The potential energy surfaces (PES), molecular and vibrational structure of hypophosphours acid (HPA) were investigated by HF, MP2 and DFTB3LYP level of theory using 631G** basis set. In order to approach solid state spectra we optimized mono, di, tri, tetra and pentamer structures and computed frequencies and intensities of the vibrational modes of VCD and IR. It is found that by increasing the number of HPA molecules in the chain, some of calculated vibrational frequencies approach to the experimental solid state values. The potential energy surfaces of HPA are calculated in a wide range on the plane perpendicular to the PO bond where the hydrogen can rotate 360 degree through O=POH dihedral angle. A circular valley is found going up and down on the plane, the valley is centered to the continuation of PO bond. There are two minima at angles ±42.5
^{0}
to the O=PO plane giving two mirror conformers and one saddle point in between with a height of 284.87 cm
^{1}
at the angles 0˚ and a complex barrier with a height of 2089.40 cm
^{1}
at the angle 180˚ to the same plane. On top of the complex barrier, there is a small well with depth of 15.65 cm
^{1}
. To study the tunneling effect and pathway between the two conformers, the molecule is considered to have C
_{S}
symmetry and a symmetric double minimum potential energy well with a barrier of 284.87 cm
^{1}
height in the middle. With the constructed potential, the torsional motion of POH (Hindered Rotation) of the monomer, using variation method and harmonic oscillator wave functions is studied and IR frequencies and relative intensities of vibrational modes are calculated. Due to the width of the well and the trigonometric shape of the barrier, tunneling can occur at the ground state and the next excited state does not feel the barrier at all.
INTRODUCTION
In spite of extensive experimental studies of molecules containing phosphate moieties,
1
only sporadic data exist for small organophosphates. In addition, few theoretical studies, most of which involve lowlevel calculations with small basis sets, are available for these molecules.
Ab initio calculations usually are carried out in order to obtain conformational, vibrational and other molecular information for a set of small oxygencontaining phosphorus compounds. Many of these molecules are fundamentally important since they are analogous to macrostructures that play a central role in biological processes. It is anticipated that the chemical and physical properties of these phosphorus compounds will provide valuable insight into problems in structural biology.
2
In the present work, our attention will be focused on the conformational and vibrational analyses of HPA and its deuterated analogous in the gas phase.
The structure of HPA crystals features chain association of the acid molecules connected by very short hydrogen bonds with symmetric potential wells. Diffraction work
3
has left the problem of the “true” symmetry of these bonds. Previous IR investigations of HPA were handicapped by the lack of both crystal structure data and experience with very short hydrogen bonds.
4

7
Crystalline structure of HPA is determined by diffraction method,
8
it is orthorhombic with space symmetry group P2
_{1}
2
_{1}
2 or
(z=2) with melting point 26.5℃. The molecule aggregates in zigzag chains through hydrogen bonds. The O⋯O distance is 2.44Å parallel to the crystallographic a axis. The symmetry of a single molecule in the lattice is C
_{1}
,
. 1
. The HPA molecules have only one hydrogen atom bonded to oxygen thus it is a mono protonic oxy acid. This compound is a weak acid and forms only one series of hypophosphate salts.
9
In the liquid state, it is expected that chains of molecules resume their structures as a polymer,
. 2
. Unfortunately, in the gas phase the molecule is unstable and regroups to phosphoric acid and phosphorus tri hydrogen, therefore, its IR and Raman spectra have not been reported.
2
Optimized structure of the H_{3}PO_{2} molecule with Gaussian and displayed by Hyperchem. Atom No 1 is the Phosphorus atom, dark colored atoms are Oxygen atoms and white colored atoms are Hydrogen atom.
Proposed liquid state chain conformation of HPA.
COMPUTATIONAL METHOD
The ab initio calculations were carried out with the GAUSSIAN 98W A.6 system of program.
10
Full geometry optimizations were done at the HF/631G**,
11
MP2/631G**,
12
and B3LYP/631G**
13
levels of theory. The theoretical harmonic vibrational frequencies and IR and VCD intensities were also calculated analytically at the same levels.
In order to approach the solid state IR spectra, conformations of one, two, three, four and fivemolecules in a chain were optimized using B3LYP/ 631G**.
To obtain the potential surfaces a plane perpendicular to PO bond is chosen and the hydrogen atom in an area of 2.6×2.6 Å by step of 0.1 Å is scanned. Next the OH bond was rotated about PO direction so the HOP=O dihedral angle was changed from 0˚ to 360˚ and scanned by step of 1˚ while all other structural parameters kept constant at their equilibrium position. From which double minimum potential energy profile is constructed. Finally the OH bond is scanned from 0.1 to 1.7 Å by step of 0.01 Å.
RESULTS AND DISCUSSION
 A. HPA (Monomer)
The defined bond angles and bond lengths of the HPA are shown in
. 1
. The optimized structural parameters of single molecule calculated by different theoretical approaches are listed in
Table 1
.
In spite of the calculated free HPA geometry parameters are compared to the solid state HPA results; the parameters at MP2/631G** and B3LYP/ 631G** levels are close to the each other values while those obtained at HF/631G** level are a little different. For example the calculated OH bond length for a free HPA at B3LYP, MP2, and HF levels are 0.9689, 0.9671, 0.947 Å, respectively.
The optimized geometrical parameters of the HPA (in Angstroms and Degrees)
The optimized geometrical parameters of the HPA (in Angstroms and Degrees)
Frequency assignments are done by animating vibrational modes using Gauss View2.1 and Hyper Chem7.
14
Inspection of
Table 2
shows that calculated frequencies obtained by B3LYP and MP2 levels are in good agreement with the experimental data but markedly different from those obtained by HF approach and demonstrating the effect of electron correlation corrections. The calculated values by MP2 at low frequencies and B3LYP at high frequencies are more close to the experimental values. However, it must be pointed out that in
Table 2
gas phase frequencies are compared to those of solid state.
The IR absorption spectrum of the acid and its deuterated analogous are constructed from calculated intensities and fixed full bandwidth of 20 cm
^{1}
and presented in the
. 3
a and
. 3
c using Gaussian band shape functions.
The optical activity of dissymmetric molecules is explained when a plane polarized radiation passes through an active medium. The plane of the emergent plane polarized radiation rotates by an angle. The plane polarized beam can be considered as a superposition of two oppositely rotating circularly polarized component. The absorbance coefficient is defined
15
Δε=ε_{L}ε_{R}
and the line shape is nearly Gaussian. The absorbance coefficient of the VCD is given by
Where R is the rotational strength and Γ
_{1/2}
is the full width at the half height. Using the full line width 20 cm
^{1}
similar to IR absorbance spectra, the VCD spectra are shown in
. 3
b. As shown in
. 3
b PH
_{2}
rock (∇=784 cm
^{1}
) is strongly left polarized and PH
_{2}
twist (∇=898 Cm
^{1}
) is strong right polarized.
Assignments of the calculated frequencies (Cm1) of the HPA and HPAdwith used methods and comparison of them with the solid state spectra
Assignments of the calculated frequencies (Cm^{1}) of the HPA and HPA_{d} with used methods and comparison of them with the solid state spectra
a IR, b VCD and c deutrated absorption spectrum of the H_{3}PO_{2}.
To obtain the potential surfaces a plane perpendicular to PO bond is chosen and the hydrogen atom in an area of 2.6×2.6 Å by step of 0.1 Å is scanned. Three presentations which are prepared by using Surfer
16
soft ware are shown in
. (4
and
5)
. All of the numerical values of the potential energy of scanned area are inspected and a valley found whose deepest points going up and down on the locations of hydrogen atom if OH bond precess,
. 5
b. In another and more involved scan, the OH precession is carried out and isomeric path way, double minimum potential energy, is generated and opened up for tunneling studies,
. 7
. There are two minima at ±42.5˚ and a saddle point in between (0˚) with a height of 284.87cm
^{1}
and a complex barrier at 180˚ with the 2089.40cm
^{1}
height to the O=PO plane. On the top of the complex barrier, there is a small well with the depth 15.65cm
^{1}
.
The truncated and net presentation of the PES displayed by Surfer. The O=PO plane is perpendicular and crossing through right hand side 0. From (1, 1) corner the minimum can be clearly detected.
a the smooth and complete surface presentation, b and c contour (isopotential) map presentations of the PES displayed by Surfer.
The OH potential energy and a few vibrational energy levels; (a) wave functions and (b) probability distributions.
Spatial isomeric pathway, barrier height and tunneling effect between them a: energy levels and wave functions, b: energy levels and probabilities distributions.
The free OH stretch (C
_{1}
, to check our own generated computer program) and POH torsion (C
_{S}
) of the HPA can be seen in the gas phase spectrum of the acid if it would be available, unfortunately the acid in gas phase immediately disintegrate to PH
_{3}
and H
_{3}
PO
_{4}
. Therefore, the gas phase spectrum has not been reported.
2
The dynamics of a microscopic particle such as stretching can be appropriately described with onedimensional Schrodinger Equation.
17
For the present case
V
(
R
) of the stretching vibrational mode, which is produced by scanning the OH bond length from 0.1 Å1.75 Å and for the spatial isomeric pathway potential (torsional motion) a scanning of the torsional angle 360
^{o}
with fixed bond length and using the Gaussian 98 computer program,
. 6
and
7
. Wide double well potential curve of the pathway with a sharp and small barrier resulted. The net effect would be lowering the torsional frequency.
Introducing the dimensionless variable
17
ξ=(μω
_{e}
/ η)
^{2}
R
to the Schrödinger Equation and by using the variation method and harmonic oscillator wave functions as basis sets:
We define matrix elements H
_{jk}
, as:
Where
The matrix elements HK
_{jk}
and HU
_{jk}
are computed analytically and numerically respectively. By using Eq. (2) wave functions are generated and after computational performances the results of the both computations for three energy levels and wave functions are reflected in
. 6
and
7
.
As it is clear from the
. 7
; due to the width (minima to minima 85˚, about 2.0Å) and height (284.87 cm
^{1}
) of the well and also to the trigonometric shape of the barrier, tunneling occurred at the ground state and the next vibrational excited state does not felt the barrier at all. Therefore conformational transition energy is not required.
 B. two, three, four and five unit chain of the HPA
Vibrational spectra of crystalline HPA and its deuterated analogous have been studied with both IR and Raman techniques.
8
The structural optimization of two, three, four and five molecules in chains are performed using DFT with B3LYP/631G** level. The optimized structures
. 8
(a, b, c, d) clearly show that the chain in free space is screwing.
The optimized structures of two, three, four and five member chain of the HPA.
Optimized Parameters for central HPA unit (in Angstroms and Degrees)B3LYP/631G**
Optimized Parameters for central HPA unit (in Angstroms and Degrees)B3LYP/631G**
The effects of increasing HPA chain units are reflected in
3
. The dihedral angle, which is responsible for chain screwing changing about 10° (dimmer 128.83, trimer and 119.5, tetramer 108.5 and pentamer 101.3 degrees) P=O bond length, as expected, it is elongated about 0.013Å from monomer to trimer but the change from trimer to pentamer is small and equal to 0.001Å
3
. The reported bond length
18
for both of the PO bonds in the crystalline environment are the same and equal to the 1.512 Å (which is close to the calculated P=O bond length in free space) and the hydrogen bond is almost linear with a single minimum potential. The crystalline environment mainly is imposes on the POH and OH bond lengths and equalizes them with related ones but the gas phase calculations predicts the HPA units keeping almost their monomer structure and connected to each other through a long hydrogen bonds.
IR (a, b) and VCD (c, d) absorption spectra of triand pentamers of the HPA.
The vibrational frequencies are calculated for HPA chains using the B3LYP/631G** approach. Then the IR and VCD modeled spectra of these molecules are constructed and presented in
. (9
a, b, c, d). The superiority of VCD to IR is its analytical applications.
CONCLUSION
A DFT/B3LYP/631G** calculation is preformed to optimize a series of HPA compounds in chains, determination of the potential energy surfaces, finding spatial isomeric pathway, computation of single bond potential energy, calculations of IR, and vibrational circular dichroism spectra using Gaussian 98w package.
Our PES calculations confirm two mirror stable conformations of the HPA with C
_{1}
symmetry. The PES can be considered to consist of the many Morse type potentials with varying depth separated on a three dimensional space whose approaching to infinity sides are aligned to the PO bond axis. The variation method calculations, which are generated by us, used to determine tunneling between two isomeric conformations, vibrational energy levels, transitions and probabilities are done with it.
Assignments of the calculated frequencies (with B3LYP/6311G** in cm1) of Mono, Tri , Pentamers of the HPA, which are compared with solid state spectra.
Assignments of the calculated frequencies (with B3LYP/6311G** in cm^{1}) of Mono, Tri , Pentamers of the HPA, which are compared with solid state spectra.
a; the variation of the OP(OH) bend (∇_{2}=394 cm^{1}) and b; P(OH) stretch (∇_{4}=1015 cm^{1}) with the number of HPA unites in the chain with corresponding experimental values.
The HPA chain in free space screw itself by about 10
^{o}
for each unit. IR and VCD spectra are constructed for mono, tri and pentamer of the HPA to approach to the solid state spectra. And it is found that by increasing number HPA units in the chain it is possible to approach to the solid state spectra,
4
and
. 10
. In
. 10
the variation of the OP(OH) bend (∇
_{2}
=394 cm
^{1}
) and P(OH) stretch (∇
_{4}
=1015 cm
^{1}
) with the number of HPA unites are shown and clearly supporting our theoretical calculations.
Inspection of the
4
more closely indicate that, in general, the vibrational frequencies with increasing of the HPA units except for POH bend at 11300 cm
^{1}
and OH stretch at 1100 cm
^{1}
are improved. The reason may be arises from the point that we let the chain to optimize freely in the space. The crystalline environment imposes to the HPA units to appear in different optimization.
To show the trends of frequncy optimization ν
_{2}
and ν
_{4}
as an examples are ploted in
. 10
for visual demonstration.
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