Lowest-Lying Conformers of Alanine: Pushing Theory to Ascertain Precise Energetics and Semiexperimental R e Structures

Abstract

The two lowest-energy gas-phase conformers, Ala-I and Ala-IIA, of the natural amino acid L-alanine (Ala) have been investigated by means of rigorous ab initio computations. Born-Oppenheimer (BO) equilibrium structures (r e BO) were fully optimized at the coupled-cluster [CCSD(T)/cc-pVTZ] level of electronic structure theory. Corresponding semiexperimental (SE) equilibrium structures (r e SE) of each conformer were determined for the first time by least-squares refinement of 11-15 structural parameters on modified, experimental rotational constant data from 10 isotopologues. The SE equilibrium rotational constants were obtained by, first, refitting Fourier transform microwave spectra using the method of predicate observations and, second, correcting the resulting effective rotational constants with theoretical vibration-rotation interaction constants (R i). Careful analysis is made of the procedures to account for vibrational distortion, which proves essential to defining precise structures in flexible molecules such as Ala. Because Ala possesses no symmetry, has several large-amplitude nuclear motions, and exhibits conformers with different hydrogen bonding patterns, it is one of the most difficult cases where reliable equilibrium structures have now been determined. The relative energy of the alanine conformers was pinpointed using first-principles composite focal point analyses (FPA), which employed extrapolations using basis sets as large as aug-cc-pV5Z and electron correlation treatments as extensive as CCSD(T). The FPA computations place the Ala-IIA equilibrium structure higher in energy than that of Ala-I by a mere 0.45 kJ mol -1 (38 cm -1), showing that the two lowest-lying conformers of alanine are nearly isoenergetic; inclusion of zero-point vibrational energy increases the relative energy to 2.11 kJ mol -1 (176 cm -1). The yet unobserved Ala-IIB conformer is found to be separated from Ala-IIA by a vibrationally adiabatic isomerization barrier of only 16 cm -1 .

Full text

Page 1

Lowest-Lying Conformers of Alanine: Pushing Theory to
Ascertain Precise Energetics and Semiexperimental Re
Structures
Heather M. Jaeger,†Henry F. Schaefer III,†Jean Demaison,‡Attila G. Csa ´sza ´r,*,§and
Wesley D. Allen*,†
Center for Computational Chemistry and Department of Chemistry, UniVersity of Georgia,
Athens, Georgia 30602, Laboratoire de Physique des Lasers, Atomes et Mole ´cules, UMR
CNRS 8523, UniVersite ´ de Lille I, 59655 VilleneuVe d’Ascq Cedex, France, and
Laboratory of Molecular Spectroscopy, Institute of Chemistry, Eo ¨tVo ¨s UniVersity,
H-1518 Budapest 112, P.O. Box 32, Hungary
Received January 12, 2010
Abstract: The two lowest-energy gas-phase conformers, Ala-I and Ala-IIA, of the natural amino
acid L-alanine (Ala) have been investigated by means of rigorous ab initio computations.
Born-Oppenheimer (BO) equilibrium structures (re
[CCSD(T)/cc-pVTZ] level of electronic structure theory. Corresponding semiexperimental (SE)
equilibrium structures (re
refinement of 11-15 structural parameters on modified, experimental rotational constant data from
10 isotopologues. The SE equilibrium rotational constants were obtained by, first, refitting Fourier
transform microwave spectra using the method of predicate observations and, second, correcting
the resulting effective rotational constants with theoretical vibration-rotation interaction constants
(Ri). Careful analysis is made of the procedures to account for vibrational distortion, which proves
essential to defining precise structures in flexible molecules such as Ala. Because Ala possesses
no symmetry, has several large-amplitude nuclear motions, and exhibits conformers with different
hydrogen bonding patterns, it is one of the most difficult cases where reliable equilibrium structures
have now been determined. The relative energy of the alanine conformers was pinpointed using
first-principles composite focal point analyses (FPA), which employed extrapolations using basis
sets as large as aug-cc-pV5Z and electron correlation treatments as extensive as CCSD(T). The
FPA computations place the Ala-IIA equilibrium structure higher in energy than that of Ala-I by a
mere 0.45 kJ mol-1(38 cm-1), showing that the two lowest-lying conformers of alanine are nearly
isoenergetic; inclusion of zero-point vibrational energy increases the relative energy to 2.11 kJ mol-1
(176 cm-1). The yet unobserved Ala-IIB conformer is found to be separated from Ala-IIA by a
vibrationally adiabatic isomerization barrier of only 16 cm-1.
BO) were fully optimized at the coupled-cluster
SE) of each conformer were determined for the first time by least-squares
I. Introduction
Flexible molecules have potential energy surfaces (PESs)
characterized by flat regions and low barriers for conforma-
tional isomerization.1-3L-Alanine (Ala) and all other natural
amino acids exhibit such characteristics and have a sizable
number of low-energy conformers.4-19The primary differ-
ences between the conformers of gas-phase amino acids,
which exist exclusively in neutral form, are the number and
types of intramolecular hydrogen bonds occurring for various
configurations of the amino, carboxylic acid, and any polar
side-chain groups. In the case of Ala, the dihedral angle about
the central carbon-carbon bond, τ(O ) C-CR-N), remains
* Towhomcorrespondenceshouldbeaddressed.E-mail:wdallen@
uga.edu (W.D.A.); csaszar@chem.elte.hu (A.G.C.).
†University of Georgia.
‡Universite ´ de Lille.
§Eo ¨tvo ¨s University.
J. Chem. Theory Comput. 2010, 6, 3066–3078
3066
10.1021/ct1000236  2010 American Chemical Society
Published on Web 09/23/2010

Page 2

consistently near 0° or 180° for all conformers, despite the
variety of possible hydrogen bonds.
Experiments on the structure(s) of free Ala have included
gas-phase electron diffraction (GED),11,12jet-cooled milli-
meterwave (MMW) and Fourier transform microwave
(FTMW) spectroscopy in molecular beams,5,9,10and matrix-
isolation infrared spectroscopy.13The GED results for Ala
cannot provide a clear distinction between the multiple
conformers present at the elevated temperature of the
experiments. Moreover, the derived rg, rR, and rR
parameters differ substantially from the corresponding equi-
librium (re) values because of temperature-dependent
rotational-vibrational effects, which can be as large as those
induced by conformational changes. The low-temperature
MMW and FTMW molecular beam experiments5,9,10clearly
identified two gas-phase conformers, Ala-I and Ala-IIA
(Figure 1). The failure to observe other low-energy conform-
ers given by electronic structure computations4,6-8has been
attributed to vibrational relaxation in the free-jet expan-
sions.20The matrix-isolation infrared experiments13also
observed two conformers of alanine.
Select r0and rsparameters for Ala-I and Ala-IIA have
been determined5from two sets of FTMW rotational
constants involving 10 isotopologues of each conformer.
Unfortunately, this approach is not sufficient to obtain an
accurate, well-defined empirical structure. Equilibrium struc-
tures, free from undesirable isotopic, rotational-vibrational,
and temperature effects, are often difficult, if not impossible,
to obtain experimentally, especially for flexible molecules.
Vibrational distortion, arising from flat, anharmonic regions
on the PES, can greatly influence the effective, experimental
rotational constants, leading to sizable isotopic effects even
at low temperature. Consequently, for conformers of flexible
molecules, only equilibrium structures can be compared to
one another with any degree of validity. For example,
0structural
differences between the backbone structures of glycine and
alanine should be ascertained from reparameters (see Section
III.F).
A protocol has been established whereby a semiexperi-
mental equilibrium structure (reSE) can be determined by first
correcting empirical, effective ground-state rotational con-
stants with ab initio vibration-rotation interaction constants
(Ri) and then performing a structural refinement on the
resulting “experimental” equilibrium rotational constants
(BeSE).21This combined experimental and theoretical approach
has been successfully applied in many studies,21-34including
work that has given reSEstructures for the lowest-energy
conformers of the neutral amino acids glycine (Gly)24and
proline (Pro).23In this investigation, accurate reSEstructures
of Ala-I and Ala-IIA are determined after refitting spectro-
scopic constants to the observed rotational transitions,5
deriving BeSEconstants for 10 isotopologues of each con-
former,andimposinggeometricconstraintsfromBorn-Oppen-
heimer equilibrium structures (reBO) obtained at the highest
feasible level of ab initio electronic structure theory [CCSD(T)/
cc-pVTZ, vide infra]. This is the first study to conjoin theory
and experiment to derive reliable equilibrium structures,
including detailed error analyses for both theoretical and
experimental procedures, for a molecule as large and flexible
as Ala.
All low-energy conformers of Ala possess intramolecular
hydrogen bonds that significantly stabilize these structures,
increase their rigidity, and provide challenges for electronic
structure theory, as shown in numerous previous ab initio
studies.1,7,14,35-37The sensitivity of Ala conformational
energies to the level of electronic structure theory has been
demonstrated by Csa ´sza ´r,1,7and Figure 2 vividly displays
the energetic variations observed7for Ala-I, Ala-II(A/B),
and Ala-III(A/B). The Ala-III conformers are derived from
the Ala-I structure in Figure 1 by a 180° rotation of the
Figure 1. L-Alanine conformers I, IIA, and IIB.
Lowest-Lying Conformers of Alanine
J. Chem. Theory Comput., Vol. 6, No. 10, 2010 3067

Page 3

-COOH moiety about the C-CR bond, the two variants
differing in whether the carboxyl O-H bond is oriented
toward (IIIA) or away from (IIIB) the methyl substituent
at CR.7Electron correlation reverses the energy ordering of
Ala-II(A/B) and Ala-III(A/B), in accord with known
deficiencies of Hartree-Fock theory in predicting confor-
mational energies of amino acids.1,14,38Strong basis set
dependence of conformational energies is also exhibited;
large basis sets with diffuse functions are necessary to fully
capture the differences in intramolecular hydrogen bonding
interactions. In this work, the relative energy of Ala-IIA with
respect to Ala-I in the nonrelativistic, ab initio limit is
determined by applying the composite focal point analysis
(FPA) approach39-44that has been used successfully in
previous studies on amino acids1,7,8,14,23,24and many other
species.40,43,45-50
II. Computational Methods
II.A. Semiexperimental Equilibrium Structures. The
derivation of reSEstructures involves three main steps:
optimization of reliable reBOstructures, computation of an
ab initio cubic force field with subsequent evaluation of Ri
constants to extract equilibrium BeSEparameters from the
experimental rotational constants, and a tight least-squares
structural fit to selected BeSEvalues for several isotopologues,
incorporating reBOconstraints as necessary. In this study, the
reBOgeometries of Ala-I and Ala-IIA were fully optimized
using frozen-core (FC) CCSD(T) coupled-cluster theory51-53
paired with the correlation-consistent cc-pVTZ basis set of
[4s3p2d1f] and [3s2p1d] quality for {C, N, O} and H,
respectively.54While the inclusion of core electron correla-
tion during these demanding geometry optimizations was not
feasible, the corresponding effects55on the reBOparameters
are expected to lie within the uncertainties of most reSE
parameters and are partially corrected during the least-squares
fit. Geometry optimizations were carried out in natural
internal coordinates56,57using a quasi-Newton-Raphson
method implemented in the PSI3 package.58The optimization
of highly flexible coordinates was facilitated with a fixed
Hessian matrix evaluated at the MP2 level with a (9s5p)
double-? valence basis set59(DZ) at a point near the target
minimum. Energy gradients were computed by finite differ-
ences of energies provided by the MOLPRO60package using
a five-point central difference formula to ensure numerical
accuracy for both high- and low-frequency modes. Finally,
minima were verified by evaluating the molecular gradients
analytically using the MAB-ACESII61program. Cartesian
coordinates of the CCSD(T)/cc-pVTZ reBOstructures of Ala-I
and Ala-IIA are provided in Supporting Information (Table
S1).
For both conformers of Ala, anharmonic force fields were
determined at the all-electron MP2/6-31G(d)62level at the
corresponding minima to avoid the nonzero force dilemma.63
The cubic and semidiagonal quartic force constants in normal
coordinates were evaluated by numerical differentiation of
analytically computed second derivatives. Built-in features64
of MAB-ACESII then gave the vibration-rotation interaction
constants for all isotopologues according to the second-order
vibrational perturbation theory65(VPT2) formula
ωi[∑
in which indices (i,j) denote normal coordinates (Qi, Qj) with
harmonic vibrational frequencies (ωi, ωj), I?is a principal
moment of inertia, aib?is a first derivative of inertial tensor
element Ib? with respect to Qi, ?ij
constant, and φiij is a cubic force constant in the reduced
normal coordinate space. In lowest-order and without
centrifugal distortion corrections, the effective ground-state
rotational constants (B0) are related to their equilibrium
counterparts by the expression
bis a Coriolis coupling
Figure 2. Equilibrium energies relative to Ala-I at various levels of electronic structure theory.
Ri
B) -2Be
2
?)a,b,c
3(ai
4I?
b?)2
+ ∑
j(*i)
(?ij
b)2(3ωi
2+ ωj
2- ωj
2)
ωi
2
+
π(
c
h)
1/2∑
j
φiijaj
bb(
ωi
ωj
3/2)](1)
3068
J. Chem. Theory Comput., Vol. 6, No. 10, 2010
Jaeger et al.

Page 4

which was employed in this study to obtain semiexperimental
BeSEconstants. Note that all Coriolis resonance terms
appearing in eq 1 are canceled in the reduced form on the
right side of eq 2, an important point often not fully
appreciated.
The weighted least-squares refinement66-68for the reSE
structures employed linear combinations of simple valence
internal coordinates and was carried out with the MolStruct69
code. The weights were chosen as the reciprocal statistical
uncertainties in the experimentally derived rotational con-
stants. For both Ala-I and Ala-IIA, experimental data is
available for ten isotopologues, yielding 30 BeSEconstants
each (Supporting Information, Table S2). However, not all
of these constants proved suitable for the reSErefinements.
Because Ala-I and Ala-IIA possess no symmetry, the
number of independent geometric parameters (33) is greater
than the experimental data set, necessitating the use of reBO
structural constraints. The least-squares refinements were
performed on select sets of internal coordinates and rotational
constants. Within least-squares fits, the standard errors
intrinsic to each variable and the deviations for the rotational
constants were monitored carefully.
The success of the reSEprocedure depends on the number
of isotopologues with accurate experimental rotational
constants that can be used to determine meaningful structural
parameters, the accuracy of the anharmonic force fields and
theoretical Riconstants, the quality of the reBOleast-squares
constraints, and the validity of modeling vibrational effects
via first-order vibration-rotation interaction (eq 2). The
utility of Ri constants suffers more from the inherent
approximations within VPT2 for large, flexible molecules
with highly anharmonic vibrational modes than for small,
rigid molecules exhibiting predominantly harmonic motions
and small rovibrational couplings. By employing eq 2,
higher-order vibration-rotation interactions and centrifugal
distortion are neglected, despite their enhanced significance
for flexible molecules. Centrifugal distortion contamination
appears in both the experimental rotational constants and the
theoretical correction of B0to extract BeSE.70Thus, while the
effective rotational constants of certain isotopologues may
describe the observables accurately, caution must be exer-
cised in using these constants to refine the semiexperimental
structure.
II.B. Conformational Energetics. The method of focal
point analysis (FPA)39-44provides a means of systematically
approaching and monitoring convergence of ab initio com-
putations toward the one-particle complete basis set (CBS)
limit and the fully correlated many-electron wave function
(full configuration interaction, FCI). In this study, an FPA
investigation of the Ala-IIA-Ala-I relative energy was
executed with correlation-consistent basis sets augmented
with diffuse functions,54,71aug-cc-pVXZ (X ) D, T, Q, 5).
Hartree-Fock (X ) T, Q, 5) and MP2 (X ) Q, 5) energies
were extrapolated to the CBS limit using standard exponen-
tial and inverse cubic formulas, respectively.72,73Higher-
order correlation effects were incorporated by means of
additive CCSD/aug-cc-pVQZ and CCSD(T)/aug-cc-pVTZ
increments. Core correlation was included by appending the
difference between all-electron and frozen-core CCSD(T)/
cc-pCVTZ results to the valence FPA limit. The frozen-core
CCSD(T)/cc-pVTZ reBOgeometries were adopted as reference
structures in the FPA computations.
The zero-point vibrational energies (ZPVEs) of Ala-I and
Ala-IIA were first computed from the MP2/6-31G(d) an-
harmonic force fields via the expression
where ?ijdenotes the second-order vibrational anharmonicity
constants derived from VPT2.65The effect of anharmonicity
on the ZPVE correction (∆ZPVE) to the Ala-IIA-Ala-I
energy separation was less than 0.02 kJ mol-1. Therefore,
our final ∆ZPVEvalue (+1.66 kJ mol-1) was evaluated from
harmonic vibrational frequencies computed at the highest
feasible level of theory, all-electron MP2 with a pared aug-
cc-pVTZ basis set.74
III. Results and Discussion
III.A. Lowest-Energy Conformers of Ala. Extensive
conformational searching for Gly14and Ala,4,6,7the two
smallest amino acids, has revealed 8 and 13 distinct
conformers, respectively. An unmistakable correspondence
exists between the Gly and Ala conformers because both
have inert side groups (-H for Gly, -CH3for Ala) leading
to the same intramolecular hydrogen bonding possibilities.
A bifurcated hydrogen bond forms between the carbonyl
oxygen atom and the amino hydrogen atoms in the global
minima Gly-I and Ala-I. Upon ∼180° rotation of the
-COOH plane, hydrogen bonding occurs with -OH as the
proton donor and -NH2as the acceptor, resulting in the Gly-
IIn and the Ala-II conformers. The suffix in the Gly-IIn
designation indicates a non-planar backbone, although ac-
curate FPA computations find a barrier to planarity of only
21 ( 5 cm-1.24The two Ala structures corresponding to
Gly-IIn exist as a nearly isoenergetic pair, Ala-IIA and Ala-
IIB, having the same H-bonding arrangement but different
orientations of the methyl group (Figure 1). Ala-I has
repeatedly been observed as the predominant conformer in
the rotational spectra of alanine,5,9,10in accord with high-
level theoretical results. In fact, large basis CCSD, CCSD(T),
and MP4 single-point energy computations at MP2/
6-311++G** optimum geometries determine Ala-I to be
more stable than the Ala-II conformers by 200-300 cm-1.7
The same levels of theory predict that the next conformers
(Ala-III) are, again, 200-300 cm-1higher in energy than
the Ala-II conformers. While the Ala-I and Ala-IIA
conformers were identified5,9in the observed rotational
spectra by14N nuclear quadrupole coupling, Ala-IIB and
higher-energy conformers were never observed.
Prior speculation on the absence of Ala-IIB in the
observed rotational spectra was based on a presumably low
Be- B0)1
2∑
i
Ri
B) -Be
2[
3
4∑
i?
(ai
ωiI?
b?)2
-
∑
i<j
(?ij
ωiωj(ωi+ ωj)+ π(
b)2(ωi- ωj)2
c
h)
1/2∑
ij
φiijaj
bbωj
-3/2](2)
ZPVE )1
2∑
i
ωi+1
4∑
iej
?ij
(3)
Lowest-Lying Conformers of Alanine
J. Chem. Theory Comput., Vol. 6, No. 10, 2010 3069

Page 5

interconversion barrier for Ala-IIB f Ala-IIA. To elucidate
this issue, we computed CCSD(T) energy points with the
aug-cc-pVTZ basis set at the MP2/6-311++G(d,p) stationary
structures of Ala-IIA, Ala-IIB, and the connecting transition
state optimized in this work. The resulting well depth of Ala-
IIB with respect to the interconversion barrier is only 34
cm-1, which is reduced to a minuscule 16 cm-1upon
vibrational correction. To obtain this vibrationally adiabatic
barrier, MP2/cc-pVTZ harmonic frequencies were computed,
and ZPVEs were evaluated by excluding at each stationary
point the contribution from the normal mode connecting Ala-
IIA to Ala-IIB. In summary, the small amount of energy
required to interconvert the Ala-II conformers is indeed
representative of the conformational flexibility of Ala and
may rationalize the absence of Ala-IIB in the molecular
beam experiments.20,75,76
III.B. Refitting the Rotational Spectra of Ala. Before
determining reSEstructures, we refit the existing rotational
spectra of alanine to more firmly establish the rotational
constants and their uncertainties for the structural analysis.
In the original spectroscopic study,5the rotational, centrifugal
distortion, and nuclear quadrupole hyperfine constants of
alanine were simultaneously determined from a global fit of
a chosen Hamiltonian to the measured transitions. From a
statistical point of view, this method is meritorious and has
the advantage of being simple. However, overly optimistic
uncertainties are produced when the data set for the global
fit is small, as is the case here. Moreover, from a numerical
perspective, correlations are induced between the centrifugal
distortion constants and the remaining rotational parameters,
worsening the condition number.77Finally, “masked” errors
that do not yield outlying residuals become more prevalent.78
For these reasons, we first corrected the transitions for the
nuclear quadrupole hyperfine structure and then fit the
hypothetical unperturbed rotational transitions to a standard
Watson Hamiltonian.79It could be argued that this approach
might give biased rotational parameters containing systematic
errors due to inaccuracies in the nuclear quadrupole hyperfine
constants. However, when several hyperfine components of
the same rotational transition are measured, as for a great
majority of the reported transitions,5the hypothetical,
unperturbed frequencies may be calculated using the intensity-
weighted mean of the multiplets.80As a consequence,
accurate knowledge of the nuclear quadrupole hyperfine
constants is unnecessary and the possible contribution of the
spin-rotation interaction is canceled. Furthermore, our ap-
proach permits the elimination of outliers, the estimation of
the uncertainty of the measurements, and an increase in the
reliability of the rotational frequencies.
Another issue in the original fits5is that the full set of
quartic centrifugal distortion constants was not determinable
for many isotopologues, and hence these constants were fixed
to values for the parent (or15N) species. Our computations
revealed significant variations in the centrifugal distortion
constants from one isotopologue to another (vide infra).
Therefore, we used the method of predicate observations81
in our refitting, in which the ab initio “scaled” centrifugal
distortion constants (or the constants of another isotopologue)
are input data in a weighted least-squares fit. Though this
method permits the approximate determination of the cen-
trifugal distortion constants, it must be used with care, and
it is essential to check that the derived constants are really
compatible with the experimental data. In our fits the weights
of the predicate observations were varied to keep the
corresponding “jackknifed” residuals, t(i), small (typically
less than 3), where t(i) is the ith residual divided by its
standard deviation calculated by omitting the ith transition.78
Parent values and isotopic shifts for the effective rotational
constants and quartic centrifugal distortion constants of the
Ala-I and Ala-IIA isotopologues are reported in Tables 1
and 2, respectively. Three sets of data are tabulated: our
results from refitting the observed lines (refit), our CCSD(T)/
cc-pVTZ theoretical values (theor), and the original experi-
mental constants (expt).5Rotational constant shifts associated
with heavy-atom (non-hydrogen) isotopic substitution exhibit
modest differences (2-5 kHz) between original and refit
values and are relatively independent of the method used to
fit the rotational spectra. However, much larger deviations
are found between the original and refit values for many of
the D-substituted isotopologues. The largest discrepancies
(in kHz) are 868 for B0 of O-D (Ala-I), 476 for A0 of
Cm-3D (Ala-IIA), 84 for A0of N-Da(Ala-I), 47 for A0of
N-Da (Ala-IIA), and 46 for B0 of Cm-3D (Ala-IIA).
Comparing these discrepancies to the average residual of the
structural fits for Ala and Gly, around 20 kHz (ref 24 and
below), it becomes clear that these rotational constants should
not be given much weight in the determination of reSE
structures.
The theoretical isotopic shifts (Tables 1 and 2) are based
on (A0, B0, C0) constants, which are determined by conjoining
our MP2/6-31G(d) vibration-rotation interaction constants
and CCSD(T)/cc-pVTZ equilibrium rotational constants
(BeBO). The theoretical and experimental heavy-atom isotopic
shifts of the (A0, B0, C0) constants are generally in remarkable
agreement. The mean absolute deviations between refit and
theor isotopic shifts among the (13C,
isotopologues are 0.2 and 0.4 MHz in the Ala-I and Ala-
IIA cases, respectively. On the other hand, most isotopic-
shift disparities for the deuterated isotopologues are greater
than 1 MHz. The proximity of the Dbposition to the methyl
group seems to enhance the error in the vibrationally
corrected rotational constants of the N-Db isotopologue,
especially in comparison to N-Da. The two largest absolute
discrepancies are (8.7, 3.5) MHz for [A0(Ala-IIA), B0(Ala-
I)] of the triply deuterated methyl isotopologues, Cm-3D.
Nevertheless, on a percentage basis, the discord between the
refit and theor isotopic shifts is less than 2% even in these
instances. For the centrifugal distortion constants, the refit
and theor isotopic shifts agree quite well for Ala-I, similarly
to other molecules.82,83However, considerable differences
occur for the ∆JK, ∆K, and δK isotopic shifts of Ala-IIA.
The underlying cause is not transparent and is not specific
to the deuterated isotopologues.
Relevant to the structure refinements, the number of fitted
transitions for the15N isotopologues of Ala-I and Ala-IIA
is relatively small. This is particularly true in the Ala-IIA
case, where 17 lines were used to determine 8 parameters
(3 rotational and 5 quartic centrifugal distortion constants).
13CR,
13Cm,
15N)
3070
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Jaeger et al.

Page 6

Accordingly, the standard deviation of the15N(Ala-IIA) fit
is only 0.2 kHz, less than 10% of the estimated experimental
accuracy (3 kHz). For this reason, the standard deviations
of the15N parameters are perhaps one order of magnitude
too small.
Highly anharmonic vibrational motions, such as the
internal rotation of the methyl group, twisting along the
backbone, or fluid rocking motion of the amino group,
complicate the determination of vibrational corrections to
the effective experimental rotational constants. Fortunately,
for isotopologues that exhibit similar vibrational effects as
the parent, the error in the vibrational corrections is
systematic and the least-squares refinement can still produce
equilibrium structures with small standard errors. The
statistical outliers (among the rotational constants) stem from
isotopologues for which the substituted atom undergoes
large-amplitude, anharmonic motion or yields large isotopic
shifts. As such, isotopic substitutions at peripheral hydrogen
Table 1. Isotopic Shifts of Effective Rotational Constants (A0, B0, C0) and A-Reduced Quartic Centrifugal Distortion
Constants (∆J, ∆JK, ∆K, δJ, δK) for Ala-I: Original Experimental Constants from Ref 5 (expt), Current Refitting of Observed
Lines (refit), and CCSD(T)/cc-pVTZ Theoretical Values (theor)a
constant
A0expt
refit
theor
B0expt
refit
theor
C0expt
refit
theor
∆Jexpt
refit
theor
∆JKexpt
refit
theor
∆Kexpt
refit
theor
δJexpt
refit
theor
δKexpt
refit
theor
parent
13C
13CR
-8.821
-8.821
-8.995
-12.419
-12.421
-12.209
-5.343
-5.342
-5.370
-0.029
-0.086
-0.040
0
0.45
0.127
0
-0.09
-0.114
-0.0216
-0.028
-0.014
0.2823
-0.31
-0.058
13Cm
15N
CR-D
-113.253
-113.250
-112.952
-51.813
-51.818
-50.240
-5.462
-5.458
-6.150
-0.026
-0.138
-0.195
0
0.74
0.590
0
-0.69
-0.568
0
-0.061
-0.070
0.5423
-0.71
-0.775
Cm-3D
-462.026
-462.025
-459.265
-175.397
-175.404
-171.944
-141.514
-141.510
-141.609
0
-0.312
-0.325
0
1.61
1.613
0
-1.55
-1.570
0
-0.094
-0.095
0
-1.80
-1.734
O-D
-13.968
-13.965
-12.775
-109.991
-110.859
-109.247
-61.745
-61.749
-61.727
0
-0.262
-0.245
0
0.69
0.634
0
-0.28
-0.324
0
-0.066
-0.053
0
-0.11
-0.303
N-Da
-104.850
-104.934
-104.774
-57.095
-57.103
-54.348
-41.615
-41.608
-40.245
0
-0.281
-0.262
0
0.77
0.694
0
-0.36
-0.413
0
-0.084
-0.077
0
-1.36
-1.442
N-Db
-176.847
-176.846
-175.431
-49.805
-49.804
-48.269
-45.195
-45.197
-44.884
0
0.007
0.108
0
-0.74
-0.741
0
0.53
0.478
0
0.058
0.064
0
0.22
-0.042
MAD
5066.1456(4)
5066.1455(7)
5031.4685
3100.9506(3)
3100.9507(5)
3067.4442
2264.0134(2)
2264.0131(4)
2258.8416
2.452
2.445(7)
2.409
-6.391
-6.38(1)
-6.373
5.410
5.37(5)
5.424
0.5696
0.574(2)
0.570
10.3777
10.37(3)
9.656
-0.941
-0.941
-0.939
-9.668
-9.667
-9.505
-5.178
-5.178
-5.199
-0.035
-0.024
-0.027
0.052
0.03
0.104
0.022
0.07
-0.077
0.0013
0.008
-0.009
0.0083
0.07
-0.025
-95.254
-95.254
-94.714
-33.767
-33.767
-33.324
-31.628
-31.628
-31.518
-0.069
-0.072
-0.042
0.324
0.29
0.292
-0.21
-0.18
-0.298
-0.0109
-0.010
-0.011
-0.4577
-0.36
-0.297
-48.851
-48.851
-48.400
-50.457
-50.458
-50.093
-34.806
-34.806
-34.921
-0.121
-0.113
-0.100
0.112
0.11
0.126
0.124
0.15
-0.032
-0.0294
-0.033
-0.023
-0.3647
-0.34
-0.273
0.777
1.347
0.307
0.033
0.08
0.08
0.009
0.13
aUnits: MHz for (A0, B0, C0) and kHz for (∆J, ∆JK, ∆K, δJ, δK); MAD ) mean absolute deviation between refit and theor isotopic shifts.
Large deviations of theoretical and experimental rotational constants are italicized. The CCSD(T)/cc-pVTZ rotational constants include MP2/
6-31G(d) vibrational corrections.
Table 2. Isotopic Shifts of Effective Rotational Constants (A0, B0, C0) and A-Reduced Quartic Centrifugal Distortion
Constants (∆J, ∆JK, ∆K, δJ, δK) for Ala-IIA: Original Experimental Constants from Ref 5 (expt), Current Refitting of Observed
Lines (refit), and CCSD(T)/cc-pVTZ Theoretical Values (theor)a
constant
A0expt
refit
theor
B0expt
refit
theor
C0expt
refit
theor
∆Jexpt
refit
theor
∆JKexpt
refit
theor
∆Kexpt
refit
theor
δJexpt
refit
theor
δKexpt
refit
theor
parent
13C
-0.138
-0.136
-0.177
-12.458
-12.456
-12.216
-6.190
-6.191
-6.326
0.038
0.10
-0.016
-0.175
-0.37
0.047
0
0.67
-0.032
-0.010
-0.01
-0.004
0
0.59
-0.008
13CR
-10.402
-10.399
-11.079
-13.622
-13.622
-13.218
-5.382
-5.382
-5.539
-0.036
-0.02
-0.022
0.207
0.13
0.055
0
0.44
-0.069
-0.025
-0.03
-0.006
0
0.11
-0.026
13Cm
15N
CR-D
-115.510
-115.537
-117.566
-54.464
-54.462
-51.598
-8.888
-8.890
-10.313
-0.055
-0.06
-0.107
-0.358
-0.18
0.232
-0.002
0.42
-0.328
-0.009
-0.01
-0.033
0
0.97
-0.388
Cm-3D
-441.476
-441.952
-433.218
-198.172
-198.218
-195.056
-148.755
-148.704
-148.500
-0.004
-0.06
-0.152
-0.358
-0.18
0.459
-0.002
0.42
-0.574
-0.009
-0.01
-0.025
0
0.97
-0.940
O-D
-138.202
-138.198
-134.674
-8.122
-8.124
-7.333
-27.187
-27.182
-26.600
-0.004
-0.01
0.016
-0.358
-0.27
-0.100
-0.002
0.44
0.009
-0.009
-0.01
0.007
0
-1.79
-0.320
N-Da
-35.075
-35.028
-31.794
-114.542
-114.543
-113.036
-61.942
-61.935
-65.042
-0.004
0.16
-0.149
-0.358
-0.17
0.306
-0.002
0.43
-0.124
-0.009
-0.01
-0.023
0
-1.68
-0.099
N-Db
-164.893
-164.887
-168.219
-77.573
-77.576
-70.879
-44.052
-44.047
-45.800
-0.004
-0.01
-0.086
-0.358
-0.25
0.279
-0.002
0.43
-0.390
-0.009
-0.01
-0.047
0
-1.78
-0.317
MAD
4973.0558(6)
4973.0546(35)
4950.175
3228.3379(5)
3228.3375(56)
3183.801
2307.8090(3)
2307.8090(42)
2316.254
2.13(1)
2.11(6)
1.397
-4.84(6)
-4.8(3)
-2.611
4.98(2)
4.6(5)
2.772
0.41(1)
0.41(2)
0.257
7.35(1)
7.2(7)
4.686
-88.351
-88.356
-88.826
-39.366
-39.366
-38.315
-33.334
-33.333
-33.356
0.036
0.09
-0.016
0.199
-0.03
0.067
0
-0.63
-0.092
-0.015
-0.04
-0.0002
0
0.26
-0.172
-54.385
-54.384
-53.339
-42.997
-42.997
-42.527
-31.976
-31.977
-32.264
-0.004
0.01
-0.055
-0.358
-0.43
0.098
0
0.43
-0.058
-0.0087
-0.01
-0.012
0
0.15
-0.127
2.566
1.910
0.858
0.09
0.37
0.64
0.02
1.02
aUnits: MHz for (A0, B0, C0) and kHz for (∆J, ∆JK, ∆K, δJ, δK); MAD ) mean absolute deviation between refit and theor isotopic shifts.
Large deviations of theoretical and experimental rotational constants are italicized. The CCSD(T)/cc-pVTZ rotational constants include MP2/
6-31G(d) vibrational corrections.
Lowest-Lying Conformers of Alanine
J. Chem. Theory Comput., Vol. 6, No. 10, 2010 3071

Page 7

atoms may be difficult to fit and should be treated judiciously
to avoid vibrational contamination of reSEstructures.
III.C. reSEStructure of Ala-I. The semiexperimental
structures of Ala-I resulting from three different least-squares
refinements, labeled Fit 1 through Fit 3, are reported in Table
3, along with the associated frozen-core CCSD(T)/cc-pVTZ
reBOparameters/constraints. The values refined in each fit are
highlighted in boldface type with standard errors in paren-
theses, whereas all other parameters necessary to define the
molecular structure were constrained to the CCSD(T)/cc-
pVTZ values listed in normal type. In Fit 1 only the rotational
constants of the parent and isotopologues involving heavy-
atom substitution were used; accordingly, all hydrogen atoms
were fully positioned by the reBOconstraints. By omitting
the deuterated species, the errors in the BeSEdata arising from
large-amplitude vibrational effects are reduced and become
more systematic. In Fit 1, the weighted root-mean-square
(rms) residual of the 15 chosen rotational constants is only
16 kHz, and the standard errors of the fit for bond distances
and angles are no greater than 0.007 Å and 0.6°, respectively.
Clearly, the rotational constants of the parent, the15N, and
the three unique13C isotopologues provide enough informa-
tion to determine the positions of all heavy atoms in Ala-I.
Nonetheless, even in the highly constrained Fit 1 some of
the optimized parameters are strongly correlated, hindering
their explicit determination. The introduction of further
constraints, for example fixing either r(C-O) or r(CdO),
gave similar results. We note that the standard deviations of
the reSE(Fit 1) parameters are underestimations because the
uncertainty of the several fixed parameters is not taken into
account.
Fit 2 employed the same structural variables and con-
straints as Fit 1 but added selected rotational constants from
the deuterated isotopologues to the BeSEdata set. In particular,
Fit 2 included AeSE(CR-D), BeSE(Cm-3D), BeSE(O-D),
CeSE(O-D), AeSE(N-Db), and CeSE(N-Db), all of which had
a residual <0.5 MHz in Fit 1. Fit 2 reduces the standard error
of each structural parameter (Table 3) vis-a `-vis Fit 1, while
maintaining a reasonably small residual (24 kHz).
Fit 3 incorporated all of the observed rotational constants
except those for the Cm-3D and N-Db isotopologues; in
addition, BeSE(N-Da) was excluded and the weight of
Table 3. Equilibrium Structures of Ala-Ia
re
BO
semiexperimental re
parametersb
CCSD(T)/cc-pVTZ Fit 1Fit 2Fit 3
r(C-CR)
r(CR-Cm)
r(CR-N)
r(CdO)
r(C-O)
r(N-H)Avg
∠(C-CR-Cm)
∠(C-CR-N)
∠(CR-CdO)
∠(O-CdO)
∠(C-O-H)
∠(C-CR-H)
τ(O-C-CR-Cm)
τ(O-C-CR-H)
τ(O ) C-CR-N)
1.5236
1.5316
1.4570
1.2085
1.3551
1.0156
108.70
113.24
125.36
122.81
105.82
107.39
-73.65
43.98
-17.27
1.519(2)
1.524(4)
1.446(4)
1.208(6)
1.347(5)
1.0156
109.0(2)
113.4(3)
124.8(4)
122.7(1)
105.82
107.39
-71.9(3)
43.98
-16.2(5)
1.518(2)
1.526(3)
1.445(3)
1.208(5)
1.348(4)
1.0156
108.8(2)
113.5(3)
126.1(4)
124.9(3)
105.82
107.39
-71.8(3)
43.98
-16.1(4)
1.520(3)
1.522(4)
1.448(4)
1.207(7)
1.349(6)
1.014(4)
109.0(3)
113.3(4)
125.1(4)
122.7(2)
105.9(6)
106.5(5)
-71.9(4)
47.5(9)
-16.2(8)
CCSD(T)/cc-pVTZ re
BOconstraints
r(O-H)
r(CR-H)
r(N-H)Diff
r(Cm-H)Avg
r(Cm-H)Diff1
r(Cm-H)Diff2
∠(CR-N-H)Avg
∠(Ha-N-Hb)
∠(CR-Cm-H)Avg
0.9680
1.0925
0.0012
1.0911
0.0075
0.0007
108.66
104.72
110.08
∠(CR-Cm-H)Diff1
∠(CR-Cm-H)Diff2
τ(OdC-O-H)
τ(CR-C-O-H)
τ(C-CR-N-Ha)
τ(C-CR-N-Hb)
τ(H-CR-Cm-H1)
τ(H-CR-Cm-H2)
τ(H-CR-Cm-H3)
-0.54
2.02
-0.90
177.80
54.01
-59.37
180.86
-58.90
62.11
coordinate definitions
r(N-H)Avg) [r(N-Ha) + r(N-Hb)]/2
r(N-H)Diff) [r(N-Ha) - r(N-Hb)]
∠(CR-N-H)Avg) [∠(CR-N-Ha) + ∠(CR-N-Hb)]/2
r(Cm-H)Avg) [r(Cm-H1) + r(Cm-H2) + r(Cm-H3)]/3
r(Cm-H)Diff1) 2[r(Cm-H1)] - r(Cm-H2) - r(Cm-H3)
r(Cm-H)Diff2) r(Cm-H2) - r(Cm-H3)
∠(CR-Cm-H)Avg) [∠(CR-Cm-H1) + ∠(CR-Cm-H2) + ∠(CR-Cm-H3)]/3
∠(CR-Cm-H)Diff1) 2[∠(CR-Cm-H1)] - ∠(CR-Cm-H2) - ∠(CR-Cm-H3)
∠(CR-Cm-H)Diff2) ∠(CR-Cm-H2) - ∠(CR-Cm-H3)
aDistances in Å, angles in deg. Boldface denotes parameters included in the least-squares fits. Note that in Fits 1 and 2, all hydrogen
atoms were fully positioned by the constraints, whereas Fit 3 provided four internal coordinates involving hydrogen atoms.bRefer to Figure
1 for atom labels.
3072
J. Chem. Theory Comput., Vol. 6, No. 10, 2010
Jaeger et al.

Page 8

CeSE(N-Da) was decreased, making the N-Daisotopologue
less influential in the fit. Problems with nonsystematic errors
necessitating exclusion of rotational constant data for the
Cm-3D, N-Db, and N-Daisotopologues were identified in
section III.B above. The expanded data set for Fit 3 allowed
some hydrogen-atom coordinates to be refined, the tightest
fit to the data (weighted rms of 25 kHz) being obtained by
releasing r(N-H)Avg, ∠(C-CR-H), ∠(C-O-H), and
τ(O-C-CR-H). Additional parameters could not be refined
without introducing large deviations in both hydrogen- and
heavy-atom positions. In this regard the structures of the
methyl and carboxyl groups are under-determined by the
experimental data, due to the lack of isotopic substitution
on the oxygen atoms and on individual methyl hydrogen
atoms. In summary, Fit 3 provides the best currently possible
reSEstructure of Ala-I by refining 15 of the 33 geometric
degrees of freedom on 23 vibrationally corrected, semiex-
perimental equilibrium rotational constants.
III.D. reSEStructure of Ala-IIA. One satisfactory fit was
achieved for the semiexperimental structure of Ala-IIA.
Initially, incorporating only rotational constants of heavy-
atom isotopologues and structural parameters involving
heavy-atom positions, as in Fit 1 of Ala-I, resulted in an
reSEstructure that had surprisingly large standard errors and
poor agreement with the CCSD(T)/cc-pVTZ reBOparameters.
Most notably, the semiexperimental C-O distance had a
standard error of 0.02 Å and was 0.04 Å shorter than the
CCSD(T)/cc-pVTZ value, while the fit to the15N data was
poor. As mentioned above, the15N assignments and the fitted
data appear to be correct, but the originally reported and
refitted uncertainties are probably too optimistic. Therefore,
the structure of Ala-IIA was determined again after increas-
ing the experimental uncertainties (reciprocal weights in the
least-squares fit) of the three15N rotational constants by a
factor of 20. This modification, labeled Fit 1′, was validated
by an approximate one-half reduction in the standard errors
of the structural parameters. The C-O bond distance
displayed an error of (0.01 Å and became a much more
reasonable 0.01 Å shorter than the reBOvalue. The final
structural parameters of Ala-IIA refined in Fit 1′ are reported
in boldface in Table 4, along with the CCSD(T)/cc-pVTZ
constraints invoked. While the success of the Ala-IIA fit is
gratifying, the statistical errors are significantly larger than
observed for Fit 1 of Ala-I.
Attempts to incorporate rotational constants of the deu-
terated isotopologues in the structural refinement of Ala-
IIA did not reduce the statistical errors. Including the only
two rotational constants that had residuals under 0.5 MHz
in Fit 1′ did not improve the heavy-atom structural param-
eters, unlike Fit 2 of Ala-I. Fitting the data for the CR-3D
and N-Da isotopologues once again proved problematic.
Adding the O-D rotational constants and releasing the
∠(C-O-H) parameter distorted the Ala-IIA structure
considerably, causing the carbonyl bond distance to deviate
from the reBOvalue by an unacceptable 0.1 Å. Other
parameters for the hydroxyl hydrogen atom were released
with similar or more pronounced distortion of the overall
structure. Therefore, the BeSEdata for the O-D isotopologue
are disappointingly unable to yield the structure within the
strong OH· · ·N hydrogen bond. In summary, only the
experimental rotational constants of the heavy-atom isoto-
pologues yield useful information, and thus the reSEstructure
of Ala-IIA is considerably less well determined than that of
Ala-I.
III.E. Discussion of the Ala Structures. A comparison
of prior experimental rg, rR, rz, r0, and rs parameters with
the current reSEand reBOresults is made in Tables 5 and 6 for
Ala-I and Ala-IIA, respectively. Considerable vibrational
effects are present in all previous experimental structures,
and several structural parameters exhibit disturbing differ-
ences. The disparities are more prominent for the bond
distances than for the bond angles. Our equilibrium reSEand
reBOresults allow unphysical or misleading values to be
identified among the vibrationally averaged parameters. The
most important defects are rg(CR-Cm) ) 1.509(16) Å and
rs(CR-Cm) ) 1.57(1) Å compared to reSE(CR-Cm) ) 1.522(4)
Å for Ala-I; r0(C-O) ) 1.37(2) Å compared to reSE(C-O)
) 1.33(1) Å for Ala-IIA; and rs(CR-N) ) 1.430(9) Å
compared to reSE(CR-N) ) 1.460(4) Å for Ala-IIA. Exces-
sive deviations from the reSEand reBOvalues and underesti-
mated experimental uncertainties are exhibited in several
cases, such as rs(CR-Cm) of Ala-IIA, while anomalous
vibrationally averaged distances smaller than the correspond-
ing equilibrium bond length occur in other instances such
as rz(C-O) of Ala-I.
Several systematic studies84-87have established the
expected accuracy of CCSD(T)/cc-pVTZ geometric param-
eters, allowing a reliable assessment of our reBOand reSE
structures of alanine. For 19 small (H, C, N, O, F) molecules,
all-electron CCSD(T)/cc-pVTZ equilibrium bond distances
have a mean error (std. dev.) of +0.0002 (0.0023) Å, whereas
Table 4. Equilibrium Structures of Ala-IIAa
parametersb
CCSD(T)/cc-pVTZsemiexperimental re(Fit 1′)
1.530(3)
1.529(4)
1.460(4)
1.205(9)
1.33(1)
108.2(3)
109.8(4)
122.0(8)
123.2(4)
254.5(4)
192.5(5)
r(C-CR)
r(CR-Cm)
r(CR-N)
r(CdO)
r(C-O)
∠(C-CR-Cm)
∠(C-CR-N)
∠(CR-CdO)
∠(O-CdO)
τ(O-C-CR-Cm)
τ(OdC-CR-N)
1.5347
1.5282
1.4726
1.2052
1.3431
108.08
109.44
122.66
123.27
257.77
195.28
CCSD(T)/cc-pVTZ re
BOconstraints
r(O-H)
r(CR-H)
r(N-H)Avg
r(N-H)Diff
r(Cm-H)Avg
r(Cm-H)Diff1
r(Cm-H)Diff2
∠(C-O-H)
∠(C-CR-H)
∠(Ha-N-Hb)
∠(C-N-H)Avg
0.9789
1.0926
1.0132
0.0009
1.0915
-0.0067
0.0005
104.26
106.67
106.90
110.61
∠(CR-Cm-H)Avg
∠(CR-Cm-H)Diff1
∠(CR-Cm-H)Diff2
τ(O-C-CR-H)
τ(OdC-O-H)
τ(CR-C-O-H)
τ(C-CR-N-Ha)
τ(C-CR-N-Hb)
τ(H-CR-Cm-H1)
τ(H-CR-Cm-H2)
τ(H-CR-Cm-H3)
110.18
-0.60
-0.33
140.31
178.18
-4.10
89.86
208.10
60.01
179.80
-60.14
aDistances in Å, angles in deg. Boldface denotes parameters
included in the least-squares fits. Note that in Fit 1′ all hydrogen
atoms were fully positioned by the constraints.bRefer to Figure 1
for atom labels and Table 3 for coordinate definitions.
Lowest-Lying Conformers of Alanine
J. Chem. Theory Comput., Vol. 6, No. 10, 2010 3073

Page 9

bond angles have a mean absolute error (MAE) of about
0.5°.85A very favorable cancellation of basis set incomplete-
ness and electron correlation errors is responsible for such
high accuracy. Statistics are not available for dihedral angles,
but a larger MAE of perhaps 1-2° is probable. Because 1s
electron correlation contracts bond lengths in first-row
diatomics by 0.0005-0.0025 Å,55,88frozen-core CCSD(T)/
cc-pVTZ reBOdistances are expected to be too large by at
least 0.001-0.003 Å. Therefore, the general reBO> reSEtrend
for bond distances in Tables 3 and 4 is nicely explained.
An investigation of 18 small, rigid molecules89 showed
that the MAE in the relative magnitude of the sum of
theoretical Ri constants, ΣiRiB/B0, was only 0.225% at the
MP2/cc-pVDZ level of theory with respect to CCSD(T)/cc-
pVQZ benchmarks. The resulting MAE for reSEdistances was
a mere 0.0005 Å. Because our MP2/6-31G(d) Riconstants
were computed with a basis set comparable to cc-pVDZ,
electronic structure errors in the Be- B0VPT2 vibrational
corrections are not expected to have an appreciable effect
on our reSEresults for Ala. An important caveat to this
conclusion is that the test molecules of ref 89 did not have
the troublesome, large-amplitude vibrational modes present
in the alanine conformers. Nonetheless, the largest sources
of error in the reSEparameters are the modeling of vibrational
effects via VPT2 theory, the phenomenological nature of the
underlying empirical rotational constants, and the gaps in
the isotopologic data. Taking into account all sources of error
in both the theoretical and semiexperimental methods, the
agreement in Tables 3 and 4 between the reBOand reSE
structures of Ala-I and Ala-IIA is quite satisfactory. The
dihedral angle τ(OdC-CR-N) in Ala-I is a notable point
of accord.
The conformational change from Ala-I to Ala-IIA yields
considerable shifts in a few bond distances and angles.
Particularly prominent is the shift of the semiexperimental
∠(C-CR-N) angle from 113.3(4)° in Ala-I to 109.8(4)° in
Ala-IIA, consistent with the trans-angle rule90of hypercon-
jugative and steric effects. In the rsstructures,5there is also
a large Ala-I-Ala-IIA difference in this angle, but the shift
is overestimated, and ∠(C-CR-N) is much too large for
both conformers. The carbonyl oxygen is involved in a
bifurcated hydrogen bond in Ala-I but is uncomplexed in
Ala-IIA. In both the reSEand reBOstructures, the hydrogen
bond formation is accompanied by an expected lengthening
of r(CdO) by 0.002-0.003 Å. While the r0 structures5
exhibit CdO bond elongation, the magnitude of the effect
is 0.04(3) Å, a severe overestimation.
A key measure of the intramolecular hydrogen bonding
in the Ala conformers is the associated heavy-atom distance
R(N· · ·O). In the Ala-I [reSE, reBO] structures, R(N· · ·O) )
[2.825(12), 2.841] Å, while the corresponding values for Ala-
IIA are R(N· · ·O) ) [2.605(18), 2.607] Å. Values for
R(N· · ·O) hydrogen-bond distances computed at several
levels of electronic structure theory are presented in Table
S3 of the Supporting Information. The variations among the
results demonstrate that our CCSD(T)/cc-pVTZ reBOvalues
for R(N· · ·O) should be accurate to (0.01 Å or better. Ala-
IIA exhibits a larger, 0.034 Å discrepancy between the reSE
and reBOH-bond lengths because of the aforementioned
difficulty in determining the nitrogen-atom position. Like-
wise, both τ(OdC-CR-N) and r(CR-N) of Ala-IIA sig-
nificantly stray from the respective reBOvalues. The much
shorter R(N· · ·O) distance in Ala-IIA correctly reflects the
greater strength of the OH· · ·N hydrogen bond in this
conformer compared to the NH· · ·O bifurcated hydrogen
bonds in Ala-I. Despite these relative hydrogen bond
strengths, Ala-I is lower in energy than Ala-IIA, as
definitively shown in section III.G below. The compensating
energetic factor is the ∼5 kcal mol-1more favorable (cis)
arrangement of the carboxyl group in Ala-I.
III.F. Comparison of Ala and Gly Structures. A profit-
able comparison of the structures of the two simplest amino
acids is afforded by our determination of the first reSE
parameters for Ala-I and Ala-IIA combined with analogous
reSEresults for Gly-Ip and Gly-IIn from our earlier work.24
The Ala-I-GlyIp differences in the heavy-atom bond
distances are ∆r(C-CR) ) +0.009, ∆r(CR-N) ) +0.007,
∆r(CdO) ) 0.000, and ∆r(C-O) ) -0.004 Å, while the
corresponding Ala-IIA-GlyIIn differences are ∆r(C-CR)
) +0.006, ∆r(CR-N) ) -0.002, ∆r(CdO) ) +0.003, and
Table 5. Selected Ala-I Structural Parameters (Å and deg) from Different Methodologies
rg/rR
ref 11a
rz
ref 12
r0
ref 5
rs
ref 5
re
Fit 3
SE
re
BO
CCSD(T)/cc-VTZ
r(C-CR)
r(CR-Cm)
r(CR-N)
r(CdO)
r(C-O)
∠(C-CR-Cm)
∠(C-CR-N)
∠(CR-CdO)
∠(CR-C-O)
τ(OdC-CR-N)
1.544(10)
1.509(16)
1.471(7)
1.192(2)
1.347(3)
111.6(11)
110.1(8)
125.6(7)
110.3(7)
-17.2(18)
1.527(11)
1.536(11)
1.453(2)
1.197(1)
1.341(2)
111.9(2)
112.9(3)
125.7(3)
110.3(2)
-16.6(4)
1.51(1)
1.53(2)
1.45(1)
1.24(2)
1.33(2)
108.3(6)
115(1)
125(2)
113(2)
1.48(1)
1.57(1)
1.438(9)
1.520(3)
1.522(4)
1.448(4)
1.207(7)
1.349(6)
109.0(3)
113.3(4)
125.1(4)
1.5236
1.5316
1.4570
1.2085
1.3551
108.70
113.24
125.36
111.82
-17.27
109(1)
117(1)
-16.2(8)
argfor distances, rRfor angles.
Table 6. Selected Ala-IIA Structural Parameters (Å and
deg) from Different Methodologies
r0
ref 5
1.524(7)
1.543(8)
1.458(9)
1.20(2)
1.37(2)
107.1(3)
111.7(7)
125(1)
113(2)
167(1)
rs
ref 5
1.517(7)
1.571(9)
1.430(9)
re
SE
Fit 1′
1.530(3)
1.529(4)
1.460(4)
1.205(9)
1.33(1)
108.2(3)
109.8(4)
122.0(8)
re
BO
CCSD(T)/cc-VTZ
1.5347
1.5282
1.4726
1.2052
1.3431
108.08
109.44
122.66
114.02
195.28
r(C-CR)
r(CR-Cm)
r(CR-N)
r(CdO)
r(C-O)
∠(C-CR-Cm)
∠(C-CR-N)
∠(CR-CdO)
∠(CR-C-O)
τ(OdC-CR-N)
107.6(8)
111.8(7)
192.5(5)
3074
J. Chem. Theory Comput., Vol. 6, No. 10, 2010
Jaeger et al.

Page 10

∆r(C-O) ) -0.003 Å. Among these small changes, only
the ∆r(C-CR) shifts are clearly significant compared to the
uncertainty of the reSEparameters. Likewise, the only
significant change among the bond angles of the Gly and
Ala heavy-atom frameworks occurs for ∠(C-CR-N), whose
Ala-I-GlyIp and Ala-IIA-GlyIIn shifts are -2.1° and
-1.6°, respectively. Therefore, the main differences between
the bond distances and angles in Gly and Ala are highly
localized at the site of the methyl substitution.
The torsion angle τ(OdC-CR-N) characterizes the devia-
tion of the amino acid backbone from planarity. In Gly-Ip
this angle is zero because the molecule has a symmetrical
bifurcated hydrogen bond and adopts Cspoint-group sym-
metry. Substitution of the methyl group in Ala breaks this
symmetry significantly and leads to a torsion angle of
16.2(8)° in Ala-I. In contrast, the backbones of Gly-IIn and
Ala-IIA exhibit τ(OdC-CR-N) angles of 11(2)° and
12.5(5)°, respectively, which are essentially equivalent within
the given uncertainties.
III.G. Relative Energy of Ala Conformers. The focal-
point analysis of the energy of Ala-IIA relative to Ala-I
(∆Ee) is presented in Table 7. Showing rapid convergence
to the CBS limit, the RHF relative energy and the MP2
correlation increment are converged to better than 0.1 kJ
mol-1using the aug-cc-pVTZ basis set. Basis sets with
diffuse functions were employed specifically to treat the
hydrogen bonding interactions.
The electron correlation sequence for ∆Eeshows less rapid
convergence than the atomic-orbital basis set series. As seen
in earlier studies,1,7,14Hartree-Fock theory proves unreliable
for conformational energetics of amino acids, placing Ala-
IIA above Ala-I by a substantial 10.56 kJ mol-1. The MP2
correlation energy largely rectifies this overestimation, but
in the CBS limit, MP2 erroneously predicts that Ala-IIA is
0.65 kJ mol-1lower in energy than Ala-I. With more
sophisticated treatments of electron correlation, Ala-I is
restored as the lowest energy conformer. The final frozen-
core result is ∆Ee[CCSD(T)/CBS] ) +0.58 kJ mol-1, and
appending the effect of core electron correlation (∆core), we
obtain ∆Ee ) +0.45 kJ mol-1. The incorporation of
connected quadruple excitations in coupled-cluster wave
functions is not currently feasible for alanine, but several
benchmark studies48,91-97have shown that δ[CCSDT(Q)]
relative-energy increments are typically about an order of
magnitude smaller than δ[CCSD(T)] values. Therefore,
considering all sources of error, our final equilibrium energy
difference is ∆Ee ) +0.5(3) kJ mol-1, in which the
uncertainty estimate represents a 95% confidence interval.
Zero-point vibrational energy (ZPVE) increases the Ala-
IIA-Ala-I energy separation by 1.66 kJ mol-1, yielding ∆E0
) +2.1(3) kJ mol-1. Thus, ZPVE effects constitute almost
80% of the energy difference at 0 K. The low-frequency
vibrational modes that were problematic in the reSEanalysis
do not appear to add significant uncertainty to the ∆E0
determination, as less than 1% of the ZPVE effect arises
from anharmonic corrections.
IV. Summary
This investigation is the first to conjoin theory and experi-
ment to not only determine reliable semiexperimental re
structures (reSE) for conformers of a molecule as large and
flexible as alanine (Ala) but also to analyze in detail the
factors contributing to the accuracy of such parameters. It is
shown convincingly that an accurate reSEstructure for a
flexible molecule can indeed be determined if procedures
developed for (semi)rigid systems are carefully employed.
For alanine, we find that the outcome of the reSEleast-squares
refinement depends critically on the accuracy of the equi-
librium rotational constants, as expected, as well as the
attendant uncertainties, which is less expected. Therefore,
our study commenced by refitting all the spectroscopic
constants of Ala-I and Ala-IIA to the experimentally
measured rotational transitions to ensure a dependable
reference data set. A predicate observations scheme using
ab initio quartic centrifugal distortion information appears
to work well even for such a flexible molecule. In refining
reSEstructures for Ala, we discovered that not all effective
rotational constants can be utilized, even if their apparent
uncertainty is small. The problem results mostly from the
effective nature of the empirical rotational constants and, to
a lesser extent, from limitations of the theoretical vibration-
rotation interaction treatment. It is essential to constrain the
reSEfit using accurate Born-Oppenheimer equilibrium (reBO)
parameters, obtained here at the frozen-core CCSD(T)/cc-
pVTZ level of electronic structure theory. A proper choice
of the fitted and constrained parameters is paramount to
obtaining good reSEresults. In general, the heavy-atom
positions are well determined by the fits, whereas the
hydrogen atoms must be constrained. Avoiding overfitting
requires particular attention to statistical details.
The reSEparameters determined in this study demonstrate
that vibrational effects must be removed to get meaningful
Table 7. Focal Point Analysis of the Ala-IIA-Ala-I Energy Difference (kJ mol-1)a
∆Ee(RHF)
δ[MP2]
-10.73
-11.26
-11.28
-11.25
[-11.21]
δ[CCSD]
+2.63
+2.86
+2.97
[+2.97]
[+2.97]
additive
δ[CCSD(T)]
-1.57
-1.74
[-1.74]
[-1.74]
[-1.74]
additive
∆Ee[CCSD(T)]
+1.14
+0.35
+0.46
+0.52
[+0.58]
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
aug-cc-pV5Z
CBS
extrapolation
10.81
10.50
10.51
10.54
[10.56]
a + be-cX(X ) 3, 4, 5)
a + bX-3(X ) 4, 5)
∆E0(final) ) ∆Ee[CCSD(T)/CBS] + ∆core[CCSD(T)/cc-pCVTZ] + ∆ZPVE[MP2/aug-cc-pVTZ (pared)] ) +0.58 - 0.13 + 1.66 ) 2.11 kJ mol-1
aThe symbol δ denotes the increment in the relative energy (∆Ee) with respect to the preceding level of theory in the hierarchy RHF f
MP2 f CCSD f CCSD(T). Square brackets signify results obtained from basis set extrapolations or additivity assumptions. Final
predictions are boldfaced.
Lowest-Lying Conformers of Alanine
J. Chem. Theory Comput., Vol. 6, No. 10, 2010 3075

Page 11

structures for large and flexible systems from rotational
constants. Specifically, previous vibrationally averaged rg/
ra, rz, r0, and rsstructures for Ala are shown to be defective,
exhibiting errors as large as 0.04 Å for bond distances, 3°
for bond angles, and 25° for torsion angles. Therefore, small
and intrinsic conformation-induced changes are reliably
discerned only when precise restructures are known, because
vibrational effects can mask the true variations. Our reSE
results are significant in this regard because they provide
the first sound comparison of empirically based structures
for the two simplest amino acids, Gly and Ala.
Through convergent focal-point analysis (FPA) ab initio
computations, the energy difference between the lowest
conformers of alanine has been pinpointed for the first time,
proving that Ala-I and Ala-IIA are almost isoenergetic. The
Ala-IIA equilibrium structure is higher in energy than that
of Ala-I by a mere 0.5(3) kJ mol-1, and with inclusion of
zero-point vibrational energy (ZPVE), this relative energy
is still only 2.1(3) kJ mol-1. Our high-level computations
also reveal that the unobserved Ala-IIB conformer has a
tenuous existence as a distinct species, being separated from
Ala-IIA by a vibrationally adiabatic isomerization barrier
less than 0.2 kJ mol-1.
Much attention has been afforded glycine and alanine as
essential origin-of-life molecules, and as such, their existence
in interstellar space has been actively researched. Until now,
only a few molecules of possible biochemical interest have
been detected with certainty in interstellar environments:
glycolaldehyde, a small “sugar”;98acetamide, a molecule
with a peptide bond;99and aminoacetonitrile, a precursor of
glycine.100Glycine has been detected only tentatively.101,102
The difficulties of detecting glycine may be explained partly
by the small dipole-moment components of its most stable
conformer (Gly-Ip), for example, µa) 0.91 D.103In contrast,
for Ala-I the µbdipole component has been measured to be
1.6 D.9The present study confirms unequivocally that Ala-I
is the most stable form of R-alanine and supports the
somewhat imprecise dipole moment measurements of
Godfrey et al.9Because b-type transitions have larger line
strengths than a-type transitions, the µbcomponent of Ala-I
might be large enough to permit the interstellar detection of
R-alanine, provided it is sufficiently abundant in the source.
The interplay of theory and experiment could prove very
productive toward this goal.
Acknowledgment. Dr. Steven Wheeler is thanked for
helpful discussions. The research in Athens at the University
of Georgia was supported by the U.S. National Science
Foundation, Grant CHE-0749868. The work performed in
Hungary and the Athens/Budapest collaboration received
support from the Hungarian Scientific Research Fund, OTKA
K72885 and IN77954, respectively. The joint work between
Lille and Budapest was partially supported by EGIDE. The
high-accuracy ab initio computations used resources of the
National Energy Research Scientific Computing Center
(NERSC), which is supported by the Office of Science of
the U.S. Department of Energy under Contract No. DE-
AC02-05CH11231.
Supporting Information Available: Cartesian coor-
dinates of CCSD(T)/cc-pVTZ equilbrium structures; refit (A0,
B0, C0) and semiexperimental (Ae, Be, Ce) rotational constants
for Ala-I and Ala-IIA isotopologues; hydrogen-bond dis-
tances R(N· · ·O) for various levels of theory, and complete
refs 60 and 61. This material is available free of charge via
the Internet at http://pubs.acs.org.
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