162
6 Equilibrium Structures from Spectroscopy
Table 6.14 Substitution of two equivalent atoms
Symmetry Substitution
in position
x 2
y 2
z 2
Examples
C
z
2v
±x 0 z
Px
2m
0
Pz
μ2
H 2 O, SO 2
furan
C
z
2h
x y 0
−x −y 0
Px
2m
1 +
Py
Py −Px
Py
2m
1 +
Px
Px −Py
0
trans-1,2-difluoroethene
C
z
2
x y z
−x −y z
Px
2m
1 +
Py
Py −Px
Py
2m
1 +
Px
Px −Py
Pz
μ2
H 2 O 2
ethylene ozonide
C
xy
s
x y ±z
Px
μ2
1 +
Py
Py −Px
Py
μ2
1 +
Px
Px −Py
Pz
2m aniline
acetaldehyde
a Notations: P g = P g (2) – P g (1), 2m = M(2) – M(1), μ 2 =
2m M(1)
M(2)
References
Allen WD, Yamaguchi Y, Császár AG, Clabo DA, Remington RB, Schaefer HF III (1990)
A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction
by self-consistent-field higher-derivative methods. Linear polyatomic molecules. Chem Phys
145:427–466
Allen WD, East ALL, Császár AG (1992) Ab initio anharmonic vibrational analyses of non-rigid
molecules. In: Laane J, Dakkouri M, van der Veken B, Oberhammer H (eds) Structure and
conformations of non-rigid molecules. NATO ASI Series, Section C, vol 410, Kluwer, Dortrecht,
pp 343–373
Arunan E, Desiraju GR, Klein RA et al (2011) Defining the hydrogen bond: an account (IUPAC
technical report). Pure Appl Chem 83:1619–1636
Bak KL, Gauss J, Jørgensen P, Olsen J, Helgaker T, Stanton JF (2001) The accurate determination
of molecular equilibrium structures. J Chem Phys 114:6548–6556
Balle TJ, Flygare WH (1981) Fabry-Perot cavity pulsed Fourier transform microwave spectrometer
with a pulsed nozzle particle source. Rev Sci Instr 52:33–45
Balle TJ, Campbell EJ, Keenan MR, Flygare WH (1980) A new method for observing rotational
spectra of weak molecular complexes: KrHCl. J Chem Phys 72:922–932
Bevan JW, Legon AC, Millen DJ, Rogers SC (1975) Hydrogen-bonding in gaseous mixtures -
microwave spectroscopic detection of simple complexes. J Chem Soc Chem Comm 130–131
Blass WE, Edwards TH (1967) Molecular constants of axially symmetric molecules from
simultaneous analysis of ground-state combination differences. J Mol Spectrosc 24:111–115
Botschwina P (1988) Anharmonic potential energy functions, vibrational frequencies and infrared
intensities calculated from highly correlated wavefunctions. J Chem Soc, Faraday Trans
2(84):1263–1276
Botschwina P (2005) Accurate equilibrium structures for small polyatomic molecules, radicals and
carbene. Mol Phys 103:1441–1460
Canè E, Di Lonardo G, Fusina L, Jerzembeck W, Bürger H, Breidung J, Thiel W (2005) Rotation
spectrum and infrared fundamental bands of 123 SbD 3 . Determination of molecular geometry and
ab initio calculations of spectroscopic parameters. Mol Phys 103:557–577
Chutjian A (1964) Determination of structure by isotopic substitution in molecules with symmetrically equivalent atoms. J Mol Spectrosc 14:361–370
6 Equilibrium Structures from Spectroscopy
Table 6.14 Substitution of two equivalent atoms
Symmetry Substitution
in position
x 2
y 2
z 2
Examples
C
z
2v
±x 0 z
Px
2m
0
Pz
μ2
H 2 O, SO 2
furan
C
z
2h
x y 0
−x −y 0
Px
2m
1 +
Py
Py −Px
Py
2m
1 +
Px
Px −Py
0
trans-1,2-difluoroethene
C
z
2
x y z
−x −y z
Px
2m
1 +
Py
Py −Px
Py
2m
1 +
Px
Px −Py
Pz
μ2
H 2 O 2
ethylene ozonide
C
xy
s
x y ±z
Px
μ2
1 +
Py
Py −Px
Py
μ2
1 +
Px
Px −Py
Pz
2m aniline
acetaldehyde
a Notations: P g = P g (2) – P g (1), 2m = M(2) – M(1), μ 2 =
2m M(1)
M(2)
References
Allen WD, Yamaguchi Y, Császár AG, Clabo DA, Remington RB, Schaefer HF III (1990)
A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction
by self-consistent-field higher-derivative methods. Linear polyatomic molecules. Chem Phys
145:427–466
Allen WD, East ALL, Császár AG (1992) Ab initio anharmonic vibrational analyses of non-rigid
molecules. In: Laane J, Dakkouri M, van der Veken B, Oberhammer H (eds) Structure and
conformations of non-rigid molecules. NATO ASI Series, Section C, vol 410, Kluwer, Dortrecht,
pp 343–373
Arunan E, Desiraju GR, Klein RA et al (2011) Defining the hydrogen bond: an account (IUPAC
technical report). Pure Appl Chem 83:1619–1636
Bak KL, Gauss J, Jørgensen P, Olsen J, Helgaker T, Stanton JF (2001) The accurate determination
of molecular equilibrium structures. J Chem Phys 114:6548–6556
Balle TJ, Flygare WH (1981) Fabry-Perot cavity pulsed Fourier transform microwave spectrometer
with a pulsed nozzle particle source. Rev Sci Instr 52:33–45
Balle TJ, Campbell EJ, Keenan MR, Flygare WH (1980) A new method for observing rotational
spectra of weak molecular complexes: KrHCl. J Chem Phys 72:922–932
Bevan JW, Legon AC, Millen DJ, Rogers SC (1975) Hydrogen-bonding in gaseous mixtures -
microwave spectroscopic detection of simple complexes. J Chem Soc Chem Comm 130–131
Blass WE, Edwards TH (1967) Molecular constants of axially symmetric molecules from
simultaneous analysis of ground-state combination differences. J Mol Spectrosc 24:111–115
Botschwina P (1988) Anharmonic potential energy functions, vibrational frequencies and infrared
intensities calculated from highly correlated wavefunctions. J Chem Soc, Faraday Trans
2(84):1263–1276
Botschwina P (2005) Accurate equilibrium structures for small polyatomic molecules, radicals and
carbene. Mol Phys 103:1441–1460
Canè E, Di Lonardo G, Fusina L, Jerzembeck W, Bürger H, Breidung J, Thiel W (2005) Rotation
spectrum and infrared fundamental bands of 123 SbD 3 . Determination of molecular geometry and
ab initio calculations of spectroscopic parameters. Mol Phys 103:557–577
Chutjian A (1964) Determination of structure by isotopic substitution in molecules with symmetrically equivalent atoms. J Mol Spectrosc 14:361–370