2
The torsional path integral Monte Carlo (TPIMC) technique is used to study the five lowest-energy conformers of glycine.
Type: Result |
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ConceptID: Res1
3
The theoretical method provides an anharmonic and quantum-mechanical description of conformational free energy and is used for the first time with an ab initio potential energy surface.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res2
4
The 3-dimensional torsional potential energy surface of glycine was obtained at the MP2/6-311++G** level of theory and is optimized with respect to the non-torsional degrees of freedom.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res3
5
Calculated conformer populations compare well with those reported in recent matrix-isolation infrared spectroscopy experiments.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res4
6
An additional conformer, not yet observed, is predicted to be heavily populated in the thermal equilibria probed by experiment, and a new explanation for its elusiveness is provided.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res5
7
Quantum effects, such as zero point energy, are found to substantially alter conformer populations, and an algorithm for estimating the role of non-torsional vibrations in the conformational thermodynamics of a molecule is introduced.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res6
Introduction
8
Glycine, the simplest amino acid, is a benchmark system for the experimental and theoretical determination of molecular conformation.
Type: Background |
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ConceptID: Bac1
9
It is among the smallest compounds to exhibit intramolecular hydrogen bonds, which stabilize various structural configurations and give rise to a subtle potential energy surface.1–4
Type: Background |
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ConceptID: Bac2
10
With flexible degrees of freedom and low-energy pathways between local minima, the potential energy surface of glycine contains the basic elements of the complex configurational landscapes which govern protein folding and other sophisticated biological processes.5,6
Type: Background |
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ConceptID: Bac3
11
In the gas phase, glycine exists in the non-zwitterionic isomer.7,8
Type: Background |
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ConceptID: Bac4
12
Extensive theoretical analysis of the electronic structure of glycine has revealed multiple stable conformers arising from internal rotation about its three torsional degrees of freedom.9–18
Type: Background |
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ConceptID: Bac5
13
High level ab initio calculations predict five glycine conformers to exist within 10 kJ mol−1 of the global potential minimum.15,16
Type: Background |
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ConceptID: Bac6
14
Fig. 1 presents the structures and energies of the lowest energy conformers of glycine first reported by Császár and reproduced in the current study.
Type: Background |
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ConceptID: Bac7
15
The torsional angles = (ϕ1, ϕ2, ϕ3) in the figure indicate the coordinate of the twisting motions about the C–C bond (ϕ1),the C–O single bond (ϕ2), and the C–N bond (ϕ3).
Type: Model |
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ConceptID: Mod1
16
Conformer I is generally calculated to be the lowest energy conformer and to have a geometry of Cs symmetry.9
Type: Background |
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ConceptID: Bac8
17
However, the level of theory employed alters the prediction of whether conformer II exhibits a symmetry plane.
Type: Background |
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ConceptID: Bac9
18
Early studies found the conformer to be symmetric, but the subsequent inclusion of electron correlation and larger basis sets revealed that the minimized geometry distorts in favor of strengthening hydrogen-bonding interactions.14–16
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac10
19
The heavy atoms of conformers III–V are all calculated to be non-planar.
Type: Background |
Advantage: None |
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ConceptID: Bac11
20
Every glycine structure of C1 symmetry exhibits a mirror-image structure (with inverted torsional angles) of equivalent energy.13
Type: Background |
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ConceptID: Bac12
21
The determination of glycine conformer populations is a challenging experimental problem.
Type: Background |
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Novelty: None |
ConceptID: Bac13
22
The structure of glycine conformers in the gas phase was first probed using microwave and millimeter wave spectroscopy.19,20
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac14
23
Because of its greater dipole moment, conformer II is more easily detected using rotational spectroscopy and was observed before the lower-energy conformer I.21,22
Type: Background |
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ConceptID: Bac15
24
Other glycine conformers have not been found using millimeter wave or microwave spectroscopy, most likely because they interconvert to conformer I during the free jet expansion step of the experiments.23,24
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac16
25
Conformer interconversion is a shift in the population of molecules from one conformer to another during the cooling period between thermal equilibration and experimental observation.25
Type: Background |
Advantage: None |
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ConceptID: Bac17
26
A gas-phase electron diffraction study of the glycine conformers also identified at least two conformers of glycine.8
Type: Background |
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ConceptID: Bac18
27
In principle, this technique enables direct observation of the thermal population distribution and avoids the problem of conformer interconversion.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac19
28
However, electron diffraction only determines the heavy atom positions in a molecule, so it has difficulty determining the relative population of conformers, such as II and III, which exhibit overlapping heavy-atom thermal distributions.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac19
29
When coupled with the technique of matrix isolation, infrared (IR) spectroscopy has proven to be a valuable tool for studying the conformers of glycine.26–29
Type: Background |
Advantage: None |
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ConceptID: Bac20
30
The analysis of glycine with conventional gas-phase IR spectroscopy is precluded by the low thermal stability of the molecule.28
Type: Background |
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ConceptID: Bac21
31
Matrix-IR spectroscopy is the only experimental technique for which all three conformers in Fig. 1a have been conclusively observed.
Type: Background |
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Novelty: None |
ConceptID: Bac22
32
Matrix deposition is a more gentle process than free jet expansion, so conformer interconversion is less problematic for this technique than for microwave spectroscopy.26,28
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac23
33
Also, IR spectroscopy directly probes the structure of the glycine molecules and discriminates between conformers more readily than electron diffraction.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac24
34
Nonetheless, the non-ideal behavior of the matrix gas can affect the measurement of conformer populations, and the absence of the low-energy conformer IV from the observations of matrix-IR studies requires explanation.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac25
35
The accurate determination of glycine conformer populations also poses serious challenges for theory.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac26
36
It was previously mentioned that electron correlation and a flexible basis set are necessary for describing the intramolecular hydrogen-bonding structure of the glycine conformers.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac27
37
However, the theoretical difficulties of calculating the conformer populations of glycine extend beyond those of electronic structure theory.
Type: Background |
Advantage: None |
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ConceptID: Bac28
38
Glycine is a highly flexible molecule with shallow potential barriers separating minima of competitive energy.13,23,24
Type: Background |
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ConceptID: Bac29
39
Moreover, the pathways of interconversion between conformers coincide with torsional degrees of freedom exhibiting low moments of inertia.
Type: Background |
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Novelty: None |
ConceptID: Bac30
40
Quantitative theoretical determination of the equilibrium population distribution of glycine therefore requires an anharmonic, quantum-mechanical description of the conformational thermodynamics.
Type: Motivation |
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Novelty: None |
ConceptID: Mot1
41
To interpret experiment, it is not sufficient to calculate only the potential energy of the conformers.
Type: Motivation |
Advantage: None |
Novelty: None |
ConceptID: Mot2
42
The temperature-dependent free energy must also be computed.
Type: Motivation |
Advantage: None |
Novelty: None |
ConceptID: Mot3
43
In the current study, the recently developed torsional path integral Monte Carlo (TPIMC) technique is used to study the conformer free energies of glycine.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met1
44
The TPIMC technique provides a completely anharmonic description of the intramolecular torsional degrees of freedom and systematically includes quantum effects such as zero point energy.30,31
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac31
45
Although TPIMC has been successfully employed for the prediction of molecular conformation,32 this is the first study in which the technique is performed on an ab initio potential energy surface.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac32
Methodology
Torsional path integral Monte Carlo
46
Torsional path integral Monte Carlo (TPIMC) is a quantum mechanical technique for calculating the equilibrium thermodynamics of molecules at finite temperature.30,31
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac33
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac34
48
The TPIMC technique extends the applicability of the more general path integral Monte Carlo (PIMC) technique33–35 to larger molecules by explicitly treating only the intramolecular torsional degrees of freedom.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac35
49
Other implementations of PIMC have enabled the calculation of molecular thermodynamics for two- and three-atom systems using high-quality potentials,36,37 but the authors are unaware of any previous study in which the technique has been employed with an ab initio potential to explore the conformer free energies of a biomolecule.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac36
50
A convenient feature of path integral theory is that a single parameter nb modulates the accuracy of the calculations between exact classical mechanics (nb = 1) and exact quantum mechanics (nb = ∞), neglecting Monte Carlo sampling error.34
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac37
51
For intramolecular torsions, it has been shown that the bulk of quantum effects are recovered using only a value of nb ≈ .531
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac38
52
Upon varying the parameter nb, TPIMC calculations explore the extent to which quantum effects are significant in the conformational thermodynamics of biomolecules.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac39
53
The details of the TPIMC technique have been explained elsewhere,30,31 so we include only the major features of the calculations reported in this study.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac40
54
All three torsional degrees of freedom in the glycine molecule were treated explicitly.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met2
55
Simulations were performed at 100 K, 150 K, 200 K, 300 K, 400 K, 500 K, and 700 K. At each temperature, TPIMC calculations were performed with the parameter nb set to 1, 5, and 15.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met3
56
We will subsequently refer to the TPIMC technique employed with nb = 1 as “classical TPIMC” and to the TPIMC technique employed with nb = 15 as “quantum TPIMC”.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac41
57
Torsional sampling was performed using the free rotor (FR-TPIMC) algorithm to ensure that the entire torsional configuration space of glycine was explored.31
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met4
58
Simulations were tightly converged to ensure minimal uncertainty and negligible estimator bias.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met5
59
Total enthalpies and free energies for glycine were calculated with estimated standard deviation of less than 0.0129 kJ mol−1 and 0.0066 kJ mol−1, respectively.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met6
60
In every case, estimator bias was calculated to be within the standard deviation of the corresponding value.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met7
61
The TPIMC program developed in our research group uses several subroutines from the TINKER software package.38
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met8
Ab initio torsional potential energy surface
The TPIMC technique can be employed using any torsional potential energy surface.
62
All previous studies have used atom-atom molecular mechanics force fields to describe intramolecular potential energy.30–32
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac42
63
The current study is the first application of the TPIMC technique on an ab initio potential energy surface.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met9
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met10
65
An important conclusion from previous theoretical work is that MP2 theory with a sufficiently large basis set accurately describes the relative energies of the conformers of glycine.15,16
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac43
66
Recent studies of glycine anharmonic vibrational frequencies further indicate that this level of theory provides a satisfactory description of the anharmonic regions of the potential energy surface.24,41,42
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac44
67
The Gaussian 98 package was employed for all electronic structure calculations.43
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met11
68
The glycine potential energy surface calculated in this study has three dimensions corresponding to torsional angles = (ϕ1, ϕ2, ϕ3).
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met12
69
A 12 × 12 × 12 grid was constructed by calculating the glycine energy at each ϕi = 30n°, n = 1,2,…,12.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met13
70
At each grid point, a constrained energy minimization was performed to optimize all non-torsional degrees of freedom.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met14
71
This minimization allowed the bond angles and stretches to relax with respect to the changing torsional angles.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met15
72
An analytic potential energy surface was obtained by interpolating the grid points with an expansion of periodic functions of the form g(ϕ1, ϕ2, ϕ3) = f1(ϕ1) f2(ϕ2) f3(ϕ3), where fi(ϕi) ∈ {sin(2πnϕi/360°),cos(2πnϕi/360°)} and n ∈ {0,1,…,6}.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod2
73
All 1728 orthogonal functions of this form were included in the expansion to yield an exact fit of the calculated grid points.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met16
74
The potential energy surface fit described above accurately recovers the geometry and energy of almost every major glycine conformation.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res7
75
The only exception is conformer II, for which the surface is not sufficiently flexible to predict the slight out-of-plane relaxation of the geometry to = (±12°,∓3°,±161°).
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res8
76
To include this feature, the analytical potential energy surface is supplemented with two Gaussian “dimple” functions of the form g() = αexp(( − 0)2/β2), where α = −1.0 kJ mol−1, β = 13°, and 0 = (±14.5°,∓6°,±158°).
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod3
77
Although preliminary results indicate that this minor adjustment has negligible impact on the predicted conformer populations, the correction provides a better analytical fit of this important region of the potential energy surface.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res9
78
In Table 1, we compare the stationary point energies of glycine on the torsional potential energy surface with reference energies from MP2/6-311++G** geometry optimizations.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs1
79
The conformer labels are consistent with those of Császár.15
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res10
80
For no stationary point does the torsional potential energy surface deviate from its reference value by more than 0.16 kJ mol−1.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res11
81
The average RMS difference between the torsional potential and the reference energies for the stationary points is 0.0058 kJ mol−1.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res12
82
We also point out a technical detail regarding the definition of torsional angle ϕ3.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac45
83
In the calculation of the ab initio grid points, ϕ3 was defined as the dihedral angle C1–C2–N3–X, where X is a dummy atom between H9 and H10 (Fig. 1).
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod4
84
The dihedral angle C1–C2–N3–H9 was fixed at ϕ3 + 60° so that changes in ϕ3 correspond to changes in the position of real atoms.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod5
85
The torsional angle C1–C2–N3–H10 was left unconstrained.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod6
86
For no conformer in this study does the ϕ3 angle differ from the bisector of the C1–C2–N3–H9 and C1–C2–N3–H10 dihedral angles by more than 2°.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod7
Conformer coordinate ranges
87
The TPIMC technique uses quantum Boltzmann statistics to generate a multidimensional probability distribution function in terms of the torsional angles.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met17
88
Conformer populations are calculated by integrating this function over the range of coordinates ascribed to each particular conformer.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met18
89
The integral of the entire distribution function over all coordinates is unity.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met19
90
A similar energy distribution is also generated to enable the evaluation of conformer enthalpies.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met20
91
To calculate the conformer populations (and other thermodynamic quantities), it is necessary to pre-define the coordinate ranges of each conformer.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac46
92
In general, the torsional configuration space is partitioned into coordinate ranges approximately along the potential barriers that separate the minima of neighboring conformers.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met21
93
Because the probability distribution function is largest in the potential wells and smallest in the barrier regions, the exact choice of partition has little effect on calculated quantities.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res13
94
Informed by analysis of the ab initio torsional potential energy surface of glycine, we chose the conformer coordinate ranges reported in Table 2.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs2
95
The ϕ1 and ϕ2 ranges were divided into two partitions, and the ϕ3 range was divided into three partitions.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met22
96
The ϕ1 boundaries for conformers I and III were chosen carefully because the torsional distribution is non-zero in the barrier range separating these conformers at higher temperatures, as will be seen later.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met23
97
Other conformers, in addition to conformers I–V, were also analysed in this study.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res14
98
However, they were effectively unpopulated at the temperatures considered and are not discussed in detail.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res15
Harmonic frequency calculations
99
For conformers I–V, unconstrained geometry optimizations and harmonic frequency calculations were also performed at the 6-311++G**/MP2 level of theory.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met24
100
Conformers II–V were allowed to converge to their non-planar minima so that all frequencies were positive.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met25
101
The conformer frequency vibrations are included in the electronic supplementary information (ESI). Harmonic thermodynamic quantities were obtained from the standard statistical mechanical expressions for the harmonic oscillator.44
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac47
102
Because experimental conformer populations for glycine are available primarily from infrared spectroscopy studies in which the sample molecules are fixed in an inert gas matrix, the translational and rotational partition functions of the glycine conformers are neglected throughout this study28.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met26
Results and discussion
TPIMC conformer populations
103
Fig. 2 displays the calculated conformer populations of glycine as a function of temperature.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs3
104
Calculations were performed using the quantum TPIMC technique and reflect the equilibrium thermal distribution of the glycine conformers.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res16
105
The populations of conformers II–V are expanded in Fig. 2b.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs4
106
The population of no higher-energy conformer is calculated to exceed 1% in this temperature range.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod8
107
In Fig. 2b, the estimated standard deviation of the reported populations are less than 0.1% for all conformers and all temperatures.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res17
108
The TPIMC calculations predict that conformer I, which corresponds to the global minimum of the potential energy surface, is the most populated conformer at every considered temperature.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res18
109
Conformer II is the most thermally accessible of the other conformers and is found to contain 11% of the total glycine population at only 300 K (Fig. 2b).
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res19
110
With increasing temperature, the population of conformer II reaches a maximum of 12.5% at about 400 K before decreasing as higher energy conformers become thermally accessible.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res20
111
The populations of conformers III and IV are calculated to increase rapidly between 200 K and 500 K and to surpass the population of conformer II at ≈400 K. Conformer IV, though it has not yet been experimentally observed, is calculated to have a slightly higher equilibrium population than conformer III at all temperatures.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res21
112
Conformer V is also found to be a substantial component of the thermal distribution above 300 K.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res22
113
Growth in the population of conformers III–V with respect to conformer II as temperature rises (Fig. 2b) suggests that entropy plays a major role in the relative free energies of the conformers.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res23
114
Previous theoretical work has determined that conformer III exhibits high standard entropy, and this result is confirmed by the TPIMC results presented in Table .313
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res24
115
The table displays the calculated relative enthalpies and entropies of the glycine conformers at various temperatures.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs5
116
The conformer enthalpies are weakly dependent on changing temperature and reflect the relative energies of the optimized conformer structures in Fig. 1.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res25
117
The calculated entropies, however, are more dependent on temperature and vary substantially between the conformers.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res26
118
In particular, during the temperature range in which conformer III rapidly gains population (150 K to 400 K), its entropy is higher than the entropy of conformer II by about 8 kJ mol−1 and exceeds the entropy of conformer I by 4–8 kJ mol−1.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res27
119
At higher temperatures, the fact that conformers IV and V become entropically favored coincides with their calculated rise in population (Fig. 2b).
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res28
120
The calculated torsional distributions in Fig. 3 provide insight into the relative entropies of the experimentally observed conformers I, II, and III.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs6
121
In the figure, the 3-dimensional torsional probability distribution obtained with quantum TPIMC is reduced along the C–C torsional angle, ϕ1.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met27
122
The conformer populations reported in Fig. 2 may be recovered by integrating the distribution curves with respect to ϕ1.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met28
123
Because of its symmetric minimum energy structure, it is expected that the torsional distribution of conformer I has a single peak at ϕ1 = 180°.
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp1
124
However, the minimum energy geometry of conformer II deviates from Cs symmetry with ϕ1 = ±12.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res29
125
It is therefore notable that the torsional distribution of conformer II exhibits only one maxima in the heavy atom positions at ϕ1 = 0 for every temperature (Figs. 3c and 3d).
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res30
126
This is consistent with the findings of microwave spectroscopy and indicates that the shallow barrier separating the local minima of conformer II is easily overcome.22,23,45
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127
As was previously noted in regard to Fig. 2b, the population of conformer II rises with temperature until approximately 400 K, after which it diminishes.
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128
This is again illustrated in Figs. 3c and 3d.
Type: Observation |
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129
Between 300 K and 400 K, as the torsional distribution spreads, Fig. 3d shows that the distribution peak height lowers despite a slight increase in integrated conformer population.
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130
Conformer III is seen to have a flatter torsional distribution than those of conformers I and II (Fig. 3b).
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131
The flexibility of conformer III and the large volume of configuration space occupied by its distribution are consistent with the high entropy reported for the conformer in Table 3.
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132
It is seen that conformer III exhibits two peaks in the calculated torsional distribution which correspond to the symmetric, non-planar minima of the conformer at ϕ1 = ±30°.
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133
However, the peaks increasingly overlap at higher temperatures as the distribution converges toward a broad single peak spanning ϕ1 = [−60°,60°].
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134
This behavior explains the relative entropy of conformers I and III as a function of temperature (Table 3).
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135
Conformer I exhibits a single distribution peak at every temperature and therefore has a statistical degeneracy number of one.
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136
At low temperatures, when the distribution peaks of conformer III are fairly distinct, it will exhibit two-fold statistical degeneracy.
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ConceptID: Res40
137
The greater degeneracy of conformer III contributes to its larger entropy.
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138
The degeneracy number of conformer III will reduce to one as the distribution peaks merge at higher temperatures, so the corresponding decrease in the relative conformer entropies is to be expected.
Type: Hypothesis |
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ConceptID: Hyp2
139
Unlike conformer III, the equivalent minima for both conformers IV and V are well separated on the potential energy surface, so they exhibit two-fold statistical degeneracy at all temperatures.
Type: Result |
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ConceptID: Res42
140
As a result, the relative entropies of conformers IV and V rise with respect to conformer III as temperature increases.
Type: Result |
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141
For higher temperatures, it is seen in Fig. 3b that the distribution of conformer III is non-zero at ϕ1 = ±100°, the position of the potential barrier preventing interconversion of conformer III to conformer I. Therefore, depending on how the glycine molecules are cooled for experimental analysis, the ideal equilibrium populations of conformers I and III will not necessarily be observed.
Type: Result |
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ConceptID: Res44
Comparison with experiment
142
Fig. 4 displays the calculated and experimentally observed populations of glycine conformers II and III as a function of temperature.
Type: Observation |
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143
The relative populations of conformers I, II, and III have been reported in two recent matrix-IR studies performed using neon and argon matrices.28,29
Type: Background |
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144
Since conformers IV and V have not been conclusively observed experimentally, it is assumed that molecules in these conformations at equilibrium interconvert to conformer I under experimental conditions.
Type: Model |
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ConceptID: Mod9
145
The population of conformer I is therefore complementary to the sum of the populations in the figure.
Type: Model |
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ConceptID: Mod10
146
The neon matrix-IR populations were obtained by measuring the absorption intensities of the conformer CO stretching vibrations for two different temperatures.29
Type: Background |
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147
In this study, the conformer populations ratios are reported explicitly at 358 K, and the shift in the conformer equilibrium at 438 K is estimated.
Type: Background |
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ConceptID: Bac50
148
The argon matrix-IR conformer populations were obtained by comparing the calculated and observed intensities of the CO stretching vibrations at 443 K.28
Type: Background |
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ConceptID: Bac51
149
No error estimate was given for the measurements in argon.
Type: Background |
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ConceptID: Bac52
150
The conformer populations calculated using the TPIMC technique are in close agreement with the experimental results.
Type: Result |
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ConceptID: Res45
151
For conformer III, the interpolated theoretical results coincide with the experimental population of ≈13% determined at 358 K in the Ne matrix and remain within the uncertainty of that study at 438 K. The calculated population for conformer III at 443 K is also in precise agreement with the measurement in the Ar matrix.
Type: Result |
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ConceptID: Res46
152
For conformer II, the calculated results are within the error bars of the Ne matrix-IR experiments at 358 K and 438 K. At ≈440 K, it is seen that the measured population of conformer II differs by approximately 5% depending on whether the neon or argon matrix is employed.
Type: Result |
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ConceptID: Res47
153
However, it is likely that the experiments employing the lighter neon gas provides a more appropriate basis for comparison with the gas-phase calculations.
Type: Hypothesis |
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ConceptID: Hyp3
154
Despite the good agreement between theory and experiment in Fig. 4, quantitative comparison of conformer populations determined from gas-phase theoretical calculations and matrix-IR spectroscopy experiments is vulnerable to several sources of error.
Type: Result |
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ConceptID: Res48
155
In addition to the possible flaws of the potential energy surface and assumptions of the theoretical technique, the identity of the matrix is known to affect experimentally determined conformer populations.29
Type: Background |
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ConceptID: Bac53
156
Neon and argon atoms, although chemically inert, contain electron density that will alter the local environment of the sample molecules in the matrix.
Type: Model |
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ConceptID: Mod11
157
Therefore, the matrix can induce real changes in conformer populations as well as perceived changes arising from distortion of the IR spectra.
Type: Hypothesis |
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ConceptID: Hyp4
158
The development of techniques for doping helium droplets with glycine molecules improves the possibility of obtaining effectively gas-phase conformer populations of glycine in the near future.46
Type: Background |
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ConceptID: Bac54
159
For the matrix-IR results discussed above, the substrate temperature was kept very low (5 K for Ne, 8 K for Ar) with the intention of minimizing changes in the glycine conformer populations during matrix deposition.
Type: Background |
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ConceptID: Bac55
160
However, the disappearance of conformer peaks during sample cooling is difficult to avoid, particularly when low-energy pathways of interconversion are available.25
Type: Background |
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ConceptID: Bac56
161
It was mentioned previously that conformer III of glycine is not found in microwave spectroscopy experiments because the potential barrier for III → I conformer interconversion is small enough to be overcome during the collisional cooling of free jet expansion.23
Type: Background |
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162
Although the presence of conformer III in the matrix-IR experiments suggests that matrix deposition cooling is more gentle than free jet expansion, the possibility of interconversion cannot be discounted.
Type: Hypothesis |
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ConceptID: Hyp5
163
It was seen in Fig. 2b that the TPIMC technique predicts ≈15% of the total glycine population to be in conformer IV in the equilibrium distributions at 350–450 K. The absence of this conformer in the matrix-IR spectra, particularly in light of the otherwise good agreement between theory and experiment, suggests that a large portion of the equilibrium population of conformer IV is collapsing to conformer I during matrix cooling.
Type: Result |
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ConceptID: Res49
164
Previous theoretical studies have dismissed the likelihood of isolating conformer IV on the basis that the calculated barrier for IV → I interconversion was substantially lower than that for III → I interconversion.
Type: Background |
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ConceptID: Bac58
Type: Background |
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ConceptID: Bac59
166
The potential energy surface employed in the current study has neither of these deficiencies.
Type: Result |
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ConceptID: Res50
167
Fig. 5 displays the calculated potential curves along the coordinate of interconversion for conformers III and IV to conformer I. The III → I interconversion takes place along the C–C torsion, ϕ1, and IV → I occurs along the C–N torsion, ϕ3.
Type: Observation |
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ConceptID: Obs9
168
In obtaining the curves, the torsional coordinate of interconversion was fixed and the remaining torsions were allowed to relax on the potential energy surface.
Type: Method |
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Novelty: Old |
ConceptID: Met29
169
The figure reveals barrier heights of 3.15 kJ mol−1 and 2.97 kJ mol−1 for interconversions III → I and IV → I, respectively.
Type: Result |
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ConceptID: Res51
170
These barrier heights are markedly closer in energy than has been previously reported, so an alternative explanation for the absence of conformer IV in the experiments is required.
Type: Result |
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ConceptID: Res52
171
We suggest two possible explanations for the observation that conformer IV is more likely to interconvert to conformer I than conformer III.
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172
In the first explanation, we note that the the minimum energy cross section of the potential energy surface along the reaction coordinate (Fig. 5) does not necessarily provide an adequate dynamical description of conformer interconversion.
Type: Hypothesis |
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ConceptID: Hyp6
173
Among other things, this minimized surface neglects the entropic effects and internal energy arising from the other degrees of freedom.
Type: Hypothesis |
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ConceptID: Hyp7
174
It is well known from transition state theory that the free energy surface, or the potential mean force, incorporates these thermodynamic effects in an averaged fashion and may provide a more appropriate set of barrier heights.47
Type: Background |
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ConceptID: Bac60
175
Once we have obtained the glycine torsional distribution functions from the TPIMC calculations, it is a simple task to convert them into free energy surfaces for coordinates ϕ1 and ϕ3.48
Type: Result |
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ConceptID: Res54
176
Doing so for a temperature of 400 K, we find that the free energy barriers for III → I and IV → I are 3.72 kJ mol−1 and 2.98 kJ mol−1, respectively.
Type: Result |
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ConceptID: Res55
177
That is, the difference in barrier heights on the free energy surface is over four times the difference in energy on the minimized potential energy surface.
Type: Result |
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ConceptID: Res56
178
Using a simple Arrhenius analysis, we find that the ratio of interconversion rates kIV→I/kIII→I is about 20% higher using the free energy surface rather than the potential energy surface.
Type: Result |
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ConceptID: Res57
179
In agreement with experiment, this finding suggests that conformer III will be less likely to interconvert than conformer IV.
Type: Result |
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ConceptID: Res58
180
The second factor favoring the observation of conformer III in preference to conformer IV is statistical.
Type: Result |
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ConceptID: Res59
181
Note from Fig. 5 that conformers III and IV each have two corresponding local minima.
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ConceptID: Res60
182
The minima of conformer III are close neighbors on the potential energy surface separated by a low barrier, but the minima of conformer IV are separated by either a larger barrier or the deep potential well of conformer I. Therefore, in the event that a glycine molecule in one of the potential wells corresponding to conformer IV undergoes a collision strong enough to induce interconversion, the only likely outcome is that it falls into the neighboring potential well of conformer I. On the other hand, if a glycine molecule in one of the potential wells of conformer III undergoes interconversion, there are two possible results: (i) the deep potential well of conformer I or (ii) the other shallow well of conformer III.
Type: Result |
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ConceptID: Res61
183
Because the population of conformer III can shuttle between its two local minima, it is expected to survive more collisions than the population of conformer IV which can only collapse to conformer I. Although the rotationally inelastic scattering of glycine and the quantum dynamics of the ϕ1 torsional angle have been recently explored theoretically,49,50 verification of these hypothesis requires a comparative dynamical study of the III → I and IV → I conversion pathways and is currently in progress.
Type: Result |
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ConceptID: Res62
184
It is noted that other previous studies have used experimental techniques to estimate the energetics and equilibrium populations of the glycine conformers.
Type: Background |
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ConceptID: Bac61
185
The populations at ≈500 K (219 °C) have been reported using gas-phase electron diffraction by Iijima et al.8
Type: Background |
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ConceptID: Bac62
186
This study determined the combined population of conformers II and III to be 24%, which bears only qualitative agreement with the matrix-IR data and the TPIMC value of 31% in Fig. 4.
Type: Result |
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ConceptID: Res63
187
However, to interpret the electron diffraction pattern, the authors relied on structural parameters obtained from early theoretical calculations and highly simplified expressions for the glycine potential energy surface.
Type: Background |
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ConceptID: Bac63
188
Other theoretical studies have had similar difficulties in trying to reproduce the conformer structures and energies predicted in this study.15,16,18
Type: Background |
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ConceptID: Bac64
189
In 1980, Suanram and Lovas estimated the relative minimum energies of conformers I and II to be 5.9 ± 1.8 kJ mol−1 using millimeter wave spectroscopy.21
Type: Background |
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ConceptID: Bac65
190
This study neglected the glycine intramolecular partition function and relied on a crude estimate of the conformer dipole moments.21
Type: Background |
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ConceptID: Bac66
191
The discrepancy of this energy difference with subsequent theoretical evidence15,16 most likely arises from the fact that the experimental estimation did not account for the collapse of the substantial populations of conformers III and IV to conformer I. Therefore, the measured equilibrium population of conformer I would have been too large, leading to an over-estimation of the energy difference between the conformers.
Type: Result |
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ConceptID: Res64
192
More recent microwave spectroscopy experiments sacrificed frequency response in favor of sensitivity, so the relative population and energetics of conformers I and II observed in these experiments was not determined51.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac67
Quantum effects
193
Up to this point, only the TPIMC calculations which provide a quantum mechanical description of torsional motion have been discussed.
Type: Result |
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ConceptID: Res65
194
However, it is of interest to consider how the glycine conformer populations and torsional distributions are altered by quantum effects.
Type: Goal |
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ConceptID: Goa1
195
Fig. 6 reports the population of conformer II at various temperatures as determined by TPIMC calculations performed with the parameter nb set to 1, 5, and 15.
Type: Observation |
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ConceptID: Obs10
196
TPIMC calculations with nb = 1 are equivalent to a classical mechanical description, and the calculations nb = 15 are expected to recover almost all quantum effects for glycine in this temperature range.
Type: Hypothesis |
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ConceptID: Hyp8
197
In the figure, the very small differences between the nb = 5 and nb = 15 results support this conclusion.
Type: Result |
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ConceptID: Res66
198
Fig. 6 shows that quantum effects are greatest at lower temperatures, whereas the quantum and classical descriptions converge at high temperatures.
Type: Result |
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ConceptID: Res67
199
At 200 K, the classical result over-estimates the population of conformer II by a factor of ≈1.5.
Type: Result |
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Novelty: None |
ConceptID: Res68
200
Even at the higher temperatures probed by the matrix-IR experiments (350–450 K), differences arising from quantum effects remain of similar magnitude to differences attributed to the identity of the matrix gas (Fig. 4).
Type: Result |
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ConceptID: Res69
201
Necessarily, quantum effects changed the populations of the other glycine conformers, but to a lesser extent than seen here for conformer II.
Type: Result |
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Novelty: None |
ConceptID: Res70
202
Quantum effects on the torsional distribution of the glycine conformers are illustrated in Fig. 7.
Type: Observation |
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Novelty: None |
ConceptID: Obs11
203
The 3-dimensional torsional distribution of glycine is reduced over ϕ1 = [−90, 90] and plotted as a function of ϕ2 and ϕ3.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met30
204
For this range of ϕ1, the torsional distributions of conformers II, III, and V can be simultaneously displayed.
Type: Observation |
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Novelty: None |
ConceptID: Obs12
205
The left column displays the classical TPIMC distribution, and the right column displays the quantum TPIMC distribution.
Type: Observation |
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ConceptID: Obs13
206
As was noted before in Fig. 6, the role of quantum mechanics is particularly striking for conformer II.
Type: Result |
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ConceptID: Res71
207
At each temperature, the quantum distribution of conformer II about (ϕ2, ϕ3) = (360°, 180°) is diminished and broadened in comparison to the corresponding classical distribution.
Type: Result |
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ConceptID: Res72
208
These two-dimensional plots offer further insight into the reason for the sensitivity of conformer II to quantum effects.
Type: Result |
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ConceptID: Res73
209
In the classical plots, the distribution of conformer II exhibits two slight peaks corresponding to symmetric, non-planar minima of the conformer at ϕ3 ≈ 160° and 200°.
Type: Result |
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ConceptID: Res74
210
In the quantum distributions, this feature is largely washed out as the light –NH2 torsion tunnels between the neighboring minima, resulting in a single, broad distribution peak for conformer II at ϕ3 = 180°.
Type: Result |
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ConceptID: Res75
211
This tunneling effect gives rise to the notably quantum behavior of conformer II.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con1
Non-torsional modes
212
The TPIMC technique enables the efficient quantum mechanical analysis of large molecules by reducing the total number of intramolecular degrees of freedom to the number of single-bond torsions.30,31
Type: Background |
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ConceptID: Bac68
213
By not explicitly including the thermodynamic contributions of non-torsional motions, such as bond stretches and angle bends, the method assumes that these contributions are identical for every conformer and cancel in the evaluation of relative quantities.
Type: Method |
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Novelty: Old |
ConceptID: Met31
214
The motivation for this assumption is best understood within the context of the harmonic oscillator approximation.
Type: Background |
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ConceptID: Bac69
215
For the quantum harmonic oscillator, the contribution of a particular vibrational mode to the free energy of a conformer is composed of two terms.
Type: Background |
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ConceptID: Bac70
216
The first is the zero point energy, which is independent of temperature and proportional to the frequency of the vibrational mode.
Type: Background |
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ConceptID: Bac71
217
The second term vanishes exponentially for large frequencies and becomes infinite as the frequency approaches zero.
Type: Background |
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ConceptID: Bac72
218
It follows that high-frequency modes will make free energy contributions approximately equal to the zero point energy, and low-frequency modes will make potentially huge contributions to the free energy arising from the second term.
Type: Background |
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ConceptID: Bac73
219
We can now consider the relative contribution of a particular vibrational mode to the free energy of two different conformers.
Type: Goal |
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Novelty: None |
ConceptID: Goa2
220
Although high-frequency vibrations, such as bond stretches and most angle bends, will certainly vary depending on conformation, the relative free energy contribution is only proportional to the size of this frequency shift.
Type: Background |
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ConceptID: Bac74
221
A frequency shift of the same magnitude in the low-frequency range can lead to much larger relative contributions.
Type: Background |
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ConceptID: Bac75
222
It is therefore appealing to assume that relative conformer free energies are dominated by the contributions from low-frequency modes.
Type: Background |
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ConceptID: Bac76
223
Comparison of TPIMC calculations with experiment has supported the assumption that the torsional degrees of freedom dominate conformational thermodynamics.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res76
224
Quantitative agreement between calculated and observed conformer populations is reported above for glycine and in a previous study for the 2-amino-1-phenylethanol molecule.32
Type: Result |
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Novelty: None |
ConceptID: Res77
225
However, it is important to recognize that, in addition to torsional modes, flexible molecules exhibit other low frequency motions that can be conformer dependent and substantially affect the relative free energy.
Type: Background |
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ConceptID: Bac77
226
It is therefore worthwhile to estimate the influence of non-torsional motions on the glycine conformer populations calculations reported in this study.
Type: Goal |
Advantage: None |
Novelty: None |
ConceptID: Goa3
227
A straightforward algorithm for estimating the effect of non-torsional vibrations on the calculated conformer populations involves (i) calculating the harmonic frequencies of the conformers of interest, (ii) identifying the vibrational motions that most resemble torsions, (iii) using the remainder of the vibrational frequencies to calculate harmonic free energy corrections, and (iv) using these free energy corrections to adjust the conformer populations.
Type: Method |
Advantage: None |
Novelty: New |
ConceptID: Met32
228
The quantitative reliability of these corrections depends on the extent to which the torsional modes couple with other vibrations and the accuracy of the harmonic oscillator approximation for the non-torsional motions.
Type: Hypothesis |
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ConceptID: Hyp9
229
Nonetheless, comparison of the calculated populations before and after correction will indicate the extent to which non-torsional vibrations are relevant in the current study.
Type: Hypothesis |
Advantage: None |
Novelty: None |
ConceptID: Hyp10
230
The left side of Table 4 compares the quantum TPIMC conformer populations before and after non-torsional correction at the experimentally relevant temperature of 400 K. Harmonic frequencies for the five conformers used in the corrections were calculated at the MP2/6-311++G** level of theory and are listed in the ESI. The close agreement between the second and third columns of Table 4 indicates that the free energy contributions from the non-torsional modes largely cancel in the various conformers of glycine at 400 K. The non-torsional harmonic correction generally changes the calculated TPIMC populations 1–2% at 400 K. It is concluded that the above comparison of quantum TPIMC populations with experiment is not significantly effected by contributions arising from non-torsional motions.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met33
231
The harmonic vibrational frequencies of glycine, including the torsional modes, can also be used to directly calculate conformer populations.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac78
232
This is a standard electronic structure theory approach for analyzing intramolecular thermodynamics.
Type: Background |
Advantage: None |
Novelty: None |
ConceptID: Bac79
233
Harmonic vibrational analysis approximates the potential energy surface about a local minimum with a quadratic function.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met34
234
To avoid large errors in the evaluation of conformer populations, the technique requires a priori specification of each conformer that will be populated and the statistical degeneracy number gi of each conformer.
Type: Method |
Advantage: None |
Novelty: Old |
ConceptID: Met35
235
Conformer I, which has a planar energy minimum, is singly degenerate (gI = 1).
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod12
236
The symmetric, nonplanar minima of conformers IV and V are well separated on the potential energy surface, so we can reliably assign gIV = 2 and gV = 2.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod13
237
The appropriate degeneracy numbers of conformers II and III, however, are less obvious.
Type: Background |
Advantage: None |
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ConceptID: Bac80
238
It was shown in Fig. 3b that the torsional distribution of conformer III has two maxima at low temperature which converge toward a single maximum at high temperature.
Type: Result |
Advantage: None |
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ConceptID: Res78
239
Similarly, despite the fact that the quantum torsional distribution of conformer II exhibits only a single peak (Fig. 7), the conformer has a symmetric pair of minimum energy structures at = (±12°, ∓3°, ±161°).
Type: Result |
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ConceptID: Res79
240
It is therefore difficult to make an a priori selection of appropriate degeneracy numbers for conformers II and III in the harmonic vibrational thermodynamic analysis of glycine.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res80
241
The right side of Table 4 presents the glycine conformer populations calculated using three different sets of degeneracy numbers.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs14
242
In each set, it is assumed that gI = 1 and gIV = gV = 2.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod14
243
In the fourth column of the table (HO1), we set gII = gIII = 1.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod15
244
For HO2, we set gII = 1 and gIII = 2, and for HO3, we set gII = gIII = 2.
Type: Model |
Advantage: None |
Novelty: None |
ConceptID: Mod16
245
In qualitative agreement with the TPIMC results, the HOX columns in Table 4 predict the majority of molecules to be found in conformer I and smaller populations for conformers II–V.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res81
246
The HO2 degeneracy number choice of gII = 1 and gIII = 2 recovers the relative ordering of conformer populations, a finding that is consistent with the numbers of maxima in the TPIMC ϕ1 torsional distributions (Fig. 3).
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res82
247
However, the harmonic approximation can severely hinder the calculation of conformer populations,32 and it is seen in the table that the results vary depending on the choice of degeneracy numbers.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res83
248
Without prior knowledge of the TPIMC results, it would have been difficult in this case to reliably compare the harmonic approximation calculations with experiment.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res84
Conclusions
249
By combining an anharmonic, quantum-mechanical description of the glycine torsions with an ab initio description of the electronic structure of the molecule, the current study achieves a level of accuracy not previously available in the theoretical study of molecular conformation.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con2
250
The population of the three experimentally observed conformers are calculated in good agreement with recent matrix-IR experiments, and the presence of a fourth conformer is predicted at equilibrium.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con3
251
Contrary to previous conclusions, it is suggested that the absence of conformer IV from experimental observation is not primarily due to the height of the IV → I potential barrier but rather to other aspects of the dynamics of interconversion.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con4
252
Quantum effects are found to substantially alter the population of conformer II, especially at low temperature, and the role of the non-torsional vibrations of glycine is not found to significantly alter the comparison of the TPIMC calculations with experiment.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con5
253
To achieve optimal accuracy, the study employs a high-quality potential energy surface, accounts for the contributions of non-torsional modes, and utilizes conservative parameters for numerical convergence criteria and TPIMC quantum convergence.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con6
254
These measures have led to calculated results that are in strong agreement with available experimental data, but they introduce considerable computational cost.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con7
255
The longest TPIMC calculations presented took approximately eight days to complete on a single processor, and the construction of a global ab initio potential energy surface would soon become unfeasible with more degrees of freedom.
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res85
Type: Result |
Advantage: None |
Novelty: None |
ConceptID: Res86
257
Furthermore, the quantum anharmonic description provided by the TPIMC technique will be critical in future applications that consider the explicit interaction of a biomolecule with its solvent.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con8
258
When employed with a reliable potential energy surface, the TPIMC technique is a promising new method for the prediction of biomolecular conformation that is expected to gain future application on more complicated systems of biological interest.
Type: Conclusion |
Advantage: None |
Novelty: None |
ConceptID: Con9
Supporting information available
259
Tables listing the calculated harmonic frequencies of the glycine conformers.
Type: Observation |
Advantage: None |
Novelty: None |
ConceptID: Obs15