Download Computational Studies on Conformations and Properties of Peptide

CITY UNIVERSITY OF HONG KONG
香港城市大學
Computational Studies on Conformations and
Properties of Peptide and Amino Acid
Nanobiomolecular Complexes
肽及氨基酸納米生物小分子的構型和性質
的計算研究
Submitted to
Department of Physics and Materials Science
物理及材料科學系
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
哲學博士學位
by
Wang Cuihong
王翠紅
May 2012
二零一二年五月
i
Abstract
Amino acids and peptides are the building blocks of proteins and biomolecules.
Theoretical researches about the structures and properties of the former are important
for understanding the latter. In this thesis, we performed systematic researches on the
structures
and
properties
of
dipeptide
arginylglycine
and
tetrapeptide
phenylalanine-glycine-glycine-valine, and explored the possibilities to identify
amino acids using carbon nanotubes and to design cage-like molecules formed by
amino acids for drug delivery.
In chapter 1, we introduce the basic theories of quantum chemistry calculations
and several computational methods, such as Hartree-Fock theory, semi-empirical
methods, perturbation theory, configuration interaction and coupled cluster methods.
We also introduce the density functional theory, Atoms in Molecules, theory of
molecular orbital and density of states. Finally, the simulation packages (Gaussian
and DFTB+) we used in this work are briefly introduced.
In chapter 2, the structures and properties of the neutral, protonated,
deprotonated and metal cationized dipeptide arginylglycine were comprehensively
studied. For clarity, we present the results in three parts. In part one, the canonical
and zwitterionic conformers of dipeptide arginylglycine were thoroughly researched
and we found that the most stable conformer has a zwitterionic structure. Zwitterions
play important roles in the structure and function of peptides and proteins; however,
the zwitterionic structures are not stable in the gas phase. Therefore, the
arginylglycine appears to be the smallest peptide with stable zwitterions. The
properties of the low energy conformers of the arginylglycine were systematically
revealed, including the rotational constants, dipole moments and vertical ionization
energies. In part two, the protonated and deprotonated conformers of the dipeptide
arginylglycine
(ArgGly±H+)
were thoroughly searched.
We
obtained
the
thermochemical parameters, such as the proton affinity (PA), gas-phase basicity (GB),
proton dissociation energy (PDE) and gas-phase acidity (GA). These thermochemical
ii
parameters are of fundamental importance for the interpretation of the molecules’
reactivity. The coordination of metal ions can significantly influence the
intramolecular hydrogen bonds and electrostatic interactions of molecules. Thus,
there has been increasing interest in understanding the effects of metal chelation on
the structure of amino acids and peptides. In part three, we thoroughly researched the
Na+, Rb+ and Mg2+ coordinated dipeptide arginylglycine (ArgGly). Our results show
that the salt-bridge (SB) form is more stable for the sodium-cationized and
rubidium-cationized dipeptides, but the charge-solvated (CS) form is more stable for
magnesium-cationized dipeptide. The metal ion affinities (MIA) were researched too,
which are found to be 69.0kcal/mol, 43.9kcal/mol and 283.8kcal/mol for complexes
ArgGly·Na+, ArgGly·Rb+ and ArgGly·Mg2+, respectively. Finally, the IR spectra and
the AIM electronic densities were calculated, and our results show that there are
coexistence of red shift, blue shift and dihydrogen bond in the neutral, protonated
and deprotonated dipeptide. The IR spectra of the metal ion cationized complexes
shows that the same types of monovalent metal ion (Na+ and Rb+) coordinated
complexes have similar spectra, but the spectra of divalent metal ion (Mg 2+)
coordinated complexes are quite different. The conformational distributions of all the
complexes at various temperatures were investigated, which are expected to be
helpful for experimental researches.
Because the function of biological molecules is basically determined by the
structure of the molecules, the structural research about the peptides and proteins is
very helpful for knowing their functions. For most biological molecules, the aqueous
solution phase is their natural environment. Although the structures of the molecules
in solution are usually different from those in the gas phase, the research of the
molecules in the gas phase can still uncover the intrinsic properties of molecules and
shed light on the properties of the molecules in the natural environment at certain
extent. As the knowledge of the conformation of small peptides will help to predict
the structures of larger molecules and proteins, there have been many theoretical and
experimental researches about them. In chapter 3, we thoroughly researched the
neutral conformers of tetrapeptide phenylalanine-glycine-glycine-valine (FGGV) and
iii
found that most of the stable conformers have syn-carboxyl structures. Because of
the difference of the backbones, the stable conformers can be divided into 13 groups
and a γ-turn structure is the most favorite form. The relative energies, dipole
moments and conformational distributions at various temperatures of peptide FGGV
were analyzed. The IR spectrum calculation of the FGGV is expected to be helpful
for understanding experiments. We also compared the structures of FGGV with the
other tetrapeptides (GGGG, GVGG and GFGG), and found that the important
conformers of these tetrapeptides have the same backbone structures. The experience
received and the trends revealed can be used for further researches about the peptides,
which is expected to reduce the number of the initial trial conformers, and then
effectively reduce the computational costs.
Identification and detection of different amino acid molecules as well as
biological molecules have important scientific and technological significance. As an
ideal one-dimensional nanomaterial, carbon nanotube (CNT) has various novel
properties, valuable for both nanoscience and nanotechnology. The biomolecules can
be adsorbed on the surface of carbon nanotubes by weak interactions, and the
functional molecules can wrap around the nanotubes without losing their activity.
Therefore, the functional molecules can be selected using the CNTs, as the different
adsorbed complexes have different binding energies. In chapter 4, we investigated
the adsorptions of three aromatic amino acids (phenylalanine, tyrosine, and
tryptophan) on the sidewalls of a number of representative single-walled carbon
nanotubes (SWNTs) using a density-functional tight-binding method, complemented
by an empirical dispersion correction. The armchair (n, n) SWNTs (n=3-12) and
zigzag (n, 0) SWNTs (n=4-12) were thoroughly examined. We found that the most
stable amino acid/SWNT complexes for different SWNTs have similar local
structures, and that the distance between the amino acid and SWNT is about 3 Å.
Owing to the π-π and H-π stacking interactions, the benzene and indole rings in the
amino acids are not exactly parallel to the SWNTs but instead lie at a small angle. We
also investigated the diameter and chirality dependences of binding energies and
found that SWNT (5, 0) has an especially large binding energy. We believe that the
iv
research about the interactions between the aromatic amino acids and CNTs will be
helpful for the understanding of the interactions between large biomolecules and
CNTs. And, the amino acids can be identified by the different binding energies.
As the building blocks of proteins and components to build biological materials,
amino acids and peptides are attracting increasing interest in scientific researches.
The surrounded drugs by biological materials have specific controlled, sustained and
targeted release characteristics, and the nanoscale drug delivery system can increase
the parent drug solubility and maintain the structural integrity of the drug. In chapter
5, we selected the serine, one of the 20 natural amino acids, to be researched. The
possible cage-like molecules formed by serine octamer or decamer were studied by
calculations using the density functional tight-binding method, complemented by the
empirical London dispersion energy term. Chirality is the essential concepts in
chemistry and biology; it plays an important role for living organisms and has
become a major concern in drug design. Thus, both the L-handed and D-handed
serines were used to construct the complex conformers. The cage-like molecules
were linked by the hydrogen bonds. The structures linked by –COOHO=C– were
found to be the most stable conformers, as evaluated by binding energies calculations
and molecular dynamic simulations. The cage-like molecules have symmetric
structures. The relative energies, binding energies and vibrational modes of the
complexes were calculated and analyzed. In order to test the possible applications of
the cage-like structures, we put the smallest fullerene C20 into the serine decamer.
After optimization, we found that the amino acids-C20 complexes are very stable,
which means that the cage-like structures might be useful to deliver small molecules.
We expect that our results will be helpful for designing supermolecules for nanoscale
drug applications.
Chapter 6 will be a summary of the whole thesis work.
Key Words: amino acids; dipeptide, tetrapeptide, complexation, adsorption, cage
structure, density functional therory
vi
Table of Contents
Abstract ................................................................................................................... i
Acknowledgements ................................................................................................ v
Table of Contents .................................................................................................. vi
List of Figures ........................................................................................................ x
List of Tables ....................................................................................................... xiv
Chapter 1 Theoreties and Principles of Computational Methods........................ 1
1.1 Introduction .................................................................................................... 1
1.2 The principles of quantum chemistry .............................................................. 2
1.2.1 Ab initio quantum chemistry method ........................................................ 2
1.2.2 Semiempirical method .............................................................................. 7
1.2.3 Density Functional Theory ....................................................................... 8
1.3 DFTB method ................................................................................................16
1.4 Description of molecular systems ..................................................................21
1.4.1 Atoms in molecules theory (AIM) ...........................................................21
1.4.2 Molecular orbital theory ..........................................................................22
1.4.3 Density of States (DOS) ..........................................................................23
1.5 The software used in the thesis work...........................................................24
1.5.1 Gaussian .................................................................................................24
1.5.2 DFTB+ ...................................................................................................25
Chapter 2 The Conformations and Properties of Dipeptide Arginylglycine and
Coordinated Complexes ........................................................................................26
2.1 Comprehensive computational study on the conformations of neutral
arginylglycine in gas phase ..................................................................................26
2.1.1 Introduction .............................................................................................26
vii
2.1.2 Computational methods ...........................................................................27
2.1.3 Conformers and energies .........................................................................31
2.1.4 Rotational constants, dipole moments and vertical ionization energies (VIE)
........................................................................................................................38
2.1.5 Conformational distribution .....................................................................41
2.1.6 Intramolecular hydrogen bond .................................................................42
2.1.7 Vibrational spectra ...................................................................................46
2.1.8 Conclusions .............................................................................................49
2.2 The conformations and properties of protonated and deprotonated
arginylglycine ......................................................................................................50
2.2.1 Introduction .............................................................................................50
2.2.2 Computational methods ...........................................................................51
2.2.3 Conformers and energies .........................................................................53
2.2.4 Rotational constants and dipole moments ................................................58
2.2.5 Conformational distribution .....................................................................59
2.2.6 Vibrational spectra ...................................................................................61
2.2.7 The thermochemical parameters of the gaseous ArgGly ...........................63
2.2.8 Conclusions .............................................................................................64
2.3 Salt-Bridge and Charge-solvated Formation for Na+, Rb+ and Mg2+ cationized
ArgGly ................................................................................................................65
2.3.1 Introduction .............................................................................................65
2.3.2 Computational methods ...........................................................................67
2.3.3 Conformers and energies .........................................................................69
2.3.4 Rotational constants and Dipole moments................................................76
2.3.5 Conformational distribution .....................................................................77
2.3.6 Vibrational spectra ...................................................................................80
2.3.7 The metal ion affinity (MIA) ...................................................................82
2.3.8 Conclusions .............................................................................................83
Chapter 3 The Conformations of Tetrapeptide FGGV Researched by Ab Initio
viii
Calculation ............................................................................................................84
3.1 Introduction ...................................................................................................84
3.2 Computational methods .................................................................................85
3.3 Conformers and energies ...............................................................................86
3.4 Dipole moments.............................................................................................90
3.5 Conformational distribution ...........................................................................91
3.6 Vibrational spectra .........................................................................................93
3.7 The structural properties of FGGV and compared with the other tetrapeptides
............................................................................................................................95
3.7.1 The structural properties ..........................................................................95
3.7.2 Comparison with tetrapeptide GGGG, GVGG and GFGG........................96
3.8 Conclusions ...................................................................................................97
Chapter 4 Adsorptions and properties of aromatic amino acids on single-walled
carbon nanotubes ..................................................................................................99
4.1 Introduction ...................................................................................................99
4.2 Modeling and Computation Methods ........................................................... 100
4.3 Structures of the amino acid/CNT complex .................................................. 103
4.3.1 Structure of the Phe/CNT(n, n) complex ................................................ 104
4.3.2 Structure of the Phe/CNT(n, 0) complex ................................................ 107
4.3.3 Structure of the Tyr/CNT(n, n) complex ................................................ 108
4.3.4 Structure of the Trp/CNT(n, n) complex ................................................ 110
4.4 The stability and binding energy of the amino acid/CNT complex................ 112
4.5 The effect of CNT chirality .......................................................................... 113
4.6 The effect of amino acid type on adsorption ................................................. 113
4.7 The effect of CNT length ............................................................................. 113
ix
4.8 Molecular orbitals of Phe/CNT complex ...................................................... 114
4.9 Density of states (DOS) of the Phe/CNT complexes..................................... 115
4.10 Conclusions ............................................................................................... 116
Chapter 5 Possible cage-like molecules formed by amino serine octamer and
decamer ............................................................................................................... 118
5.1 Introduction ................................................................................................. 118
5.2 Modeling and Computational Methods ........................................................ 119
5.3 Stable conformers and their energetics ......................................................... 121
5.4 Stability of the structures ............................................................................. 124
5.5 Vibrational frequency analysis of the complexes .......................................... 125
5.6 Possible applications .................................................................................... 126
5.7 Conclusions ................................................................................................. 128
Chapter 6 Summary............................................................................................ 129
References ...........................................................................................................131
List of publications.............................................................................................. 146
x
List of Figures
Figure 2.1.1 The three tautomers of the neutral dipeptide arginine-glycine.
Figure 2.1.2 Illustration of the 12 internal single-bond rotamers.
Figure 2.1.3 The stable conformers of neutral ArgGly optimized at the BHandHLYP/
6-31 + G ** level (ordered by BHandHLYP/6-311++G (2df, 2p). The z1,
z2, z3, z4, z5, z10 and z20 are zwitterionic structures and c6, c7, c11,
c39 and c44 are canonical structures.
Figure 2.1.4 Contour maps of the BHandHLYP/6-31+G** electron density for
conformer z9. The circles indicate that the atoms are in the plane and the
triangles indicate that the atoms are out of the plane. Crosses indicate
critical points. The outer most contour is ρ(r)=0.001au, and the
remaining contours increase in the order of 2×10 n, 4×10n and 8×10n,
with n= -3, -2, -1 and 0.
Figure 2.1.5 Topological pattern of the electron density for conformers z9, z14, z26
and c44. The small red circles indicate critical point (BCP) and yellow
circles indicate ring critical point (RCP).
Figure 2.1.6 IR spectrum of conformers z1, z4, c6, c7, c11, z20, RG1 and RG2. The
frequency is in cm-1 and intensity in km/mol.
Figure 2.1.7 IR spectrum of conformers z1, z2, z4, z5, c6, c7, z10, c11, z20 and c44
in the 0 cm-1-2000 cm-1 and 2500 cm-1-3800 cm-1 range.
Figure 2.2.1 The three tautomers of the dipeptide arginine-glycine and their
protonated positions.
Figure 2.2.2 The three tautomers of the dipeptide arginine-glycine and their
deprotonated positions.
Figure 2.2.3 The eight most stable conformers of ArgGly + H+ optimized at the
BHandHLYP/6-31+G**
level
(ordered
by
BHandHLYP/6-311++
G(2df,2p) single point energy).
Figure 2.2.4 IR spectrum of ArgGly+H+ and ArgGly-H+. The frequency is in cm-1 and
xi
intensity in km/mol. (a) is the IRMPD spectrum of protonated ArgGly in
reference 13; (b) is the vibrational spectra of conformers p1, p5 and p8
in the range 900-1800cm-1 ; (c) is the spectra of protonated conformers
p1, p2, p3, p4, p7 and p8 in the range of 0-4000 cm-1 and (d) is the
spectra of deprotonated conformers d1, d2, d3, d4 and d36. The
frequency is scaled by 0.9288.
Figure 2.3.1 The illustration of the signs of the dipeptide arginylglycine.
Figure 2.3.2 The stable conformers of ArgGly·Na+ which were optimized at the
BHandHLYP/Gen/6-31G* level (ordered by BHandHLYP/Gen /6-311++
G(2df, 2p). They are named by their orders. The violet ball refers to the
sodium atom.
Figure 2.3.3 The stable conformers of ArgGly·Rb+ which were optimized at the
BHandHLYP/Gen/6-31G* level (ordered by BHandHLYP/Gen/ 6-311++
G (2df, 2p). The purple ball refers to the rubidium atom.
Figure 2.3.4 The stable conformers of ArgGly·Mg2+ which were optimized at the
BHandHLYP/Gen/6-31G* level (ordered by BHandHLYP/Gen/6-311++
G (2df, 2p). The yellow ball refers to the magnesium atom.
Figure 2.3.5 The IR spectra of complexes ArgGly·Na+, ArgGly·Rb+ and
ArgGly·Mg2+. The frequency is in cm-1 and intensity in km/mol.
Figure 3.1 Illustration of the 12 internal single-bond rotamers.
Figure 3.2 The conformers of 13 types of FGGV structures optimized at the
BHandHLYP/6-3 1G* level (ordered by BHandHLYP/6-311++G (2d, 2p).
They are named by their orders. The first 4 conformers are type 1, and all
the other conformers represent the other 12 types, they are named from
type 2 to type 13. Intramolecular hydrogen bonds are shown as dotted
lines.
Figure 3.3 The conformers and their distributions in room temperature.
Figure 3.4 IR spectrum of type 1-3 conformers. The frequency is in cm-1 and
intensity in km/mol. The frequencies under 2000cm-1 were scaled with
0.9484, and for over 2000cm-1 the scale factor 0.9244 were used.
xii
Figure 3.5 The structures of conformers 1, 3, 4, 5, 8, 16 (type 1a), 2, 7, 10 (type 1b),
6, 14 and 21 (type 2).
Figure 3.6 The stable conformers of the tetrapeptide FGGV, GGGG, GVGG and
GFGG, whose distributions are larger than twenty percents at room
temperature.
Figure 4.1 An illustration of the top view of the adsorption sites. The non-benzene
parts of Phe are labeled X. The letters a, b, c, and d refer to the four
adsorption sites of Phe, while 1, 2, 3, and 4 denote the rotation of Phe.
Figure 4.2 The conformers of Phe, Tyr, and Trp.
Figure 4.3 The two most stable Phe/CNT(5, 5) complexes, shown in front view and
top view. The total energy of structure (a) is 0.04 kcal/mol higher than
that of structure (b). For Phe/CNT(n, n) (n=3-5), all the most stable
structures have type (a) relative positions, but for the Phe/CNT(n, n)
(n=6-12) complexes, the most stable structures are type (b) conformers.
Figure 4.4 The concerned angles of Phe, Phe/(5, 5)(a), and Phe/(5, 5)(b).
Figure 4.5 The two stable Phe/CNT(8, 0) complexes, shown in two different views,
front and top. All type (c) Phe/CNT(n, 0) complexes are 0.3-0.4 kcal/mol
lower than type (d) complexes.
Figure 4.6 The most favorable Tyr/CNT(6, 6) and Tyr/CNT(7, 7) complexes, shown
in two different views, front and top. For n=4-6, the most favorable
conformers have a type (e) structure, while for n=7-10, they have a type (f)
structure.
Figure 4.7 The most stable Trp/CNT(6, 6) and Trp/CNT(7, 7) complexes, shown in
two different views, front and top. All stable Trp/CNT(n, n) complexes
have similar structures.
Figure 4.8 The binding energies of the Phe(n, n), Phe(n, 0), Tyr(n, n), and Trp(n, n)
complexes and the total energies of CNT(n, 0) (n=4-12) and CNT(n, n)
(n=3-12).
xiii
Figure 4.9 The highest occupied molecular orbitals (HOMOs) and the lowest
unoccupied molecular orbitals (LUMOs) for CNTs and the Phe/CNT
complexes.
Figure 4.10 Comparison between DOS graphs for an isolated Phe, an isolated CNT,
and the Phe/CNT complexes. The numbers in the graphs refer to the
Fermi energy.
Figure 5.1 The four parts of serine. The –COOH is signed by A, –OH is by B, –HN2
is by C and the rest is the fourth group.
Figure 5.2 Four kinds of possible conformers which were constructed by serine
octamer, and all the complexes were linked by hydrogen bonds.
Figure 5.3 The stable serine octamer complexes (a) constructed by L-serine. They are
shown in top view and side view. The number in the figure is the length
of the hydrogen bond (Ǻ).
Figure 5.4 The new stable serine octamer complexes (c) which were constructed by
L-serine. The two figures at the bottom are partial view structures of
(L-S)8c; The number in the figure is the length of the hydrogen bond (Å).
Figure 5.5 The stable serine decamer complexes constructed by L-serine. They are
shown in top view and side view. The number in the figure is the length of
the hydrogen bond (Å).
Figure 5.6 The vibrational frequency for single serine L-S, complexes (L-S)8a,
(L-S)8c and (L-S)10. This is a sign of the position of the vibrational modes;
the high of the line is not denotes the intensity of the vibration. The red
line is the vibration of the carboxyl hydrogen and the blue line is the
vibration of the hydroxyl hydrogen.
Figure 5.7 The stable serine decamer-C20 complexes constructed by L-serine. They
are shown in top view and side view. The number in the figure is the
length of the hydrogen bond (Å).
xiv
List of Tables
Table 2.1.1 The comparison of different basis sets. 6-31G* refers to BHandHLYP
/6-311++G (2df, 2p)//BHandHLYP/6-31G* and 6-31+G* refers to
BHandHLYP/6-311++G (2df, 2p)// BHandHLYP/6-31+G*, the rest may
be deduced by analogy. Average time is the time waste of the
optimization. All the conformers were optimized by BHandHLYP
/6-31G* first, and then be further optimized.
Table 2.1.2 Relative energies, EBH +ZPVE, EBH +H and EBH +G for gaseous
ArgGly. The zero-point vibrational energies (ZPVE), Enthalpy (H) and
Gibbs Free Energies (G) have been scaled by 0.9498, 0.9453 and 0.9288
respectively.
EBH
refers
//BHandHLYP/6-31+G**,
to
EMP2
BHandHLYP/6-311++G(2df,2p)
is
MP2/6-311++G(2df,2p)//BHand
HLYP/6-31+G**, EB3LYP is B3LYP/6-311++G(2df,2p)// BHandHLYP/
6-31+G**, EB97D refers to B97D//6-311++G(2df,2p)//BHandHLYP
/6-31+G**and ER27 refers to the relative value of the Gibbs free energies
with
the
electronic
energies
were
calculated
at
B3LYP/
6-311++G(2d,2p)//BHandHLYP /6-31+G** level and the Gibbs free
energies correction were obtained by BHandHLYP/6-31+G** frequency
calculations. The letters c and z refer to the canonical and zwitterionic
structures, respectively.
Table 2.1.3 The correction of zero-point vibrational energies (ZPVE) and Gibbs Free
Energies (G) for different functions.
E
MP 2
ZPVE
and E MPG2 mean the
MP2/6-311++G(2df, 2p) single point energied are corrected by
zero-point vibrational energies and Gibbs Free Energies respectively, the
rest may be deduced by analogy. ZPVE and G refer to the correction
of zero-point vibrational energies and Gibbs Free Energies obtained by
BHandHLYP/6-31+G** frequency calculation. ZPVE and G are scaled
by factor 0.9498 and 0.9288 respectively.
xv
Table 2.1.4 Vertical ionization energies (VIE), rotational constants and dipole
moments for ArgGly. BH and MP2 refer to the VIE were calculated at
BHandHLYP/6-311++G (2df, 2p) and MP2/6-311++G (2df, 2p) level
respectively.
Table 2.1.5 Equilibrium distributions (%) of gaseous arginine-glycine dipeptide at
various temperatures.
Table 2.1.6 Property analysis of the bond critical points (BCPs) and the hydrogen
atom involved in H-bonding for conformer z9. ρ and ▽2ρ are the
electron density and its Laplacian at the BCP, q is the atomic charge, E is
the total energy, μ is the dipolar polarization, and V is the atomic volume.
All values are in atomic units. D in Å is the distance between the BCP
and the corresponding RCP. a, b, c and d refer to the N-H…O, N-H…N,
C-H…O and C-H…H-N H-bond respectively. The last two lines are the
properties of the hydrogen atoms without involved in H-bonding.
Table 2.2.1 Relative energies, E+ZPVE, E+H, E+G rotational constants and
dipole moments for gaseous protonated ArgGly (ArgGly+H+). The
zero-point vibrational energies (ZPVE), Enthalpy (H) and Gibbs Free
Energies (G) have been scaled by the factor 0.9498, 0.9453 and 0.9288
respectively. BH refers to BHandHLYP/6-311++G(2df,2p)//BHand
HLYP/6-31+G**,
MP2
is
MP2/6-311++G(2df,2p)//BHandHLYP/
6-31+G**.
Table 2.2.2 Relative energies, E+ZPVE, E+H, E+G rotational constants and
dipole moments for gaseous deprotonated ArgGly (ArgGly-H+). The
zero-point vibrational energies (ZPVE), Enthalpy (H) and Gibbs Free
Energies (G) have been scaled by the factor 0.9498, 0.9453 and 0.9288
respectively.42,44
BH
refers
to
BHandHLYP/6-311++G(2df,2p)//
BHandHLYP/6-31+G**, MP2 is MP2/6-311++G (2df,2p)//BHandHLYP
/6-31+G**.
Table 2.2.3 Equilibrium distributions (%) of gaseous ArgGly+H+ at various
temperatures.
xvi
Table 2.2.4 Equilibrium distributions (%) of gaseous ArgGly-H+ at various
temperatures.
Table 2.2.5 Proton affinity (PA), gas-phase basicity (GB), proton dissociation energy
(PDE) and gas-phase acidity (GA), in kcal/mol.
Table 2.3.1 Relative energies of E (single point energies), E+ZPVE, E+G and E+H,
Rotational constants and dipole moments for gaseous ArgGly·M+/2+
(M=Na, Rb, Mg). The conformational equilibrium distributions at 298K
were shown in the last column too. The single point energies were
calculated by BHandHLYP/Gen/6-311++G(2df,2p) method, and the
zero-point vibrational energies (ZPVE), Enthalpy (H) and Gibbs Free
Energies (G) were obtained by BHandHLYP/Gen/6-31G* frequency
calculations and they have been scaled by the factor 0.9446, 0.94 and
0.9244 respectively.
Table 2.3.2 Equilibrium distributions (%) of ArgGly·Na+, ArgGly·Rb+ and
ArgGly·Mg2+ at various temperatures. The conformers which have no
distributions were not listed.
Table 2.3.3 The MIA (enthalpy change) (-∆H298K) and Gibbs free energy change
(-∆G298K) with and without BSSE corrections. The BSSE in the bracket
means that the BSSE correction has been used. They are in the unit of
kcal/mol.
Table 3.1 Relative energies, △ E +ZPVE, △ E+H, △ E+G and dipole moments
for gaseous FGGV. The zero-point vibrational energies (ZPVE),
Enthalpy (H) and Gibbs Free Energies (G) were obtained by
BHandHLYP/6-31G* frequency calculations and they have been scaled
by the factor 0.9446, 0.94 and 0.9244 respectively. BH(large) refers to
BHandHLYP/6-311++G(2d,2p)//BHandHLYP /6-31G* and BH(large)
refers to BHandHLYP/6-31G*//BHandHLYP/6-31G*. They are named
by their orders.
Table 3.2 Equilibrium distributions (%) of gaseous tetrapeptide phenylalanineglycine-glycine-valine (FGGV) at various temperatures. The conformers
xvii
whose distributions smaller than 1% at all the temperatures were not
shown.
Table 4.1 The angles in Phe/CNT(n, n), Tyr/CNT(n, n) and Trp/CNT(n, n) complexes.
The corresponding angles are shown in Figure 4.4.
Table 4.2 The binding energies of different length of CNT complexes.
Table 5.1 The relative energies, binding energies per unit, and the critical temperature
of the cage-like structures. The energies of L-(S)8a and S10-C20-1 are set
as the benchmark (0.00 kcal/mol) respectively.