... follows.
Recall the definition of the variance, or the square of the standard deviation
(A)
2
of measurements of the quantity A:
(A)
2
=
ˆ
A
2
−
ˆ
A
2
(1.20)
26
1. The...
... genius. He contributed to
the mathematical foundations of quantum the-
ory, computers, and game theory. Von Neu-
mann made a strange offer of a professor-
ship at the Advanced Study Institute to Ste-
fan ... spectroscopist of the XX century, author of the fundamental
three-volume work: “Spectra of Diatomic Molecules” (1939), “Infrared and Raman Spectra
of Polyatomic Molecules” (...
... 457.
8.9 Localization of molecular orbitals within the RHF method
405
of neighbouring atoms, etc. These are fascinating problems, and the issue is at the
heart of structural studies of chemistry.
Several ... otherwise
there would be no chemistry at all.
The periodicity of chemical elements discovered by Mendeleev is another fun-
damental idea of chemistry. It has its source i...
... rule of increasing number of nodes. A small
band width corresponds to small overlap integrals of the monomer orbitals. J M. André, J. Delhalle,
J L. Brédas, Quantum Chemistry Aided Design of Organic ... is certainly non-satisfactory: j
max
=
∞. In practice, however, we often take j
max
as being of the order of a few cells,
most often we take
47
j
max
=1.
• For each k from the F...
... reader will find an in-
teresting comparison of the methods used. One of the advantages (or deficiencies) of the DFT methods
is that they offer a wide variety of basis functions (in contrast to the ... function of r,andal-
ternatively as a function of ρ
1
3
.Theexactv
0
(r) represents a monotonic function in-
creasing with r and represents a modification (influence of the second ele...
... the mediation of molecule C.
When the double electron exchanges are switched on, we would obtain part of
the three-body effect of the order of S
4
.SinceS is usually of the order of 10
−2
,
this ... N) contribution to the interaction energy of N molecules (m
N) represents the sum of the interactions of m molecules (all possible com-
binations of m molecules among N molec...
... chosen in the
neighbourhood of the centres of mass (charges) of the interacting molecules. Let
1
ψ
An
1
(1) means an excited state (n
1
is the corresponding quantum number) of atom A, ψ
Bn
2
(2)
similarly ... +L
z
)
m
=x
n
y
l
z
m
+a linear combination of lower multipole moments (X.9)
If, for some reason, all the lower moments are equal to zero, this would mean the
invariance...
... quantum cleanness” in favour
of exposing the inter-relationships of problems. In this respect, any division be-
tween physics and chemistry, organic chemistry and quantum chemistry, quantum
chemistry ... drink coffee with cream at 5 p.m. possibly follows from first princi-
ples, but it would be very difficult to trace that dependence.
IDEAS OF
QUANTUM CHEMISTRY
by
LUCJAN...