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Calculations of the potential energy surface for molecules with the molecular formulas [2H, 1C, 1SI] and [2H, 2SI]

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Title:
Calculations of the potential energy surface for molecules with the molecular formulas [2H, 1C, 1SI] and [2H, 2SI]
Creator:
Noble, Anna Louise
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English
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ix, 58 leaves : ; 28 cm

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Potential energy surfaces ( lcsh )
Potential energy surfaces ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Bibliography:
Includes bibliographical references (leaves 57-58).
Thesis:
Department of Chemistry
General Note:
Department of Chemistry
Statement of Responsibility:
by Anna Louise Noble.

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|University of Colorado Denver
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Full Text
CALCULATIONS OF THE POTENTIAL ENERGY SURFACE FOR
?

!
MOLECULES WITH THE MOLECULAR FORMULAS [2H, 1C, 1SI] AND
[2H, 2SI].
By
Anna Louise Noble
B.A University of Wales, Swansea, 1998.
A thesis submitted to the
University of Colorado at Denver and Health Sciences Center
in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Chemistry
2007


This thesis for the Master of Science in Chemistry
degree by
Anna Louise Noble
has been approved
^ by
Hai Lin
7/ao/o?
Date


Noble, Anna Louise. (Master of Science, Department of Chemistry)
Calculations of the Potential Energy Surface for Molecules with the
Molecular Formulas [2H, 1C, 1 Si] and [2H, 2Si].
Thesis directed by Professor Robert Damrauer
ABSTRACT
Structures of acetylene analogs with the composition [1C, 1 Si, 2H] and
[2Si, 2H] were optimized using 6-31G++ basis set. These computations
show that the most stable structures are a doubly-bonded H2C=Si: with
trigonal planar geometry for the [1C, 1 Si, 2H] molecule and a doubly
hydrogen bridged structure for the [2hi, 2Sij moiecuie. The structures and
energies of the anions and the dianions for each of these species were
also computed and these energies were used to calculate electron
affinities for both the neutral species and the anions. These electron
affinities were positive for the neutral species and very negative for the
anionic species.
This abstract accurately represents
recommend its publication.
Signed
Robert Damrauer


DEDICATION
I dedicate this thesis to my husband, Joel, for his patience and
understanding and unwavering support. I also dedicate this to my two
children, Aidan and Eleanor for whom this has been an almost lifelong
reality of having a Mommy in grad school!


ACKNOWLEDGEMENT
My thanks to my advisor, Bob Damrauer, for his patience and flexibility
with me. I know it has taken me a long time, but I really appreciate
everything you have done for me.


TABLE OF CONTENTS
Figures..............................................................vii
Tables...............................................................viii
Chapter
1. Introduction.........................................................1
1.1 Known Neutral Carbon Silicon Structures-Silynes..................1
1.2 Known Neutral Silicon-Silicon Structures -Disilynes................8
1.3 Known Structures of Anions........................................14
1.4 Electron Affinities...............................................15
2. Computational methods.... .... ...................19
3. Results.............................................................22
3.1 Analyses and Comparison of Carbon-Silicon Neutrals.................22
3.2 Analyses and Comparison of Silicon-Silicon Neutrals...............25
3.3 Analysis of Structures of Carbon- Silicon Anions..................27
3.4 Analysis of Structures of Silicon-Silicon Anions..................29
3.5 Analysis of Structures of Carbon-Silicon Dianions.................33
3.6 Analysis of Structures of Silicon-Silicon Dianions................37
4. Analysis.........................................................42
4.1 Calculated Electron Affinities for Neutral Species.................42
4.2 Calculated Electron Affinities for Anions.........................45
4.3 Vertical Attachment Energies for the Neutral Species............48
4.4 Vertical Attachment Energies of Anions............................52
5. Conclusions......................................................56
References...........................................................57
vi


LIST OF FIGURES
Figure
1.1 Structure 1.......................................................2
1.2 Structure 2.......................................................3
1.3 Structure3........................................................5
1.4 Structure 4.......................................................9
1.5 Structure5........................................................9
1.6 Structure6.......................................................11
1.7 Structure 7......................................................11
1.8 Structure8..................................................... 12
3.1 Bent cis structure of the C-Si anion............................29
vii


LIST OF TABLES
Table
1.1 Summary of relative energies of the singlet C-Si trans structure vs. the
trigonal structure from various previous calculations..............7
1.2 Summary of calculated energies for the singlet silicon-silicon
species...........................................................13
3.1 Energies of carbon-silicon neutral species calculated using a RHF/ 6-
31++G(p,d) program........................................................24
3.2-Energies of silicon-silicon neutral species calculated using a RHF/ 6-
31++G(p,d) program.................................................26
3.3 Energies of carbon-silicon anion species calculated using a ROHF/ 6-
31++G(p,d) program...............................................28
3.4 Energies of silicon-silicon anion species calculated using a rohf 6-
31++G(p,d) program................................................31
3.5 Energies of carbon-silicon dianion singlet species calculated using a
uhf 6-31++G(p,d) program..........................................34
3.6 Energies of carbon-silicon dianion triplet species calculated using a
ROHF/ 6-31++G(p,d) program........................................36
viii


3.7 Energies of silicon-silicon dianion singlet species calculated using a
uhf 6-31++G(p,d) program......................................38
3.8 Energies of silicon-silicon dianion triplet species calculated using a
rohf 6-31++G(p,d) program.....................................40
4.1 Calculated electron affinities for the lowest energy neutral for the [1C,
1 Si, 2H] species and the [2Si, 2H] species...................44
4.2 Calculated electron affinities for the lowest energy anion for the [1C,
1 Si, 2H] and the [2Si, 2H] species..........................47
4.3 Vertical Attachment Energies for structures for which there were
minima for both the neutral and the anion geometries....50
4.4 Vertical Attachment Energies for structures for which there were
minima for both the anion and the dianion geometries...........54
IX


1. Introduction
The structure, energetics and bonding of gas phase silicon analogs of
acetylene, that is compounds with the molecular composition of either [2H,
1C, 1 Si] or [2H, 2Si] have been studied fairly extensively using computational
methods, and the results have recently been used to guide the production of
triply bonded silicon species in the lab. 1 However, electron affinities (EAs)
and gas phase acidities (AHaCid) for many of these species have not yet been
determined. Electron affinities provide useful information about the ability of
various species to gain an electron, which in turn can be used to predict
solvent effects and gain understanding of the nature of the carbon-silicon and
silicon-silicon triple bonds on a molecular orbital level.1'3
1.1 Known Neutral Carbon Silicon Structures -Silynes
As a rule, triple bonds do not form for the main group elements beyond the
first row, possibly due to repulsion from the inner electrons.3 The proximity of
the atoms required to gain sufficient pi overlap means that the atoms are
close enough that the inner electrons are repelled by one another and make
the molecule less stable.1 As a result, isolation of a Si-Si triple bond had not
1


been successfully accomplished until 2005, and isolation of a C-Si triple bond
is still proving elusive.3 These molecules could theoretically be considered as
singlets (electrons are paired) or triplets (electrons are unpaired). In H2C2, the
singlet species are all lower in energy than the triplets.4
The first obvious structural difference between acetylene and the lowest
energy (2H, 1C, 1 Si) species is the geometry. Such species were first
studied computationally by Murrel, Kroto and Guest.5 Whilst acetylene
prefers a linear geometry because of the sp-sp hybridization of the carbon
atoms, the lowest energy carbon-silicon species (structure 1) on the [2H,
1 Si, 1C] PES actually has the doubly-bonded H2C=Si: trigonal geometry,
(structure 1).1,5
Figure 1.1 -structure 1
2


Rather than a triple bond, the molecule has a double bond and a lone pair
on the silicon atom. It is about 35 kcal/mol more stable than the next lowest
energy structure, and is unlike the linear acetylene molecule.5 For
comparison, the H2C=C: analogous species is a minimum on the acetylene
PES but still higher than the global minimum, which is the linear HOCH
molecule.6
The lowest [2H, 1C, 1 Si] structure (2) which is likely to have triple bonds is
not linear, as in the case of acetylene, but instead has a trans bent
structure1 5,7 (structure 2) The silicon atom also has electrons in the 3d
orbital, which hinders its ability to form sp hybridized orbitals. 1 The energy
barrier between the trans structure and the doubly bonded trigonal structure
is relatively low (6 kcal/mol) and thus implies low kinetic and thermodynamic
stability for the trans structure1,5,7. In fact, the existence of a stable triply
bonded [2H, 1C, 1 Si] structure has been the topic of recent debate among
researchers.1,3,5
Si
Figure 1.2 structure 2
3


Although the rc-bond overlap is weakened in this geometry, the o bond is
strengthened. The larger size of the silicon atom means that the proximity
that would be required to generate sufficient n overlap results in too much
repulsion from the inner electrons. In adopting the trans geometry, the atoms
are able to move apart enough to achieve maximum a overlap, and thus a
stronger o-bond. 1 This compound has been identified in a glow discharge
plasma of a gaseous mixture of SiH4 and CO, and rotational spectral lines
have been observed.8 The calculated C-Si triple bond length of 1.635A is
shorter than a double bond (~1.70A), but not as long as might be predicted.
The linear species analogous to acetylene is not a minimum on the PES. The
energy was calculated in a single point calculation by Apeloig to be 6.3
kcal/mol higher than the trans structure at a comparable computational level.
If the linearity constraint is removed, it optimizes to the trans bent structure
2 7 Upon bending from linear to trans bent, the carbon-silicon bond length
increases slightly, but not as long as a carbon-silicon double bond.6 There
has been a long running debate as to whether or not species like structure 2
could actually be considered as true triple bonds, as valance bond analyses
give a bond order of approximately 2.5.6,7
4


The isomeric carbene species (3) with the lone pair situated on the carbon
atom, is also a minimum on the PES, but was found to be significantly higher
in energy (84.1 kcal/mol) than structure 1 7 This is likely due to the lone pair
on the silicon atom being much more stable than the analogous lone pair on
the carbon atom, due to charge dispersal (i.e the larger size of the silicon
orbitals means that the lone pair of electrons suffer less repulsion from one
another than they would on the smaller carbon atom.)
Hydrogen bridged structures, which are minima for the disilynes (see section
1.2), are not possible for molecules containing carbon atoms, since they
require the higher energy 3p and 4p orbitals, which are only energetically
accessible for the larger silicon atoms.
5


Luke and coworkers have computed the triplet energies for the (2H, 1C, 1 Si)
species. In this case, the PES minimum (again, the doubly bonded H2C=Si)
was found to be 35.6 kcal/mol above that for the corresponding singlet. The
trans-bent structure (similar to structure 2) triplet was 61.1 kcal/mol higher,
and a cis bent structure was also found with an even higher energy. The PES
of the triplet species was always higher than that of the singlet, which is the
same as for acetylene, where triplet linear acetylene and vinylidene, (H2C=C)
are 72.1 and 93.2 kcal/mol higher than the corresponding singlets.9
A summary of the energies of the singlet (2H, 1C, 1 Si) species from various
calculations, and a comparison with the corresponding triplet energies is
given in table 1.1.
6


Table 1.1- Summary of relative energies of the singlet C-Si trans structure
vs. the trigonal structure from various previous calculations.
Structure M.S Gordon and J.A. Pople 1981 MP3/6- 311G* Apeloig 1998 CCSD(T)/TZ2p(fd)/ /CCSD(T)/TZ2p+ZPE 7 Kami and Apeloig 20011 QCISD(T)/6- 311G(d,p) Energy of corresponding triplet Luke et. al.
H H * (1) 0.0 0.0 0.0 35.6 kcal/mol
H Si (2) Approx 50 kcal/mol 34.1 kcal/mol 32.9 kcal/mol 61.1 kcal/mol
Energy Barrier between 1 and 2 5-8 kcal/mol 5.1 kcal/mol 6.0kcal/mol
7


1.2 Known Neutral Silicon-Silicon Structures -Disilynes
The singlet silicon-silicon triply bonded species (disilyne) is even more
unlike acetylene. The molecules with [2H, 2Si] composition have been
studied much more extensively using much more sophisticated levels of
theory than the silynes5. The PESs of these molecules are more complex
than for the carbon silicon species. 1
In 1983 Lischka and Kohler found that the potential energy minimum for the
silicon-silicon structure is in fact a doubly hydrogen bridged structure
(structure 4)10. This structure allows for maximum orbital overlap, and it was
calculated to be 18.7 kcal/mol more stable than the trans species (structure
5).1 The Si-H-Si bond angle is 103.8, and the Si-Si bond length is 2.01 A.
These structures can be explained by considering the molecule to be formed
from 2 HSi fragments in the doublet state.1 This finding was reinforced by
higher level calculations by Binkley et. al. using polarized basis sets for
geometry optimizations. Relative energies were calculated by subsequent
single point calculations.5
8


Figure 1.4 Structure 4
The theoretical predictions about the unusual hydrogen bridged structures
were confirmed by spectroscopic studies on Si2H2 in low temperature
matrices by Bogey et al. in 1991, and Andrews et al. in 200211,12.
The triply bonded trans HSbSiH (structure 5), the closest analog to
acetylene is a minimum on the PE surface, but not a global minimum5,6 The
energy is about 18.7 kcal/mol higher than the hydrogen bridged structure.1
There is again some debate as to whether these molecules may be
considered true triple bonds, since the bond orders are very close to 2.5, and
significant lengthening upon bending does occur (the bond length for the
linear structure is 1.96A, and for the bent structure it is 2.11 A.1,3)
Figure 1.5- Structure 5.
9


The classical linear disilyne is not found as a minimum, and is approximately
25 kcal/mol less stable than the trans bent structure1,5. The proximity
required to generate sufficient overlap for a pi-bond to form between the 2
silicon atoms would cause repulsion by the inner electrons. If the structure
bends to the trans bent geometry, the silicon atoms can move further apart,
and have better o-overlap, and thus a more stable molecule.1,1 Lischka and
Kohler showed the linear structure to be a second order saddle point on the
PES.5,10 Geometry optimization of this structure without any linearity
constraints was shown to yield the trans structure (structure 5).5
Experimentally, triply bonded trans structures have been observed between
2 silicon atoms only if very bulky R groups (such as (tBusSi^MeSi) are
substituents. The tBu3Si is not bulky enough to allow triple bond formation.
These large groups effectively hinder the bridging geometry3. Such triply
bonded species have been prepared transiently by starting from
dihalodisilanes and an alkali metal (Li, Na), in a napthalene solvent3,12 DFT
calculations of these prepared species show the Si-Si bond length to be very
short at only 207.2 pm and a trans bonding angle (Si-Si-H) of 148.0. Bond
orders have been calculated above 2.5, and thus the structures may be
considered to be approaching true triple bonds. 3 6
10


The trigonal doubly bonded silicon structure (structure 6- figure 1.6) is about
12.2 kcal/mol higher in energy than the bridged structure1.
H H
\ /
Si
Si
Figurel .6 -Structure 6
Later calculations confirmed the preliminary findings of Lischka and Kohler,10
and another energy minimum, the singly hydrogen bridged isomer (structure
7) was found with an energy that is between the doubly bridged hydrogen
structure and the trans structure.4,1
Figure 1.7- Structure 7
11


These molecules also could theoretically exist as triplets. The corresponding
triplet energies were also calculated by Lishcka and Kohler, and in this case,
the most stable structure is the disilenylidene (structure 8), which was 20
kcal/mol more stable than the bridged structure. The trans-bent isomer was
again a local minimum.10 However, on the whole, the triplet states were of
higher energies than the corresponding singlets, with the exception of the
singlet silicon H2Si=Si species, where the triplet is a little lower than the
singlet1.
Figure 1.8 Structure 8
Table 1.2 gives a summary of various calculations done with these molecules
12


Table 1.2- Summary of calculated energies for the singlet silicon-silicon
species.
Structure Average Relative energy from Liscka and Kohler 1983 Huzinaga basis set with SCF. ^kcal/mol) Average relative energy from Binkley MP4/6- 311++G**5 Energy from Apeloig and Rappoport 2001 report. MP2/6-311G(2d,p) 1 Energy by Lein, Krapp and Frenking 2004. DFT BP86/QZ4P and 4 sets of polarization functions.
H\ 1 0.0 0.0 0.0 0.0
Ni l>H N/A N/A 9.0 9.9
\ /H Si Si 11.8 11.3 14.1 15.3
H Si ill Si 14.3 14.2 18.7 19.9
13


1.3 Known Structures of Anions
There are several areas of chemistry where properties of negative ions or
radicals are important, particularly in silicon chemistry. This includes
semiconductor chemistry, and processes involved in biochemical pathways
for electron transfer. There is therefore a need to examine and discuss the
implications of the structures of the anion and dianion species, compared to
those of acetylene2.
The effect of adding an electron to the disilyne molecule has been studied
and was shown to change both the shape and position of the PES. The
global minimum was shown to be the disilavinylidene anion H2SiSi~, which
was 24 kcal/mol below the dibridged anion geometry and 12.6 kcal/mol
below the monobridged anion geometry. Although the planar trans bent
structure was not a minimum, a twisted trans bent structure was found with a
relative minimum of 11.9 kcal/mol.13 There is currently no literature on the
structures of the C-Si anionic species.
14


1.4 Electron Affinities
An electron affinity (EA) is the energy difference between the ground state of
an uncharged species and the ground state of its negative ion. Equation 1.1
shows the EA of R is the transition energy from the ground vibrational and
rotational states of the anion to the ground vibrational and rotational states of
the neutral. 2
EA(R) = El R, v-O, J=0|-<-E| R, v=0,J=0^
Equation 1.1 Electron affinity definition fora species, R.
Since a goal of this study is to determine the electron affinities of both the
[2H, 1C, 1 Si] and the [2H, 2Si] species, it is important to realize that the
energy minimum for the anion may have a totally different geometry than the
energy minima of the neutral species, i.e. a shift in geometry can occur when
an electron is added to a molecule. For this reason, there are 2 possible
ways in which electron attachment can be calculated.2 The vertical
attachment energy (VAE) is the energy difference between a neutral species
and its anion, when the geometry is NOT changed upon addition of an
electron. This is useful for anions with very short lifetimes, and can be
15


measured with transmission electron spectroscopy, where there is no time
for geometry relaxation. The adiabatic electron affinity (EA) is the energy
difference between a neutral species and its ground state anion, allowing for
changes in geometry.2 For the purposes of this paper, both the VAEs and
the EAs have been found for each species.
To calculate EAs of acetylene analogs, it is necessary to examine the
structural changes that occur when an electron is added to the neutral
species. To calculate the EAs of the anions, the geometries of the dianions
must be determined. It is known that the electron affinity of acetylene is
negative, and therefore the addition of an electron cannot occur
spontaneously; i.e. the radical anion of acetylene is unstable. Adding an
electron to the pi-system means adding it to the n* molecular orbital, thus
decreasing the overall bond order of the molecule.
It is also true that the EAs of many silicon species are higher than their
carbon analogs, and it is therefore possible that triply bonded silicon species
may have a positive EA. Examples include: the EA of the C atom is 1.26 eV
whereas the EA of the Si atom is 1.39 eV; the EA of singlet methylene, CH2,
is 0.652 eV whereas the EA of singlet SiH2 is 1.12 eV; the EA of CF is 0.4
16


eV, that of SiF is 0.8 eV; finally, the EA of CH3 is 0.08eV,with that of SiH3
1,40eV2.
It is also known that the triple bond in Si2H2 is not completely sp-sp
hybridized,12 which may pave the way for the easier addition of an electron,
since there are more orbitals available for the electron to be added to. A
molecule containing a silicon atom would be possibly be more able to cope
with the extra negative charge than acetylene because of silicons size and
the orbital locations.
A theoretical study of electron attachment to these [2H, 1C, 1 Si] and [2H,
2Si] species may provide useful insight into how these compounds might
behave, particularly in the role of silicon compounds in semiconductor
chemistry. If the EA of the silicon species was positive, then this may prove
useful knowledge in building semiconductor materials, which require easy
translocation of electrons.2 An understanding of how an extra electron alters
structure, bond length and bond order will hopefully provide a deeper
understanding of how electrons are situated within these species and which
electrons are first to detach the pi-system.
17


The only study so far into electron affinities of these species was a study by
Pak, Rienstra-Kirakofe, and Schaefer in 2000. This study determined the
zero-point energy corrected EA of the H2Si=Si species to be 1.87 eV and the
EA of the doubly hydrogen bridged structure was found to be 0.45eV. 1,10,13
18


2. Computational Methods
Computational methods allow us to examine possible structures in the gas
phase eliminating any solvent effects and also to calculate energies for
structures, which have not yet been elucidated in the lab. Density Functional
Theory (DFT) calculations have been used for several years in computing
electron affinities, and have been proven to be a close estimate to
experimentally obtained values.2 In DFT, the molecular orbital wave functions
are calculated using the atomic orbital wave functions obtained from a basis
set, in this case 6-311 G++(d,p).
Different basis sets give different levels of accuracy in calculations. The more
detailed the atomic orbital terms, the closer a molecular calculation will come
to an actual energy. However, the extra detail compromises time and the
ability to come to an efficient conclusion. The 6-311++G (d,p) basis set gives
good, consistent molecular orbital approximations. The d and p notation
refers to the use of polarization functions in the atomic orbital calculations,
and the ++ notation refers to diffuse functions. The energy can then be
calculated through a series of ab-initio methods, such as Hartree-Fock,
19


whereby the energy minima are obtained by substituting the energies back
into the original equation and recalculating until a minimum is reached.
For the purposes of this study, a variety of possible geometries were
computed using GAMESS, and the structures that were optimized (minimum
points on a potential energy surface) were the ones that were considered
further. Such optimized structures were visualized using the MacMol Plot
software package. Four possible geometries for the [2H, 1C, 1 Si] structure
and 6 possible geometries for the [2H, 2Si] structure were considered. These
were chosen after a thorough search of current literature on the subject, and
after several preliminary optimization calculations of a variety of possible
starting geometries. These neutral geometries were studied using an MP2
electron correlation at the 6-311 ++G(d,p) level of theory. There is substantial
evidence that this level of computation provides acceptable results within
close range of the true electron affinities.2 The computed energies and
geometries were then compared with recent publications to ensure that this
level of theory is sufficient. Since the triplet species were known to be of
higher energy than the singlets, these were not run as neutrals.
20


The anionic species which, as radicals, were run using a restricted open shell
Hartree-Fock calculation. The optimized neutral structures were starting
coordinates for the anion optimizations. Some structures retained an almost
identical geometry to the input, whereas others changed significantly. Other
geometries that were not minima as neutrals were also studied.
The dianionic species could theoretically exist as either a singlet (all
electrons are paired), or a triplet (electrons are unpaired).14 For the purposes
of this paper, both possibilities were considered and calculated. The
dianionic singlet species were run at rhf 6-311++G(d,p), and the triplets were
run at rohf 6-311++G(d,p) beginning from optimized neutral structures.
All energies were corrected using the zero point energy contributions
obtained from the vibrational analysis of the optimized structures.
Approximate bond lengths and angles were obtained from the MacMol plot
analysis.
21


3. Results
3.1 Analyses and Comparisons of Carbon-Silicon Neutrals
Initially, the structures of the neutral species were analyzed and compared
with previous studies by Apeloig and Jutzi. The results of these calculations
for the neutral species are shown in tables 3.1 & 3.2.
The results in table 3.1 show that the structures and energies of the carbon-
silicon species are consistent with those in the 2001 Rappoport and Apeloig
report.14 These calculations were done using a restricted Hartree-Fock
method. The minimum energy is the trigonally bound carbon species (1),
which is about 30 kcal/mol lower than the triply bonded trans structure (2).
The trigonally bound silicon species (3) was much higher in energy (84
kcal/mol), which is to be expected since this would require the lone pair to be
situated much more unstably on the carbon atom. The cis structure (4)
optimizes to the trans structure, and the bridging structures are not minima in
this case. The linear geometry was not a minimum for any of the structures
(neutrals, anions, or dianions). Bond lengths and angles were found to be
22


similar to the Apeloig report. The closeness to previously published values
demonstrates the reliability of the level of calculation used.
23


Table 3.1 Energies of carbon-silicon neutral species calculated using a
RHF/ 6-311 ++G(p,d) program, s-squared =0.0, freq =0.0 for all species.
Values in parentheses are those from the 2001 Apeloig and Rappoport
report. 14
Starting geometry Ending geometry Corrected Energy (kcal/mol) Relative Energy (kcal/mol)
H \ 1 Similar to input -205863.1 0.0 (0.0)
C h"! 3i 2 Similar to input -205833.3 29.8 (32.9)
c c \ H 3 Similar to input -205778.7 84.4 (90.0)
Cis c^H III Changes to trans (3)
III Si H 4
24


3.2 Analyses and Comparison of Silicon-Silicon Neutrals.
The results in table 3.2 show a similar consistency with previously calculated
energies. The lowest energy species was found to be the doubly bridged
hydrogen species (5). This was 9.8 kcal/mol lower in energy than the singly
bridged hydrogen (6) and 16.6 kcal/mol lower than the doubly-bonded
trigonal species (7). The trans species (8) was the highest energy minimum
with an energy 19.6 kcal/mol higher than the doubly hydrogen bridged
structure. The values obtained are also very close to the Lein, Krapp and
Frenkling 2004 report.4 Bond lengths and angles again were similar to those
previously published. The cis structure (9) on optimization yields the trans
structure and hence is not a PE minimum.
25


Table 3.2 Energies of Silicon-Silicon Neutral Species calculated using a
RHF/ 6-311 ++G(p,d) program, s-squared =0.0, freq =0.0 for all species.
Values in parentheses are those from the 2001 Apeloig and Rappoport
report. 14
Starting geometry Ending geometry Corrected Energy (kcal/mol) Relative Energy (kcal/mol)
2 Bri< H\ dging H 3i 3i 5 Similar to Input -363381.4 0.0 (0.0)
H\ Si I Si-"^ 6 Similar to input -363371.6 9.8 (9.7)
Tri H \ C gonal >i 7 Similar to Input -363364.8 16.6 (14.1)
Trans H Si 111 Si 8 Similar to Input -363361.8 19.6 (18.7)
Cis Si II Si H 9 Changes to Trans
26


3.3 Analysis of Structures of Carbon- Silicon Anions
Once the reliability of the calculation techniques were confirmed, the
optimized geometries of the neutrals were optimized as anion doublets as a
restricted open shell hartree-fock calculation. The results of these
calculations are summarized in tables 3.3 and 3.4.
Table 3.3 shows the optimized geometries of the carbon-silicon anion
species. The energy minimum in this case is the trigonal carbon species (10)
with similar geometry to (1). This has a zero point corrected energy that is
slightly lower energy than the neutral species. The carbon-silicon bond length
is approx 1.8 A, a little longer than 1.7 A for the neutral. The triply bonded
trans structure (11) is 31.8 kcal per mole higher than (10) in energy, and the
trigonal silicon structure (12) is much higher almost 60kcal per mol. Input
geometries for structure (13), and for the singly and doubly bridged
structures changed to the trans structure upon optimization.
27


Table 3.3 Energies of Carbon-Silicon Anion Species calculated using a
ROHF/ 6-311++G(p,d) program, s-squared =0.75, freq =0.0 for all species.
Starting geometry Ending geometry Corrected Energy (kcal/mol) Relative Energy (kcal/mol)
H \ S i 10 Same as input -205883.5 0.0
( y l 11 Same as Input -205851.7 31.8
c < H "S \ H 12 Same as Input -205823.8 59.7
r /H c III Si H 13 Changes to Trans
28


3.4 Analysis of Structures of Silicon-Silicon Anions
Silicon radical anion species were also calculated and compared to the
previous report by C. Pak, J.C. Rienstra-Kiracofe, H.F Schaefer et al.15 The
global minimum was found to be the trigonal species (14) which is lower in
energy than all of the neutral silicon-silicon species. Our finding was in
accordance with those of Pak et al. The next highest energy optimized
species was a twisted cis -bent structure (15) (figure 3.1), that was obtained
from inputting the trans geomety. It is unclear at this point how this structure
compares to the trans bent geometry from the C.Pak report, since the
energies obtained from (15) and (16) are very similar in energy.
Figure 3.1 Bent cis structure of C-Si anion(15)
29


The doubly bridged hydrogen structure (17) was, in this case, much higher
than the trigonal structure, suggesting that the addition of the extra electron
disrupts the stability of the bridging hydrogens. Although C. Pak, et al were
able to find a minimum for the singly bridged hydrogen species (18), this was
not found to be a minimum at the level of calculation that we used.
30


Table 3.4 Energies of Silicon-Silicon Anion Species calculated using a rohf
6-311++G(p,d) program, s-squared =0.75,3.4 freq =0.0 for all species.
Values in parentheses are from the C. Pak et. Al. report, J. Phys Chem,
2000.
Starting geometry Ending geometry Corrected Energy (kcal/mol) Relative Energy (kcal/mol)
14 Si II /s\ H H Same as input -363402.1 0.0 (0.0)
15 H Si III Si J Becomes twisted -363391.6 10.4
16 r a/H i III Si H Becomes twisted -363391.4 10.6 (11.9)
17 [ /Si\ >- Same as Input -363378.4 23.7 (24)
31


Table 3.4 continued
32


3.5 Analysis of Structures of Carbon-Silicon Dianions
Carbon-silicon dianions were computed as both singlets and triplets (tables
3.5 and 3.6). Overall, the singlet species were slightly lower in energy than
the triplets. Only 2 minima on the PES were found, the lowest being the cis
structure (19) and the trigonal carbon (20) structure being about 4kcal per
mol higher than this. The trigonal silicon structure (21) could not be optimized
and the cis structure changed to the trans geometry upon optimization.
33


Table 3.5 Energies of Carbon-Silicon Dianion Singlet Species calculated
using a uhf 6-311++G(p,d) program, s-squared =0.0, freq =0.0 for all species.
Starting geometry Ending geometry Corrected Energy (kcal/mol) Relative Energy (kcal/mol)
r i 2- III Si\ H J 19 Same as input -205752.7 0.0
H H \ / C Si 20 2- Same as Input -205748.8 3.4
c /Si\ H H 1 2' 21 Does not optimize
Trans II 2- 22 Changes to cis
34


The PES for the triplets showed the minimum being a trans structure (23)
with the trigonal carbon structure (24) almost 20kcal/mol higher. The trigonal
silicon structure (25) atom was also a local minimum, but was even higher in
relative energy at 34 kcal/mol. Inputting coordinates for the cis geometry will
output the trans structure. The results of these geometry optimizations are
shown in table 3.6.
35


Table 3.6 Energies of Carbon-Silicon Dianion Triplet Species calculated
using a ROHF/ 6-311 ++G(p,d) program, s-squared =2.0, freq =0.0 for all
species.
Starting geometry Ending geometry Corrected Energy (kcal/mol) Relative Energy (kcal/mol)
i 1 X \ O CO \ X I I 2- 23 Same as Input -205748.2 0.0
H H II Si 1 2' 24 Same as Input -205728.5 19.7
C /Si\ H H 2- 25 Same as Input -205713.9 34.3
i 1 \ / O CO 1 1 2- 26 Changes to Trigonal Carbon (23)
36


3.6 Analysis of Structures of Silicon-Silicon Dianions
For the disilyne species, the singlet species are again lower in energy than
the corresponding triplets. A trans structure (27) is the lowest energy singlet.
A cis structure (28) only 2.5 kcal/mol higher than this in relative energy. This,
together with the information from the carbon silicon dianion structures,
implies that the dianion makes the cis form more stable, likely because of the
lone pair of electrons causing repulsion. The trigonal structure (29) has an
energy 14.7 kcal/mol higher and the bridging silicon (30) is much higher still
(44.2 kcal/mol). The singly bridged hydrogen (31) was, unsurprisingly, not a
minimum in this case. These results are summarized in table 3.7.
37


Table 3.7 Energies of Silicon-Silicon Dianion Singlet Species calculated
using a uhf 6-311++G(p,d) program, s-squared =0.0, freq =0.0 for all species.
Starting geometry Ending geometry Corrected Energy (kcai/mol) Relative Energy (kcal/mol)
1 1 X \ X 1 1 2- 27 Same as Input -363324.5 0.0
" V'H 1 Si III Si H 2- 28 Same as Input -363322.0 2.5
- H \ S s i i 2- 29 Same as Input -363309.8 14.7
< Si Si^ 2- 30 Same as Input -363280.2 44.2
rH^ Si l>H 2- 31 Changes to Trans
38


On the PES of the triplet, however, the bridging structure (32) is the lowest
energy minimum. This is only 0.8 kcal per mol more stable than the trans
structure (33) and 5.1 kcal/mol lower than the trigonal structure (34). The
highest minimum found in this case is the cis structure (35), which is 16.0
kcal/mol higher than the bridging structure (32). The singly bridged hydrogen
structure (36) will optimize to the doubly bridged structure (32). The results of
these findings are shown in table 3.8.
39


Table 3.8 Energies of Silicon-Silicon Dianion Triplet Species calculated
using a rohf 6-311 ++G(p,d) program, s-squared =2.0, freq =0.0 for all
species.
Starting geometry Ending geometry Corrected Energy (kcal/mol) Relative Energy (kcal/mol)
< Si Si ^ 2- 32 Same as Input -363303.2 0.0
1 1 X \ X 1 1 2- 33 Same as Input -363302.4 0.8
/ X 1 1 i i 2- 34 Same as Input -363298.0 5.1
/H l2' Si Si H J 35 Same as Input -363287.2 16.0
40


Table 3.8 continued
2- Changes to 2 Bridging H
36 (32)
41


4 Analysis of Calculated Electron Affinities.
4.1 Calculated Electron Affinities for Neutral Species
Table 4.1 shows that for the [1C, 1 Si, 2H] species, the lowest energy
optimized geometry and the lowest energy optimized anion geometry both
had the H2C=Si: silyene structure (1). The difference in energy, between the
anion (10) and neutral was 20.4 kcal/mol or 0.88eV. This is the adiabatic
electron affinity, which means the positive value indicates that the anion is
more stable than the neutral species, and that it is possible for an electron to
spontaneously add to the [1C, 1 Si, 2H] structure.
For the [2Si, 2H] structure, the lowest energy geometries were the doubly
bridged hydrogen structure (5) for the neutral and the H2Si=Si: disilyene for
the anion (14). The energy difference (adiabatic EA) between these 2
species was 37.6 kcal/mol or 1.61 eV. This value is even more positive than
for the carbon-silicon structure, suggesting that it becomes even easier to
add an electron.
42


Adding an electron to either a 1 or a 2 silicon atom species, such as (1) or (2)
is related to various properties of the silicon, namely its smaller
electronegativity compared to carbon, its increased size and more dispersed
orbitals. Recall that acetylene has a negative EA. Additionally, the structures
of the silicon analogs are not triply bonded like acetylene and already contain
a lone pair on one of the silicon atom. This could mean that there are empty
orbitals that are able to accept the extra electron.
43


Table 4.1- Calculated electron affinities for the lowest energy neutral for the
[1C, 1 Si, 2H] species and the [2Si, 2H] species.
Starting Geometry Ending Geometry Electron Affinity (kcal/mol) (Edianion Eanion) Electron Affinity (eV) (Eanion"Erieutral)
H H ?i 1 H \ :/H Si 10 20.29 0.88
H | H Si 5 r H \ s \ "\ X I I 14 37.30 1.61
44


4.2 Calculated Electron Affinities for Anions
The ionization energies of the anions were also calculated by determining the
difference in energy from the lowest energy anions to the lowest energy
dianions for both the [1C, 1 Si, 2H] species and the [2Si, 2H] species(see
table 4.2). For the former, the lowest energy anion is the H2C=Si: silyene
radical anion (10), and the lowest energy dianion is the singlet cis species
(19) leading to an EA of -130.8 kcal/mol or -5.67eV. Clearly, this very
negative number indicates that a second electron cannot be added to the C-
Si structure.
The [2Si, 2H] species gives similar results, where the lowest energy anion is
the H2Si=Si disilyene anion radical (14), and the lowest energy dianion is the
singlet trans radical dianion species (28). The difference in energy between
these gives an electron affinity of -77.6 kcal/mol or -3.36eV. This result,
although still very negative, is less so than that for the carbon silicon
structure, again suggesting that the silicon atoms stabilize the negative
charge.
45


These results reinforce the notion that dianions are extremely unstable,
particularly in the gas phase. The two negative charges are not able to get
far enough away from each other when the molecule is in the gas phase and
cannot be stabilized by solvent effects. The molecules are not large enough
for the charge to be stabilized by resonance effects, and although the [2H,
2Si] molecule may be a little more stable (this molecule is a little bigger than
the [1 Si, 1C, 2H]) both are still very unstable dianions in the gas phase.
46


Table 4.2 Calculated electron affinities for the lowest energy anion for the
[1C, 1 Si, 2H] and the [2Si, 2H] species.
47


4.3 Vertical Attachment Energies for the Neutral Species.
We also have computed the vertical attachment energies (VAEs) of these
molecules. These results are shown in table 4.3. The VAE keeps the
geometry fixed from the neutral species to the anion. For the [1C, 1 Si, 2H]
species, there are 3 structures that are minima for both the neutral and the
anion. These are the trigonal carbon (1) with the lowest energy to anion (10),
the trigonal silicon (3), which is about 85 kcal/mol higher to anion (12), and
the trans structure (2), which was about 30 kcal/mol higher than the neutral
to anion (11). The vertical attachment energies are 0.88 eV, 1.95 eV, 0.80 eV
respectively.
Note that all values are positive and the largest value is that for the trigonal
silicon species, H2Si=C: This is much more stable as an anion than as a
neutral. This suggests that the trigonal structure is the easiest way to add the
electron, possibly because it contains empty orbital for the electron to add to.
However, it is questionable whether this is possible, since the trigonal silicon
structure is not the global minimum for either the neutral or the anion.
48


For the [2H, 2Si] species, there are also 3 structures that exist for both the
neutral and the radical anion. These are the trigonal species (7) which was
16 kcal/mol higher than the doubly bridging hydrogen species(5), the lowest
energy, and the trans species(8), which was about 20 kcal/mol higher. These
optimized to structures (14), (17), and (16) respectively. The vertical
attachment energies for these species were 1.62 eV, 0.13 eV, 1.29 eV
respectively.
Note these values are also all positive. The highest value is again for the
trigonal structure, again suggesting that the orbital location in this particular
geometry favors addition of the electron. As a counterpoint, the doubly
bridged hydrogen structure, which is the global minimum for the neutral has
an electron affinity very close to zero, suggesting that the bridging hydrogens
somehow inhibit the addition of the electron.
49


Table 4.3- Vertical Attachment Energies for structures for which there were
minima for both the neutral and the anion geometries.
Geometry of Neutral Geometry of Anion same as neutral Calculated VAE (kcal/mol) (Eanion- Eneutral) Calculated VAE (eV) (Eanion"Eneutral)
H \ C 1 H H Si 10 20.24 0.88
\ X N H3 C II /s'\ H H 12 45.10 1.95
c 1 h"£ ;i 2 H c- 11 18.45 0.80
50


Table 4.3 continued
51


4.4 Vertical Attachment Energies of Anions
The vertical attachment energies of the anionic species were calculated by
taking the difference between the energy of the dianionic species (either a
singlet or a triplet) with the same geometry as the anion. For the [1C, 1 Si,
2H] species, there were 3 possible structures for the VAE: the H2C=Si radical
anion (10) to the corresponding singlet (20), the H2Si=C anion (12) to the
corresponding triplet (25), and the trans anion (11) to the trans triplet (23).
These gave VAEs of -5.84 eV, -4.76veV and -4.48 eV respectively.
For the [2Si, 2H] species, there were 4 possible VAEs to calculate: The
H2Si=Si disilyene radical anion (16) to the corresponding singlet dianion
(28), the trans anion (14) to the corresponding singlet (29), the cis radical
anion (15) to the corresponding singlet dianion (27) and the doubly bridged
radical anion (26) to the corresponding triplet dianion (32). These gave VAEs
of -3.01 eV, -4.00 eV, -2.91 eV, and -3.26 eV. Again, these values are all very
negative, suggesting the non-spontaneity of adding the electron to the anion.
Notice that all values are very negative, suggesting a second electron is not
added spontaneously. Again, this is likely due to the instability of dianions,
52


and the insufficiently small size of the molecule for the double charge to be
stabilized by charge dispersal.
53


Table 4.4 Vertical Attachment Energies for structures for which there were
minima for both the anion and the dianion geometries
Geometry of anion Geometry of Dianion VAE (Kcal/mol) Vertical Attachm ent Energy (eV) (Edianion" Eanion)
H H Si 10 20 H H II Si 2- singlet -134.67 -5.84
r c i ii /s\ H H L J 12 25 c /Si\ H H 2- triplet -109.77 -4.76
54


Table 4.4 continued
-H II /Si H 11 23 i 1 i \ o in \ X i i 2- triplet -103.31 -4.48
C C 1 ;i !i\ H 16 28 j t ;i-H_ 2- singlet -69.41 -3.01
r H \ /H 1 Bi 14 29 H \ S : /H 1 i 2- singlet -92.24 -4.00
- X \ X 15 27 i i X \ X i i 2- singlet -67.11 -2.91
vl/" 17 32 < a\ > 'S/ 2- triplet -75.18 -3.26
55


5. Conclusions
These results give an interesting study on the various geometries of carbon
and silicon acetylene analogs. It is worth note that the optimized geometries
differ greatly to that of acetylene. Additionally, whereas the electron affinity of
acetylene is negative, the electron affinity and the VAEs for the silicon
analogs are positive, suggesting that is becomes easier to add an electron
when either one or 2 silicon atoms are present.
Areas for future study would be an in-depth analysis of the location of the
electrons within the structure, and how the geometry affects where the extra
electron is added.
56


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58