Electron Momentum Spectroscopy and Its Applications to Molecules of Biological Interest

Feng Wang

Centre for Molecular Simulation, Swinburne University of Technology, P. O. Box 218, Hawthorn,

Melbourne, Victoria, 3122, Australia

Abstract. Energy and wave function are the heart and soul of Schrodinger quantum mechanics. Electron

momentum spectroscopy (EMS) so far provides the most stringent test for quantum mechanical models

(theory, basis sets and the combination of both) through observables such as binding energy spectra and

Dyson orbital momentum distributions. The capability of EMS to measure Dyson orbitals of a molecule as

momentum distributions provides a unique opportunity to assess the models of quantum mechanics based

on orbitals, rather than on energy dominated (mostly isotropic) properties. Recently, the author introduced

a technique called dual space analysis (DSA), which is based on EMS and quantum mechanics to analyze

orbital based information in the more familiar position space as well as the less familiar momentum space.

In this article, the development of EMS and DSA is reviewed through the applications to molecules of

biological interest such as amino acids, nucleic acid bases and recently nucleosides. The emphasis is the

applications of DSA to study isomerization processes and chemical bonding mechanisms of these

molecules.

Keywords: Electron momentum spectroscopy, density functional theory calculations, binding energy

spectra, orbital momentum distributions, dual space analysis, atoms in molecules, conformers and

tautomers.

PACS:31.15.Fx, 31.25.Qmand36.20Kd

INTRODUCTION

Structure dictates function. Nowhere is this more apparent than in biological systems (Pratt,

2006). Noble Laureate Francis Crick indicated: "if you wish to know function, study shape." This is

particularly true in the study of biological systems, such as genetic materials, proteins and enzymes.

Many biological phenomena can be traced back to fundamental properties of molecular components.

For example, the base of the famous Watson-Crick D N A structure discovery (Watson & Crick, 1953)

is the insight into the structure of genetic material, e.g., DNA, at molecular level. Shape (structure)

determines whether the atoms that can form bonds to the atoms of another molecule are in close

proximity of each other. Properties of related fragments and molecules, such as D N A / R N A fragments

CP963, Vol. 1, Computational Methods in Science and Engineering, Theory and Computation: Old Problems and New Challenges, edited by G. Maroulis and T. Simos

© 2007 American Institute of Physics 978-0-7354-0477-9/07/$23.00

54

and amino acids, are fundamental to the understanding of complex structures such as proteins, drug

discovery and even in novel electronic and optoelectronic devices based on or modified by molecular

species.

Electronic structure is central for the properties of a system built up of atoms, such as molecules,

liquids and solids. A fundamental understanding of the electronic structure in small molecules and

fragments is crucial for the understanding of many-atom systems, such as drugs and proteins. It is also

the microscopic origin of such macroscopic properties as well as chemical bonding mechanisms and to

certain extent, chemical reactions. Three-dimensional (3D) geometries primarily determine the shape of

bio-molecular systems but do not explicitly provide information about distributions of the electrons and

it is the distributions of electrons which are responsible for chemical structures, properties and

reactions (Wang, 2007a). For example, adenine and unsubstituted purine (Saha et al, 2007b) have

almost the same purine ring with nearly identical purine ring perimeter, R<5 (Wang et a l , 2005).

However, they are simply different molecules with very different properties. The electronic structure of

these molecular systems is usually described in terms of molecular orbital theory, i.e., the interaction of

independent-particle configurations (McCarthy, 2001).

Spectroscopy provides a close link between detailed electronic structures and processes. Rapid

development of synchrotron sourced spectroscopic techniques ensures one to measure larger biological

molecules from valence space to core space (e.g., Plekan et a l , 2006; Mochzuki et a l , 2001; Harada et

al, 2006; MacNaughton et al, 2005; Magulick et al, 2006), which brings serious challenges to

theoretical spectroscopy (Falzon et. al, 2005; Takahata et al, 2006; Wang, 2006b; Saha et al, 2006;

Vazquez et al, 2006). Accurate prediction of electron spectra, particularly for core shell, is still largely

for small molecules. Quantitative treatment of the near-edge X-ray absorption fine structure (NEXAFS)

spectra for even small bio-molecules such as amino acids (Mochzuki et al, 2001) and DNA bases

(Harada et al, 2006; MacNaughton et al, 2005; Magulick et al, 2006) are not yet fully understood, as

calculations far from trivial are necessary. In the most recent photoabsorption spectra of small amino

acids in gas phase (Plekan et a l , 2006), the observed results were semi-empirically assigned for the

core ionization potentials (IPs) by subtracting the number of 2.6 eV from the DFT calculated core

energies. A simple mean for the IPs was employed using the B3LYP and RHF orbital energies without

any rigorous scientific basis in a spectral analysis of L-alanine (Mochzuki et al, 2001). Very recently,

the O-K, N-K and C-K ionization spectra of polycytidine (Magulick et al, 2006) were analyzed semi-

empirically without a support from solid quantum mechanical calculations. The assignment for the N-K

spectrum of cytidine (Magulick et al, 2006) was found to be incorrect (Wang, 2006b; Thompson et al,

2007), which has been supported by the observation of a very recent soft X-ray experiment of DNA

bases and base dimmers (Harada et al, 2006).

The centerpiece of Schrodinger quantum mechanics is energy and wave function. Unlike the

energy, quality of wave functions is usually assessed indirectly through other measurable molecular

properties and qualitatively by electron density contours. Molecular wave function anisotropy has been

a great challenge to quantum mechanics, which does not automatically guarantee the angular behavior

55

of the electronic wave functions, particularly in the long-range region (McCarthy and Weigold, 1991).

Due to the isotropic nature of the wave function generation, improvement of angular behavior of wave

functions does not lead to a significant lowering in total energy. This has caused the ignorance of the

importance of wave function anisotropy in quantum mechanical research until apparently unexpected

results have occurred. Significant advances in computational power combined with third generation

synchrotron sourced spectroscopy promise to tackle the structures of larger bio-molecules such as

nucleic acid bases and nucleosides in detail with spectroscopic accuracy. Conventional ab initio

methods, such as MP2 and CCSD(T), usually do not offer computationally feasible solutions to larger

bio-molecules for the size of nucleic acids, nucleosides and larger amino acids. Complexity and

biodiversity of bio-molecules with their unique structures and properties present a range of new

challenges for theoretical/computational chemists to develop a variety of smart and innovative

techniques. As a result, in addition to the need to develop novel, more efficient with less computational

demanding quantum mechanical methods, we also need smaller and more efficient basis sets such as

Slater basis sets for molecules with larger molecular weight. A paradigm, which smartly facilitates the

available methods and techniques with accessible computer power to reveal the structure based

bioactivities, is the state-of-the-art in computational biochemistry.

No single process is best for all purposes in biochemistry. The large existence of conformers and

tautomers in bio-molecules makes the uniqueness and complexity of these systems. In such species,

compounds and fragments interact in a defined arrangement with not only the chemical composition,

but also their precise stereochemistry. In addition to their biological significance as building blocks of

peptides and proteins, amino acids and DNA/RNA fragments are interesting species from a chemical

point of view. For instance, the conformational flexibility associated with their backbone and side

chains produces many local minimum structures on the torsional potential energy surfaces of amino

acids. As energy barriers associated with these conformational changes are typically large, these amino

acids generally exist as single conformers. For other molecules, these energy barriers are quite small

and isolation of a specific conformer is difficult. The conformational variety of amino acids is,

however, imperative in determining the 3D structure of proteins and thus controlling their dynamics.

In computational biochemistry, if the phenomena such as explicit bond breaking and formation in

an enzymatic active site are concerned, accurate quantum mechanical methods must resort. These

phenomena are usually highly localized, and thus only involve a small number of functional groups,

usually in vacuum (isolation) or surrounded by a dielectric continuum that mimics bulk solution effects

(Raber et al, 2003). Ionization energy is a useful property to study the mechanism of photoactivation

when a bio-molecule or drug is ionized by the radiation and the electron is taken up by the target

compound (e.g. a nucleobase), with subsequent rearrangements, fragmentations, dimmerizations, and

other reactions (Raber et al., 2003). As a result, laser spectroscopy (such as EMS) and theoretical

methods (such as DSA) will continue to demonstrate a great potential to elucidating the structures and

dynamic of these bio-molecules.

56

In this article, the application of theoretical electron (momentum) spectroscopy, using dual space

analysis (DSA, Wang, 2003) is reviewed. The focus is placed on the applications of the DSA into study

isomers including tautomers and conformers which largely exist in biological species. It is not the

intention (and not possible) of the article to cover all areas in the applications of EMS.

ELECTRON MOMENTUM SPETROSCOPY

It was suggested that the (e,2e) reaction could be employed to probe electron orbitals of many

electron systems (Baker et al, 1960). Ortho-normal orbitals of a molecule can be extracted from the

experimental data of electron momentum spectroscopy (EMS) using a statistical inversion procedure to

reconstructing the single-particle density matrix from experiments (Nicholson et a l , 1999; Schmider et

al, 1993) in the ground electronic state. EMS is based on a kinematically complete measurement of the

differential cross section for ionization on an electronic many-body system. Electronic states of the ion

produced are resolved by the experiment. The differential cross section for ionization scanned at the

difference between the initial and final electron momenta and energies, is very sensitive to the energy-

momentum density. EMS is therefore the measurement of the momenta or velocities of electrons in a

sample.

Ionization process provides rich information of the electronic structure of the target. The focus is a

simple direct ionization process where most of the energy of the incoming electron is converted into the

energy of two fast emitted electrons, and the kinematics of the incoming and outgoing electrons is

completed determined. Hence, the ionization collision process is described as (Weigold and McCarthy,

1999),

where the subscripts 0, s and f label the momenta k and energies E of the incident, slow and fast

outgoing electrons, respectively. The binding energies (or ionization potentials) of orbital i can be

obtained using energy conservation of the process as (Weigold and McCarthy, 1999),

^i =Ea-E,-Ef (2)

while the momentum conservation gives,

P = K-k,-kf (3)

The ionization energies and recoil momentum are related to observed kinetic energies and

momenta, respectively and are the quantities measured by EMS. Vibration and rotation states are not

resolved but averaged (Weigold and McCarthy, 1999). By careful kinematic arrangement in the

experiment, such as non-coplanar symmetric kinematics (McCarthy and Weigold, 1991) by setting up

0 = 0^ =6*2 = 45 °, in combination with appropriate experimental energy and momentum settings.

57

which is particular sensitive to probe structural information (Chen and Zheng, 2000), the relative

azimuthal angle

(4)

is varied so that the recoil momentum is given by (Weigold and McCarthy, 1999).

{2k^ cosO-k^f+Akl sin' ^sin'l ^ (5)

The theory of EMS is developed fully (Weigold and McCarthy, 1999). The EMS region of the

(e,2e) reaction, and the cross section, as a function of ion recoil momentum and electron separate

energy, depend very sensitively on the orbitals and on electron correlations in the target and residual-

ion systems. The differential cross section depends directly on the electronic structure amplitude of the

quasi-particle or Dyson orbital, which is approximated by the one-electron momentum-space overlap

between the initial target state and the energy selected final state. Under the Bom-Oppenheimer

approximation, molecular orbital theory and the plane wave impulse approximation (PWIA) (Weigold

and McCarthy, 1999), the triple differential EMS cross section (momentum distributiona) is given by

(McCarthy and Weigold, 1991),

2 \P N-\ Vf/^ dn (6)

The overlap of the residual ion and neutral wave functions is known as the E)yson orbital (McCarthy,

2001). Applying weak-coupling approximation, the overlap is related to the orbital on which the

ionization occurs.

^EMs °^l\<f>j(p)\^dn (7)

where (|)j(P) is the Fourier transformed form of the orbital in momentum space (p) and p is the

momentum of the target electron at the instant of ionization. Here the integration performs the spherical

averaging of the initial rotational states. It is noted that averaging over initial vibrational states is

approximated by evaluating the orbitals of the molecule at the equilibrium geometry, whilst closure

eliminates the final rotational and vibrational state dependence (Weigold and McCarthy, 1999). E)yson

orbitals represent the changes in electronic structure accompanying the detachment of an electron from

a molecule (Dolgounitcheva et a l , 2000).

Weak-coupling approximation ignores the first-order perturbation to the orbital binding energy

(ionization energy), which means that all momentum profiles of the orbital manifold have the same

shape (McCarthy, 2001). Dyson orbitals can be calculated using a truncated configuration interaction

(CI) expansion (Bawagan et al, 1987; Clark et al, 1990), or can be obtained from solving the quasi-

particle equation using perturbation theory by Green's function technique (von Niessen et al, 1984).

Dyson orbitals may be also approximated by Hartree-Fock orbitals and Kohn-Sham orbitals (Duffy et

al, 1994, Gritsenko et al, 2003). For sufficiently high impact energies, the PWIA is a good

58

approximation for valence orbitals in ground electronic states of molecules, as confirmed by a recent

EMS measurement for NNO (Khajuria et al. 2003). Under the Born-Oppenheimer approximation, the

total electron density is measured in EMS as the sum of the E)yson orbital densities, which establishes a

strong relationship between the exchange-correlation potential of the weak coupling approximation to

the quasi-particle equation and that of exact DFT (McCarthy, 2001).

Electron momentum spectroscopy has been very attractive to quantum chemists due to the

uniqueness of detection of both energy and orbital. However, further application of EMS has been

largely limited by its low coincidence count rate and poor energy resolution (currently 0.5-1.0 eV),

which results in clusters of valence orbitals leading to the loss of important chemical bonding

information. Such limitations restrict broader applications of the EMS technique into the study of larger

bio-molecules, and result in a couple of general directions of development (Weigold and McCarthy,

1999). One is to combine EMS with other spectroscopic techniques including momentum density

focused techniques of Compton scattering, (y, 2y) spectroscopy and positron scattering etc., as well as

energy based spectroscopic techniques such as photoelectron spectroscopy (PES). In particular PES is

in complementary with EMS due to its high energy resolution. The other direction is to improve the

energy resolution and the sensitivity of the EMS spectrometers. One option is to base on the symmetric

co-planar kinematics as originally developed by McCarthy and Weigold (1991) but to improve the

position sensitive detectors (PSD) (Ning et. al 2004) as developed recently in Tsinghua University

(Deng et al, 2007). The other is to apply asymmetric non-coplanar kinematics which recently

developed at the University of Science and Technology, China (Chen et a l , 2007). A new three-

dimensional EMS spectrometer which has been successfully applied to hydrogen molecules has been

developed by Takahashi and Udagawa (2007).

Electron momentum spectroscopy has been applied to study bio-molecules such as glycine (Neville,

et a l , 1995; Falzon and Wang, 2005), the smallest amino acid, and most recently tetrahydrofuran

(Yang, et a l , 2007), the sugar moiety of DNA and RNA as well as formic acid monomer and dimmer

(Nixon et a l , 2007). However, following the theory of EMS (Weigold and McCarthy, 1999) as well as

the pioneer work of Coulson (Coulson and Duncanson, 1941, 1942, 1943) in momentum space for

quantum chemical applications, we have come to employ the information from both position space and

momentum space of a molecular system to study electronic structures through Fourier transform

theoretically, that is, dual space analysis (DSA, Wang 2003). It is found that such the orbital based

approach is particularly useful to study conformations (Falzon and Wang, 2005; Falzon et a l , 2006;

Yang et a l , 2007) and tautomerism for bio-molecules (Wang et a l , 2005; Jones et a l , 2006; Saha et al.

2006; Saha et al, 2007a).

DUAL SPACE ANALYSIS

Quantum chemistry can be described in two equivalent pictures: position space and momentum

space. Position space has dominated the development of quantum chemistry. This is probably because

our chemical understanding is based on position space pictures (Weigold and McCarthy, 1999). In

59

addition, the Schrodinger equation in position representation is a differential equation but becomes an

integral equation in momentum representation. However, momentum space calculations exhibit two

advantages over position space (Navaza and Tsoucaris, 1981): First, the numerical solution of Hartree-

Fock equation is feasible without expansion of the wave functions in a particular basis. Equations only

exhibit one avoidable singularity even for the multi-center case. Second, momentum representation

contributes in an original way to a better understanding of several physical problems arising in

quantum chemistry. If an expansion in Gaussian functions is used, momentum space renders feasible

the obtainment of a multidimensional fully correlated wave function, starting from the Hartree-Fock

solution. Although Coulson and Duncanson (Coulson and Duncanson, 1941, 1942, 1943) pioneered in

the examination of the electron structure of molecules and chemical bonding in momentum space over

half century ago, momentum space quantum chemistry develops relatively slowly.

In a speech about molecular structural calculations some half century ago, Coulson (1960) indicated

five directions of future development in quantum chemistry, including the recognition that energy is

not the only criterion of goodness of a wave function; concerns of the electronic excited states; electron

correlation; intermolecular interactions and spreading of quantum mechanics into biology. This is true

not just for the "next few years" after the speech but a few decades later. Coulson (1960) further

pointed out that in the past quantum mechanics has been preoccupied with energy. Theoretically, this is

because the most powerful and widely used technique for getting approximate solutions to the

Schrodinger equation obtained almost exclusively on energy minimization. Experimentally, almost all

measurable properties of molecular systems are energy (or isotropic) dominant until the development

of the theory and experiment of electron momentum spectroscopy (McCarthy and Weigold, 1991).

It is equivalent to solve the Schrodinger equation in position representation and in momentum

representation. One can solve Schrodinger equation in position representation, (Dirac-) Fourier

transform to the wave function ^(x,y,z) into momentum space <I'(px, Py, Pz). Alternatively, one can

solve the Schrodinger equation in momentum representation directly (e.g., Holstein, 1995; Gadre et al,

2006) for momentum space wave function, <I'(px, Py, Pz). Dual space analysis (DSA) focuses on the

former. From the wave function in the Cartesian position space representation, ^(x,y,z), the wave

function in the Cartesian momentum space representation, <I'(px, Py, Pz) is obtained by a three

dimensional Fourier transform, i.e. (Smith, 2001),

^{p.,Py,P.) = i27rhr"lnx,y,z)e-''''''''''''''"dxdydz (8)

and vice versa. The Fourier transform provides a unique relationship between momentum space and

position space representation of a particle. If ^ (x ) is normalized then <I'(p) is normalized,

j Y * {x)nx)dx = j o * (pJOipJdp, = 1 (9)

Position and momentum are complementary physical variables, product of which has dimensions of the

Planck constant, which is the wave-particle duality of the uncertainty principle. A wave of definite

wave-length represents a particle with definite momentum. The experimental revelation of the

60

uncertainty principle, namely the relation between the statistical variance in position and the statistical

variance in momentum space, obtained by the evaluation of large number of position and momentum

measurements with identically prepared wave functions, is a consequence of two facts: (1) the trivial

mathematical relation between the average spread of the wave function in real space and in momentum

space as a consequence of Fourier transformations. (2) The fact that the squared magnitude of the wave

function gives the probability of detection at a particular position or of measuring a particular

momentum (Gurel and Gurel, 2004).

The technique of dual space analysis (Wang, 2003) explores information from both position space

and momentum space for electronic structures of molecules. The solution of the Schrodinger equation

is obtained using position space quantum mechanical methods, such as ab initio methods and density

functional theory (DFT) methods. Geometries and other physical and chemical properties such as

energies and dipole moments etc. are calculated in position space. Applying molecular orbital theory,

ionization and/or excitation energies can be obtained using various molecular spectroscopic

measurements. Electron density distributions of the orbitals can be presented as qualitative orbital

contours in position space, whereas the orbital MDs can be directly measured by electron momentum

spectroscopy. With the help of the complementary information from position space and momentum

space, DSA ensures us to study orbital based chemical bonding mechanism for a number of processes

in which the energy is not a particularly sensitive property such as conformational process.

DSA consolidates the association between theory and experiment through the predictive power of

quantum chemistry and validity power of experiment; connects information in coordinate space and

momentum space through a Fourier transform (FT); facilitates interpretation of electronic structure in

terms of one-electron concepts (molecular orbital theory) through the association of E)yson orbitals to

electron binding energy spectra; and achieves quantitative assessment of wave functions (orbitals),

which has long been a challenge for quantum chemistry (Eugen Schwarz, 2006). DSA has been

successfully applied for conformation analyses of bio-molecules (Saha et al, 2007b; Jones et al, 2006;

Wang et al, 2005; Falzon & Wang, 2005, Saha et al, 2006a) and recently was applied to diagnose the

most stable structure of tetrahydrofuran (THF), a sugar prototype (Yang et al, 2007).

APPLICATIONS TO MOLECULES

Orbital momentum distributions (MDs) not only quantitatively assess the accuracy of the orbital

wave functions of a particular quantum mechanical model (theory and basis set) by agreement between

the simulated and the measured in a range rather than at the equilibrium, but also qualitatively provide

chemical bonding information when combined with the orbital electron density contour plots in

position space. For example, if an orbital does not have any node (n=0) in position space, the bond is

likely formed by s-electrons which in momentum space usually gives a half bell shaped momentum

distribution. This is the case in atomic species, but for molecular species, an anti-bonding orbital such

as the Ibug orbital of diborane (Wang et al, 2006) may result in nodal planes. If the orbital has one node

61

(n=l) the bond is likely formed by p-electrons, which in momentum space gives a bell shaped orbital

momentum distribution. A large class of bio-molecules, such as amino acids and nucleobases, consists

of first and second row elements dominated by s and p electrons. As a result, the chemical bonding

picture can be recognized by the shape of the MDs of an orbital. In this section, we provide some

examples focusing on ionization spectra and chemical bonding mechanisms using DSA.

1. Orbital Based Quantum Chemistry Model Assessment

The quality of a DFT model has been shown to depend on the functionals and basis sets applied, the

properties compared, and the molecules studied. For example, the study by Perdew and co-workers

(Burke et al, 1994) showed that none of the commonly used functionals satisfies all the known exact

conditions, and that it is not clear how violations of these conditions will affect the quality of the

results. The correlation functional of Lee, Yang and Parr (1988) violates a large number of exact

conditions. However, it was successfully used for chemical problems with Becke's (1988) exchange

functional. Moreover, the form of the exact exchange is known from the HF theory and some so called

hybrid functionals includes it in a semi-empirical way (Becke, 1993). Although the results obtained

with these functionals are usually sufficiently accurate for most applications, there is no systematic way

of improving them. Hence in the current DFT approaches, it is not possible to estimate the error of the

calculations without comparing them to other methods or experiment. Lack of methods which

gradually improve the quality of the DFT methods makes DFT methods less attractive for some

researchers. The only currently available way to test a functional is to perform systematic comparisons

between the results calculated with various functionals and the best theoretical estimations and

experimental results (Wang et a l , 2007).

Apart from DFT functionals, basis set dependence is another issue. In many quantum chemical

calculations, there exists a dogma that higher levels of theory automatically produce more reliable

results, and that has led to use the largest basis sets possible. This too needs to be examined (Klein &

Mottola, 2006). Information concerning the likely accuracy of a specific basis for a particular property

is essential in order to judge the adequacy of the computational method and, hence, the soundness of

the results (Davidson & Feller, 1986). In quantum chemical calculations, the fact that the GTOs can

lead to the evaluation of the two-electron integrals more efficiently than with STOs, makes GTOs more

widely used in computational chemistry. As a result, the majority of DFT performance studies have

mainly been undertaken with GTOs and rarely with STOs (Wang et al, 2007).

Properties of molecules in the systematic assessment of quantum chemistry models are largely

geometric and isotropic at the equilibrium, even though some studies assessed more anisotropic

properties such as dipole moments, polarizabilities and electron densities. Very few studies focused on

molecular orbitals (Wang, 2003; Zhang and Musgrave, 2007; Wang et al, 2007). In molecular orbital

theory, orbitals in particular frontier orbitals are very important for small organic molecules and their

reactions. This explains why a recent systematic comparison of DFT methods focusing on HOMO-

62

LUMO gaps or the first ionization potentials (IPs) for a number of small molecules (Zhang and

Musgrave, 2007) quickly drew a significant attention and became one of the most accessed articles in

January-March, 2007 in JPCA. However, it was found from previous studies on bio-molecules (da

Silva et al, 2006; Falzon et al. 2006) that not all chemical reactions happen at frontier orbitals, as bio-

molecules often engage with more than one functional groups and with various chemical reactions. In

our recent study of DFT models and basis sets for outer valence orbitals of water (Wang et a l , 2007a),

it was found that performance of quantum mechanical models and basis sets is also orbital dependent.

As a result, conclusions drawn from HOMO or LUMO may not be applicable to other orbitals of the

same molecule.

There is no systematic assessment of DFT functionals and basis sets for properties, such as orbital

distributions, as a function of r in position space or p in momentum space until very recently (Wang et

a l , 2007), in which Wang et al. (2007) assessed a number of DFT functionals in combination with a

selected set of both Gaussian and Slater basis sets, on the valence space orbital MDs of water against

earlier experimental results. More recently, in a study of the outer valence orbitals of NNO, the same

group found that the combination of DFT functional and basis set also matters when compared the

simulated valence orbital MDs, say, the la orbital of NNO. Figure 1 and figure 2 compare the

simulated orbital MDs for la orbital of NNO in the electronic ground state, using various models and

basis sets.

0.18

0.16

0.14

0.12

0.08

0.06

0.04

0.02

'•G-6-311G" "0-6-31G"

"G-aug-pVTZ" ••S-D2Pp" "S-pVQZ" "S-qZ3P"

••S-qZP5P" "G-TZVP"

Fig.l Orbital momentum distributions of 7a orbital of NNO using B3LYP with selected Guassian (G) and even tempered Slater (S) basis sets. The MDs of the 7CT orbital of NNO show a basis set dependency.

63

0.18

0.16 -

0.14 -

0.12 -

••G-6-311G" '•G-6-31G"

G-aug-pVTZ' •S-DZPp' ••S-pVQZ" ••S-qZ3P"

••S-q2P5P' "G-TZVP"

0.08

0.06

0.04

0.02

Fig 2 Orbital momentum distributions of the la orbital of NNO using PW91 with selected Guassian (G) and even tempered Slater (S) basis sets. The orbital MDs exhibit a model (theory/basis set) dependency rather than basis set dependency. It is noted that the Gaussian aug-pVTZ and Gaussian TZPV basis sets, when combined with the PW91 functional, converge to the Slater basis sets.

2. Outer Valence Orbitals of Normal Butane Conformations

Isomerization process including conformational and tautomeric processes is one of the most

important but most challenging processes associated with bio-molecules. The large existence of

conformers in bio-molecules makes the uniqueness and diversity of these systems. In these species,

compounds and fragments interact in a defined arrangement with not only the chemical composition,

but also their precise stereochemistry. One of the challenges in conformational analysis is that there is

no single approach which is best for all purposes (Wiberg, 1993). Small and subtle energy differences

among the conformations of many bio-molecular conformers are often within the error bars of many

quantum mechanical models and any single experiment hardly provides sufficient and unambiguous

evidences for a particular conformation such as glycine (Nevill et a l , 1996, Falzon and Wang, 2005),

tetrahydrofuran (Yang et al, 2007) and tautomers of nucleobases such as adenine (Wang et al, 2005;

Saha et a l , 2006; Saha et al 2007) and guanine (Jones et al. 2006). However, it is almost always true

that appropriate properties to identify those bio-molecular isomers are dominated by anisotropic, rather

than isotropic properties. For example, Nguyen and Pratt (2006) employed dipole moments to

differentiate conformers of tryptamine. Among the anisotropic property alternations, a particular group

of molecular orbitals are responsible for certain conformations (Falzon and Wang, 2005). In this

section, we will concentrate on orbital based response in position and momentum space to

conformational and tautomerism processes.

Normal butane (n-butane) is perhaps the most classical example in organic chemistry text books for

conformational processes. Summaries of previous work on butane can be found in an incomplete list of

64

references (Allinger et a l , 1997; Deleuze et al, 2001; Wang, 2003). It is known (McMurry, 1996;

Kimura et al. 1981) that of the four rotational conformations of n-butane, only anti-butane (with a C2h

symmetry) and gauche-butane (with a C2 symmetry) are stable isomers as they possess energy minima

on the torsional potential surface, whereas the eclipsed-butane and cis-butane structures are transition

states. However, as pointed by McMurry (1996) when one states a particular conformer as being "more

stable" than another, one does not mean the molecule in question adopts and maintains only the more

stable conformation. At room temperature, sufficient thermal energy is present to ensure that rotation

around the a-bonds occurs very rapidly and that all possible conformers are in a fluid equilibrium and

based on the Boltzmann distribution. Moreover, initial interaction of frontier MOs of molecules often

leads to the expected products when reaction is exothermic and for endothermic reactions, information

with respect to the structure and stability of the a transition state is necessary to decide upon the

reaction pathway (Rauk, 2001).

> ID

0.5 -,

0.4

0 3

B ^ 0.2

LU

0.1

0.0 A (c,,)

B(C,)

C(C,)

60"

Torsional angle / 120^ 0

D (C,.)

180°

Fig. 3 Torsional energy diagram of the four conformations of n-butane calculated using the B3LYP/TZVP model (Wang and Downton, 2004).

It is important to understand the electronic structures of the transition states in order to probe

chemical reactions of n-butane. The electronic structures of the transition states are also important with

respect to their orbital topologies as the dihedral angle gradually changes, in order to avoid orbital

symmetry violation. Although relatively simple, n-butane has small orbital energy splitting in the outer

valence shell, which has brought challenges to the resolution of modem EMS experimental techniques.

Consequently, the orbital momentum distributions are only partially resolved (Pang et al, 1998; Deng et

65

al, 2001, Deng et al, 1999), leading to information loss in the chemically most significant region

(Wang, 2003). In addition, valence orbitals of n-butane from position and momentum space help us to

improve our knowledge in orbital symmetry correlation (Deleuze et al. 2003) and the assignment of the

photoelectron spectroscopy (PES) experiment (Kimura et al, 1981).

In the outer valence shell of the conformers, the orbital wave functions are considerably delocalized

with the inclusion of possibly all symmetries (Wang and Pang, 2007). The molecular orbitals (MOs)

among the conformers correlate as (ag, au) ^ a ^ (ai, a2) and (bg, bu) ^ b ^ (bi, b2), if the principal

C2-axis coincides with the Cartesian z-axis as the torsional angle varies.

S.OKIO"*

•*.Qi:1D(*

a.OxlD

zoariD'

KBtlOf*

D.O 0.0 0.5 1.0 1.S

Momentum/a.u. 2ja 2.5

B(9a)

Fig. 4 Electron charge distributions and momentum distributions of orbital (lau) of the four conformations of n-butane. This orbital is the only EMS resolved orbital in the outer valence space of butane (Wang and Pang, 2007).

3. Orbital Response to the Cj Conformers of Glycine

As the smallest naturally existing amino acid, the conformational behavior of glycine has brought

many challenges to experimental and theoretical investigations. The ability of glycine residue to

generate flexible dihedral angles in protein structures has proven difficult for many methods.

Theoretical studies have found as many as eight minimum-energy conformers present in the gas phase

(Csaszar, 1992), although only a few of these conformers have been observed experimentally due to

their thermal instability (Stepanian, et a l , 1998). We recently examined four glycine conformers

possessing Cj symmetry (Falzon and Wang, 2005), formed by rotation of the single C-C, C-O and C-N

bonds shown in Fig. 5 (Falzon and Wang, 2005)

66

a

Pi

0 -

> T ^

3 V = H

5.27 k c a l - m o l - '

c-o

274 A / " ^ J V^

1.61 kcal-mol-^

c-c O . N —

H ' 1 .908 A

J 0 .56 kcal-mol-> c-c, C-N, C-O

II III IV

Glycine C o n f o r m e r s Fig. 5 Relative energy of four glycine Cs conformers (Falzon and Wang, 2005).

The calculated binding energy (ionization energy) spectrum of glycine (Falzon and Wang, 2005)

using various quantum mechanical models compares favorably with the observed using PES (EClasinc,

1976) and EMS (Neville et al, 1996), as indicated in Table 1 (Falzon and Wang, 2005). Fingerprint

(signature) orbitals of a conformer (or rotation of a single bond) with respect to a reference

configuration, usually the global minimum configuration, are defined as orbitals with the most

significant changes in the orbital MDs (Wang and Downton, 2004). For conformers containing a a^

(molecular) plane, the most significant variation in conformation is dominated by a' orbitals, this is also

seen in other molecules such as adenine (Saha et al, 2006; Saha et al, 2007) and guanine (Jones et al,

2006). The signature orbitals lie in the molecular plane which is dominated by a-bonds.

Table 1 Six outer most valence ionization energies (eV) of glycine calculated using the RHF, DFT-SAOP and OVGF models, together with available experimental results and a previous P3 model for conformer I.

Orbital

16a' (HOMO)

15a'

4a"

3a"

14a'

13a'

SAOP/ATZP'

10.4(10.5)

11.4(11.5)

12.7(12.7)

13.5(13.6)

14.3 (14.4)

15.0(15.0)

OVGF/TZVP

(pole strength)

10.0(0.93)

11.4(0.91)

12.4(0.91)

13.6(0.90)

14.8 (0.92)

15.1 (0.92)

RHF/TZVP

11.3

12.8

13.4

14.6

16.0

16.5

P3/6-311G** "

9.9

11.0

12.2

13.5

14.6

14.8

Expt"

10 (-10)"

11.1 (-11.2)"

12.1 (-12.2)"

13.6 (-13.5)"

14.4 (-14.2)"

15.0 (-15.0)"

i Values based on the DFT-SAOP/TZ2P method are given in parenthesis. ii P3/6-311G** model (Herrera, 2004). iii Photoelectron Spectroscopy using He I (584 A) and He II (304 A) radiation lines (Debies and Rabalais, 1974). iv He I Photoelectron Spectroscopy (Klasinc, 1976).

67

HOMO (16a')

5.0x10"

NHOMO(15a')

«

.0x10"*-

0.0-

«

— I

- - n

IV

^ W

5.0x10 1

2.5x10 •

1.6x10"

8.0x10"

10 20 30

3a'

13a'

Azimuthal A i^e (p/^

Fig.6 Orbital momentum distributions of the six outermost valence orbitals of the four glycine Cs conformers.

In Fig. 6 the orbital MDs of six outer most orbitals of the four Cj glycine conformers are presented.

No all of the outer most valence orbitals are affected by the rotations of related single bond of glycine.

It is seen that two orbitals, 4a" and 3a", which exhibit Ti-bonding nature as shown in the orbital

electron density distributions in the middle (4a"), do not change significantly in orbital MDs.

However, almost all orbitals with a' symmetry, including the HOMO (16a'), next HOMO (15a'), 14a'

and 13 a' demonstrate conformer related changes. As a result, the orbital MDs are very sensitive to the

in-plane a-bonding of the Cj glycine conformers, whereas the out of plane Ti-bonds remain little

affected.

4. Orbital Signatures for Adenine Tautomers (Base)

The lone-pair electrons of nitrogen atoms in DNA (RNA) bases lead to a number of tautomers of

comparable energies in the electronic ground states. Vital for understanding chemical reactivity,

tautomerization is widely believed to lead to various biochemical processes including point mutation

(Harris et al, 2003). Hence, even the minor tautomers should not be ignored (Harris et a l , 2003). The

existence of adenine tautomers is confirmed by experimental studies (Gu and Leszczynski, 1999; Luhrs

et. a l , 2001), often in the presence of metal (Vrkic et a l , 2004). For example, existence of tautomeric

forms of adenine in a complex with transition metal ions is also revealed (Rubina and Rubin, 2005).

Although many DNA (RNA) tautomers can be observed using jet-cooled spectroscopy such as

resonance two-photon ionization (R2PI), the mobility of certain hydrogen atoms has brought

considerable difficulties to experiment (Sobolewski et a 1., 2002), in which the signal assignment has

largely relied on theoretical calculations (Lee et al., 2002; Lee et a l , 2003). Adenine could form as

many as 14 different tautomers considering the different positions of the protons (Hanus et a l , 2004;

Fonseca Guerra et al, 2006). Adenine prototropic tautomers can be produced by transferring the mobile

proton on N(9) position (canonical form (Ramaekers et a l , 2002)) to N(7), N(3) and N(l) positions,

respectively, in the purine ring. Canonical adenine, the most abundant adenine tautomer, is believed to

be the most stable adenine structure in gas phase (Holmen and Broo, 1995; Fonseca Guerra et al, 2006).

3D geometry of a molecule in space primarily determines the shape of the molecule, but does not

distinguish the distribution of electrons. It is the electrons which define the molecular properties.

Ground electronic states of the adenine tautomers are all in (X^A) states, with closed shells of 35

doubly occupied molecular orbitals (MOs), including 15 outer valence MOs, accordingly. As indicated

before (Wang et a l , 2005), adenine and tautomers are slightly non-planar but here for the purpose of

simplicity and orbital correlation, the species are treated as planar species with a Cj point group

symmetry (Saha et al, 2007a). A Cj point group produces MOs with a' and a" symmetries only,

reflecting in-plane a bonding or out of plane (anti-symmetric) % bonding characters. Of the 15 outer

valence MOs of the canonical adenine, six MOs possess a " symmetry, whereas nine MOs have an

orbital symmetry of a'. The configuration is given by our SAOP/pVQZ model as,

2la'22a '23a 'la "24a '25a '26a D 2a "3a "27 a '4aD28a '5a "29a '6a "(HOMO).

69

16

1 4 -

1 2 -

o J

ul

'E> <u c LJ

>

cu

1 0 -

8 -

6 -

4 -

2 -

0 -

Ade-N9 1

Ade-N7 Ade-imi1n1n9 Ade-imi1n1n7

Fig. 7 Relative energy of adenine amino N9 and N7 tautomers and adenine imino N1N9 and adenine imino N1N7 tautomers (Saha et al., 2007a)

Here SAOP (Schipper et al, 2000) is one of the recently developed asymptotically correct forms of Vxc

in DFT, which is available in the Amsterdam Density Functional (ADF) computational chemistry

package (2006). Here the pVQZ basis set is a Slater basis set and has been found to produce good

agreement of anisotropic properties to experiment (Chong et al, 2004, Wang et al, 2007a).

From screening the symmetry correlated orbital theoretical momentum distributions (TMDs) of the

four adenine tautomers in the outer valence space. As observed before (Jones et al, 2006; Fonseca

Guerra et al, 2006; Saha et a l , 2007a), not all the in-plane a orbitals exhibit significant changes with

respect to the mobile proton positions. The a (i.e., a') orbitals vary more significantly toward the inner

valence shell, whereas the n (i.e., a") orbitals (bell shape) remain almost unchanged. Interestingly, the

outermost orbitals, i.e., 6a" (HOMO), 29a' (HOMO-1) and 5a" (HOMO-2), do not exhibit significant

impact on the proton relocation as they (HOMO and HOMO-2) are dominated by n orbitals. The

phenomenon that the frontier orbitals are not always the most active orbitals in reactions has also been

observed previously in relation to bio-molecules (Jones et al, 2006; Fonseca Guerra et al, 2006; Saha et

a l , 2007a; Wang, Gu and Leszczynski, 2006; da Silva et al, 2006). Figure 8 displays one of the

signature orbital TMDs, i.e., orbital 25a' in the outer valence space from our recent SAOP/pVQZ

calculations. This orbital differentiates the behavior of the four adenine tautomers caused by a proton

transfer, indicating that proton transfer is not a small effect affecting only outermost valence orbitals

but may have profound effect on the entire electronic structure of the species.

70

Ade N7 Ade N9 Ade imi1 N7 Ade imi1 N9

Orbital Momentum (a.u.)

Ade-i9N Ade-i7N

Fig.8 Orbital MDs in momentum space and corresponding orbital electron charge distributions of the 25a' orbitals of the four adenine tautomers. This orbital (25a') has been identified as one of the important signature orbitals responsible for the tautomerism of adenine.

71

5. Diagnostic of the Most Populated Conformer of Tetrahydrofuran (Sugar)

Structural variability and flexibility of bio-molecules such as DNA/RNA are related to their

biological functions (Saenger, 1988). The sugar moiety occupies a central position in the structure of

DNA/RNA, and is of crucial importance in shaping their structure and dynamics, as evidenced by the

striking difference in properties between DNA and RNA which differ only by the chemical nature of

sugar. Previous research (Clowney, 1996) indicated that important changes occurring upon the

nucleoside conformational transitions are those related to the sugar moiety, whereas the base moiety is

relatively rigid structurally (Gelbin, 1996). Tetrahydrofuran (THF) is a prototype of heterocyclic five-

member-ring structures, and an important structural prototype (sugar) of carbohydrates and biological

molecules. However, conformations of THF, which are flexible along the pseudo-rotation path as a

function of the pseudo-rotation angle cp, have haunted structural chemists for many years due to

ambiguous experimental and theoretical results until very recently when Yang et al. (2007) diagnosed

the most popular conformation of THF in gas phase, jointly using experimental and theoretical EMS.

Cs conformer of THF C2 conformer of THF

Fig. 9 Structures of the pair of competitive conformers of Cs and C2 symmetry for tetrahydrofuran (THF) (Yang et al, 2007).

It is almost impossible to differentiate the three possible structures of Ci, C2 and Cj for THF without

combining experiment with theory. First, their total energy differences were within the error bars of

applicable quantum chemistry models; Second, the size of THF is prohibited from higher-level

quantum mechanical models such as CCSD(T); Third, most of their properties including dipole

moment are close in values among the conformations; and forth, experiments such as microwave and

far-infrared spectroscopy and photoelectron spectroscopy (PES) have been unable to identify the most

stable structure of THF without contradictions (Rayon and Sordo, 2006). The Cj conformer was

theoretically indicated as the most stable conformer of THF using a higher level model of MP2/aug-cc-

pVTZ (Rayon and Sordo, 2006), without solid experimental evidence. In our recent joint experimental

and theoretical EMS study (Yang et al, 2007), the configuration of Ci was found to possess imaginary

frequencies so that this conformation was excluded from the candidate conformers. Fortunately, due to

72

the point group symmetries of the C2 and Cs conformers, the highest occupied molecular orbital

(HOMO) of the C2 and C^ conformers of THF possess b and a symmetries, respectively, which can be

differentiated by EMS using the orbital MDs (Yang et al.2007) shown in Fig. 10.

0.08

^ 0.06

CO

CD

CD >

0.04-^

_C0

^ 0.02

0.00

0.0

• Exp

1 Cs12a'

2 C2 9b

0.5 1.0 1.5 2.0

Momentum (a.u.) 2.5

Fig. 10 Diagnostic of the Cs and C2 conformers of THF based on the symmetries of their HOMOs (Yang et al, 2007).

To resolve the valence space structure of THF, it is critical to further explore the structure and

function relationship for this sugar prototype. However, due to experimental difficulties, the outer

valence space of the THF conformers has not been fully revealed by EMS measurement at the moment

and further experiment with higher impact energies and better resolution is undertaking. From our

previous experience in 1,3-butandiene (Saha et al, 2003), it is likely due to thermal motion at the

temperature under the experimental conditions (usually room temperature), the pseudo-rotation

puckering of the sugar ring could be possible in gas phase. As a result, the Cs and C2 conformers of

THF may co-exist in a dynamic balance which can further complicate the experimental signal analysis.

We therefore, have taken theoretical examinations on the orbital based behavior in the outer valence

space (Duffy et al, 2007) of the C2 and Cs conformers, which hopefully could assist further

experimental analysis of the THF conformers in valence space, with insight electronic structural

understanding of the conformations of this important bio-molecular fragment.

6. Orbital Signatures of C=C Bond in Sugar Modified Nucleoside Antibiotics (Base+Sugar)

Bio-molecules such as nucleosides and analogues are significant in life science. Nucleosides consist

of a free base such as cytosine and a furanose type ring (sugar), connecting at the Nl position of

73

pyrimidine bases or the N9 position of purine bases by a p-glycosyl bond. Beside the basic nucleosides

of adenosine (A), guanosine (G), cytidine (C), thymidine (T) and uridine (U), numerous naturally

occurring and chemically synthesized or modified nucleosides—nucleoside analogues exist. As

consequences of minor modification in parent nucleosides, the analogues have very similar structural

and conformational preferences to their parent nucleosides. Many of them exhibit antibiotic activities

and have important medicinal and pharmaceutical applications (Isono, 1991; Matasuda & Sasaki, 2004;

Saran, 1998). Nucleoside analogue antibiotics easily get incorporated in growing chains of DNA/RNA

by mimicking their parent nucleosides to bring about the inhibition of protein, DNA/RNA syntheses

hereby exhibiting a wide variety of antiviral and anti-tumor properties (Saran, 1998).

One of the methods in medicinal chemistry over the past several years is to construct "drug-like"

small molecules or ligands (Ohlstein, et al, 2000). In a search for novel compounds for genotype-

specific effects, a pair of recently synthesized cytidine nucleoside antibiotics, sulfinyl cytidine

derivatives (SC-Dl and SC-D2) was reported by Torrance et al (2001). The chemical names of SC-Dl

and SC-D2 are given as r,2'-didehydro-3',4'-deoxycytidine (Structure I) and its isomer 3',4'-

didehydro-2',4'-deoxycytidine (Structure II) in a recent study (Wang, 2007b). Although the drug pair

was claimed (Torrance et al, 2001) to meet the standard criteria for drugs established by the National

Cancer Institute (NCI, USA, http://wwww.cancer.gov), very little information about the new drugs,

such as their chemical names, structures and relative stability, of the pair was known. The isomer pair

was originally described by library sources as sulfinyl cytidine (Torrance et al, 2001), but mass-

spectrometric analysis revealed that SC-Dl and SC-D2 represent deoxycytidine analogues containing

an unsaturated sugar moiety. At the discovery, it was unable to determine whether the C=C bond

resides at either V,T- or 3',4'-positions of the sugar ring, or if a mixture of both isomers was present

Torrance et al (2001). As a result, theoretical electron spectroscopy is applied for insight understanding

of the structure and functionality of new drugs.

The chemical structures of SC-Dl and SC-D2 differ only by the location of a C=C bond in the

sugar ring, as shown in Fig. 11. The C=C double bond makes the sugar ring less flexible for puckering

and as a result, both isomers exhibit flat sugar rings. The nucleoside pair possesses unusual sugar

structures as shown in the Cambridge Structural Database for nucleosides (Allen, 2002). It was found

(Roey et a l , 1993) that such a class of nucleosides with an unsaturated sugar ring often associates with

anti-AIDS and anti-cancer drugs. Therefore, insight structural understanding of the drugs is necessary.

Fully optimized structures of I and II molecules in 3D space are obtained using B3LYP/6-

311++G** model. Relocation of the C=C bond, from the CI '=C2' position to the C3'=C4' position in

the sugar ring, results in an energy lowering of 5.28 kJ-mol-1, indicating that II is more stable in

isolation than its isomer I, from an energy point of view. It is also found (Wang, 2007b) that the

positions of the C=C bond do not change the bond lengths noticeably but have significantly changed

the shape of the nucleosides in the 3D space. For example, perimeters (Wang et. al, 2005) of the

hexagon and pentagon rings, R6 and R5, remain almost unchanged in the isomers. The C=C locations,

either C r = C 2 ' or C3'=C4', do not alter the number of C-C and C=C bonds in the respective rings of

the isomers. Anisotropic properties such as dipole moments (\i) exhibit a large variation of 1.25 D

74

between the two isomers, from 6.79 D in 1 to 5.54 D in 11, which suggests that the isomer pair maybe

able to be characterized by their dipole moment, as Nguyen and Pratt (2006) implemented.

S>-^ OK

1',2-D3C H „ H

.X O^ « •

J^^.

o

5.28 kJ mol 1

3',4'-D3C

Fig. 11 Chemical structures of the SC-Dl (I) and SC-D2 (II) of the drug isomer pair (Wang, 2007a).

Valence ionization spectra of the isomer pair were further investigated from single point

calculations using the SAOP/pVQZ model (Schipper et al, 2000; Chong et al, 2004), which shows the

approximately satisfactory of the Koopmans' theorem (Gritsenko et al, 2003). The highest occupied

molecular orbital (HOMO) and next HOMO contain interesting structural information to differentiate

the isomers in their ionization energies. For example, the first ionization energies for 1 and 11 are 9.48

and 10.06 eV, respectively, a difference of 0.58 eV which is within the resolution of a number of

experiments such as PES and EMS. Fig. 12 indicates that the orbital electron density contours of 1 and

11 indeed show a very different features in their HOMOs. Further theoretical investigation for their

orbital based chemical bonding mechanism is under investigation.

HOMO of Structure I HOMO of Structure II

Fig 12 Orbital electron density distribution of the HOMOs of Structure I and Structure II. The bonding mechanisms in this orbital is very different: with HOMO of Structure I concentrating on the C=C bond of the sugar moiety whereas with the HOMO of Structure II depositing on the base ring (Wang, 2007a)

75

7. Extension of Atoms-in-Molecules: Fragment in Molecules

Progress requires a quantitative understanding of all different fragments, as many biologically

relevant molecules have their basic skeleton as an aromatic ring with a short alkyl or alkylamine side

chain. In proteins, the smallest amino acid is glycine whereas the smallest and most abundant aromatic

residue is L-phenylalanine. Recent data mining experiments have shown that amide-aromatic

interactions of phenylalanine are very important in the stabilization of protein residues over large

configurational spaces (Duan et al, 2002). L-phenylalanine can be considered as one of the hydrogen

atoms of benzene is replaced by L-alanine. The latter (L-alanine) is considered as the product that a

hydrogen atom of glycine on the C atom is replaced by a methyl (CH3) group (Falzon et a l , 2006). It is

useful if one could determine which orbital or a group of orbitals in both core and valence space

approximately belong to which fragment. The knowledge of fragments in bio-molecules will largely

enhance rational drug design.

sia -

4QQ-

44a -

4 3 0 -

2?Q-

D-H

27H

CO_H

B e n z e n e a l a n i n e P h e n y l

Fig 13 Core orbital ionization energy diagrams of benzene, alanine and phenylalanine. The pattern clearly demonstrates an interesting pattern and association of the three species.

76

Ground electronic state configurations of glycine and L-alanine indicate that three more molecular

orbitals (MO) are in L-alanine than in glycine: one in the core space and two in the valence space

(Falzon et a l , 2006). From our previous work on L-alanine and glycine, we are able to determine

which groups of orbitals are responsible for the glycosyl fragment, for the methyl fragment and for the

interactions of the two fragments, approximately. Here we extend this method to study the association

of canonical L-phenylalanine (Phe-X, ^ A ) , L-alanine and benzene. Figure 13 gives the core orbital

energies of the three species generated using the DFT-B3LYP/6-311++G model. It is interesting that

the core orbital energy patterns of Phe-X and L-alanine are very much assemble, whereas the core

orbitals of benzene are very much "degenerate", which in fact, split into a 1,2,2,1 fold of four lines with

better resolution which will be discussed further elsewhere (Wang et al. 2007). From this figure, it is

learned (1) the L-alanine "fragmenf contributes to the apparently split into a core orbital energy band

of the phenyl fragment of Phe-X, due to the symmetry lowing as a result of the interaction with the

alanine fragment; (2) chemical shift in core orbital energies indeed provides some useful information

related to the chemical environment of a particular element.

In the valence space, similar to L-alanine, glycosyl and methyl (Falzon et al, 2006), the valence

orbitals of Phe-X can be divided into alanine related (group I), phenyl related (group II) and mixed

(group III) orbitals. Figure 14 (a) gives a representative orbital in the alanine related group I, orbital

22a for alanine and orbital 40a for Phe-X. The orbital TMDs in the same figure indicate that the

attachment of the phenyl fragment does not show sufficient impact on this alanine dominant orbital and

its 71-like bonding character. Figure 14 (b) shows that a doubly degenerate benzene orbital, 3e2g, splits

into two orbitals of 38a and 39a in Phe-X, as a result of the high point group symmetry of benzene

(Dgh) reduction (Ci) in Phe-X. The orbital TMDs and electron density distributions of the four related

orbitals in this figure, clearly demonstrate the phenyl fragment in L-phenylalanine. Therefore, amino

acids are not only important as building blocks of life, but also provide important information for us to

understand basic science such as chemical bonding mechanisms.

77

Ala | M 0 22a)

3 4.0x10 Id

C a

n E 3 C u E a

Id

o

2.0x10

15 Azimuthal Angle ^f

he | M 0 4Da|

30

Fig. 14 (a). Evidences in orbital MDs in momentum space and orbital electron density distributions in position space of the associated orbitals 22« of alanine and 40« of phenylalanine. It has quantitatively demonstrated "fragment in molecule" model.

E •

3 J3

° 2.3x10"'

30 Phe (MO 39a)

Azimuthil Angle ^f

Fig. 14 (b). Orbital MDs in momentum space and orbital electron density distributions in position space of a doubly degenerated orbital 3e2g of benzene, which splits into two orbitals of 38« and 39« in phenylalanine. It has quantitatively demonstrated "fragment in molecule" model.

78

CONCLUSIONS

Dual space analysis is a powerful technique associated with electron momentum spectroscopic

analysis and interpretation. It consolidates the association between theory and experiment through the

predictive power of quantum chemistry and validity power of experiment; connects information in

coordinate space and momentum space through a Fourier transform (FT); facilitates interpretation of

electronic structure in terms of one-electron concepts through the association of Dyson orbitals to

electron binding energies in molecular orbital theory; and achieves quantitative assessment of wave

functions (orbitals), which has long been a challenge for quantum chemistry (Eugen Schwarz, 2006).

The present review gives a few examples of the applications of DSA to bio-molecules.

ACKNOLEDGEMENT

I would like to acknowledge the Vice-Chancellor's Strategic Research Initiative Grant of

Swinburne University of Technology (2004-2006), which enabled me to reshape of my research in the

past few years. I would like to thank Vice-Chancellor's Research Award in 2006 for the recognition of

the work done. Australian Research Council (ARC) is acknowledged for research grants through the

Discovery Project and International Linkage Schemes. The Australian Partnership for Advanced

Computing (APAC) should be acknowledged for using the state-of-the-art National Supercomputing

Facilities.

I sincerely wish to thank my advisers and collaborators for their support and contribution to the

work in the review. In particular, I wish to thank A/Prof M. J. Brunger for his long term collaboration

and constant support in the past decade. The excellent contribution of Dr. M. T. Downton, Dr. C. T.

Falzon and Dr. K. Nixon (postdoctoral fellows), Mr. S. Saha and Mr. D. Jones (Ph.D. students) is much

appreciated.

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