Base Pair

The excited states of the double hydrogen bond in the adeninethymine nucleotide base pair has been investigated in the semiempirical CNDO/S-CI approximation. Double-minimum potential curves are obtained for several nuclear configurations characterizing simultaneous tautomeric rearrangements of the NH-N and 0-HN bonds. The energy profdes for the coupled movement of the hydrogen bonding show that the Watson-Crick configuration of the adenine-thymine base pair is the most stable for all of the excited states studied. Estimates are made within the WKB approximation of the tunneling rate and tunneling probability. The results indicate that increasing the energy of the excited states would increase the probability of double protonic transfer by tunnel effect and thus for irreversible mutation. A comparison of the composition of the potentials for the single movement of the protons with the double-minimum potential of the concerted movement shows that the potential is nonseparable. The shortcomings that follow from the WKB approximation as applied to the present problem are discussed.

a sufficiently high concentration of unligated silver adatoms that their incorporation into the lattice occurs at an appreciable rate. It should be noted that even at -0.6 or -0.7 V the Raman intensity slowly decays.
Our hypothesis is that metastable adatoms are created during, or perhaps immediately after, an ORC and are trapped by complexation before they can merge into the metal lattice. These surface complexes are the Raman active sites. This picture explains qualitatively why an ORC is required for SERS, the decrease in intensity at negative potentials, and the irreversible quenching at very negative potentials. The dependence of the number of surface complexes on the halide concentration also explains why water spectra have only been observed at high salt concentrations. With water's small Raman cross section and interference from bulk water, a large number of Raman active surface complexes is needed to produce an observable signal. Other factors, e.g., surface topography, also contribute to the SER effect, but an adatom-adsorbate complex seems to be a necessary component in electrochemically generated SERS. Further investigation is required to confirm this hypothesis and to determine whether this mechanism is a general feature of SERS or is operating only in a few specific cases.
As previously noted, the behavior of the Cu-X (X = C1, Br) spectra is generally similar to the corresponding Ag systems, but there are differences. The replacement of chloride by bromide (see Figures 5 and 6) does not result in a spectrum with bands shifted to lower frequency according to the mass ratio of the halide ions. This implies a difference in the structure of surface complexes on copper and silver, which may be related to the different solution chemistry of these metals.

Introduction
The prevalence of hydrogen bonding in chemical and biological systems has led to extensive research into the nature of this interaction by various techniques including molecular orbital methods. In the majority of these studies, the interacting species have been connected by a single hydrogen bond.2 There are, however, a number of  bases and their analogues has been partly motivated by the proposeed relationship between the presence of the rare tautomeric form of the base and point mutations that occur during replicati~n.~-~-~ Lowdin: in effect, suggested that hydrogen-bonded protons can be transferred from one base of DNA to its complement and may play a key role in mutagenesis. These transfers, which could take place either via quantum-mechanical "tunneling" or via more classical means, were proposed to lead to a pair of "rare" tautomeric bases that might be "read" incorrectly during the replication process and result in an altered form of the original DNA molecule. Early molecular orbital studies of DNA base pairs"12 assumed separability of the u-and ?r-electron systems. In this approximation, single proton transfers between the bases were found to be characterized by double-well potentials'l as was assumed by Lowdin. More recently, however, an ab initio all-electron calculation of the guanine-cytosine pair13 yielded a single-well potential for the transfer of each proton taken one at a time. In an effort to examine multiple simultaneous transfers, the calculations were extended to the study of the hydrogen bonding of the formic acid dimer. Clementi et al.I3 found that a single transfer, which leads to a pair of charged species, is characterized by a monotonically increasing energy function. The double transfer was examined by synchronously coupling the motions of the two protons. This preserves electroneutrality in both species and results in a double-well potential. It was thus concluded that double proton transfers are more likely to produce double-well potentials than are single transfers.
Double-minimum potentials are probably also produced by simultaneous transfer of both protons in singlet and triplet excited states when the nucleic base pairs are exposed to UV electromagnetic radiation. In fact, Lamola et have proposed the phosphorescence of DNA to be a consequence of the double proton transfer in the adenine-thymine base pair. Semiempirical calculations of the double-minimum potential in excited states for the guanine-cytosine pair were performed by Rein et al.lOJ1b Later, Blizzard's CNDO/2 calculations seemed to confirm the hypothesis of a double-well potential for the simultaneous transfer of only two protons (upper protons) in the ground state. An extension of the calculations to singlet excited states using the singly occupied virtual orbital approximation seemed to yield no double well. 15 Since the spectral properties of the bases are chiefly caused by ?r electrons, interpretations of the electronic spectra may be given within the framework of quantummechanical calculations of a-electronic excitations. Since the middle of the 1960s a number of calculations on the a-electronic excited states of nucleic bases have been publisheda4J6 Most of these calculations were performed by the CI method using the SCF orbitals, and only singly excited configurations were taken into account. Early studies" including a number of doubly excited configurations seemed to have no significant effect on the calculated spectrum. However, a series of important spectroscopic features points out that the knowledge of ?r-electronic wave functions is not sufficient. In this connection the study of the excited singlet and triplet states of the bases with the help of the CND0/2 method, which permits one to directly take into account the interaction of all valence electrons, has also been ~n d e r t a k e n .~~J~ The controversy between different approximations, which was illustrated in a previous paperm for the ground electronic state study, has become so central to the interpretation of hydrogen bonding in nucleic base pairs that the challenge of studying excited states is irresistible. Therefore, considering the scarcity of theoretical results that enable one to prove the possible existence of the double proton transfer in excited states of the nucleic base pairs, as well as a hypothesis of phosphorescence in and taking into consideration previous results related to the tautomerization equilibrium of the isolated bases in excited electronic we have undertaken a systematic study of the coupled proton transfer in both singlet and triplet excited states of the adenine-thymine base pair. Part of this program is reported in the present paper. In order to analyze the possibility of an error mechanism in the genetic code caused by nonradiative processes, such as donor-acceptor interactions between DNA and chemical mutagens, as well as radiation damage, we also include our findings on the tunneling and tautomeric equilibrium of the NH-N and O.-HN bonds in the base pair.

Method of Computation
All valence electron semiempirical theories are widely used for a variety of purposes. The underlying theory is contained in the early CNDO papers of Pople and coworkers,22 but a large number of modifications and new parameterization have emerged23 in attempts to develop reliable calculations of ground-and excited-state properties. An important success of CNDO-type theories is that they offer a general scheme for further development. Thus, the natural hierarchy of approximations from CNDO to NDDO and their various modifications such as CNDO/S and MIND0 all fall within the original framework. For many small molecules, semiempirical theories have been superseded by ab initio calculations either of the STO-NG type or by a more extended CI treatment. However, for moderate-and large-size molecules, these calculations are highly costly and not necessarily more reliable than semiempirical theories. This is particularly true for excited-state properties where ab initio calculations encounter extreme difficulties and where conflicting results have been reported even for small molecules.24 In contrast, semiempirical theories have for many years provided reliable spectroscopic calculations that have found widespread applications. It has been found, for example, that a-electron theories provide a good qualitative understanding of the spectroscopic properties of visual pigm e n t~;~~ however, there are a large number of related problems, such as the description of excited states of the nucleic base pair for which all valence-electron calculations are mandatory.

Excited States of H Bonds in the A-T Base Palr
The failure of the CNDO/2 approximation to correctly reproduce u-a separation in planar conjugated molecules seemed to be a particularly severe breakdown in the theory.
An incorrect ordering of the u and a eigenvectors is obtained,23c and higher approximations such as INDO or NDDO are not expected to introduce significant improvement. Yet u-a separation seems too fundamental a property to be missed at any level of approximation. Since the CNDO/S-CI method does account for a-a sepby removing unnecessary restrictions on the original parameterizations, we have chosen to use this approximation for a description of the singlet and triplet states of the adenine-thymine base pair. It is one of the best methods available at present to study the electronic transitions of large molecules, enabling us to follow the general NDO procedure and making it possible to use a standard Hamiltonian which is applicable to a wide range of problems, minimally including optical spectra, multiplet splittings, oscillator strengths, excited-state charge, and bond-order matrixes; further ground-state information has recently been shown to reproduce closely ab initio calculations.20 The numbering structure of the hydrogen-bonded system under consideration is shown schematically in Figure  1. Bond lengths and angles were obtained from Sutton2' and references cited there. The interatomic distances for the atoms involved in the hydrogen bonds were taken from Arnott et a1. 28 Excited-state wave functions were generated from the ground state occupied and virtual orbitals through a configuration interaction procedure between the 30 lowestenergy, singly excited states.% It was felt that inclusion of more Slater determinants would probably not qualitatively alter the present findingsS3O The problem is some of these s t~d i e s~l~l -~~ is that, since the exact geometries of the rare tautomeric forms are not known experimentally, the energies were determined by using assumed geometries, which retained the ring structure of the normal form for the rare form.

Results and Discussion
On theoretical grounds the detailed description of the proton transfer or exchange in hydrogen-bonding systems seems to include two separated steps. The first step is to calculate the potential energy surface for the proton motion. The second problem is to solve the equation of motion for protons on a given potential surface and to evaluate the equilibrium constant or the rate of proton transfer after statistical averaging. In order to describe the first step, one has to define the reaction coordinate, the curve leading from the bottom valley of the initial state over the transition state to the valley of the final state on the potential energy surface inherent to the system concerned. To this end protons H29 and H30 (Figure 1) were allowed to move independently along the lines joining Nlo and 022 and joining N1 and NI5, respectively. All other nuclei were held stationary.
The potential energy curves are shown in Figures 2-5 for both a*u and a*a singlet and triplet excited states as a function of the distance X, defined as an orthogonal transformation of the distances of H29 and H30 to Nlo and N15, respectively, in the following way: (1) An isoenergetic scheme of the path followed by the coupled movement of the protons involved in the double hydrogen bonding as given by eq 1 is shown in Figure 6.
In the adenine-thymine base pair there are 10 carbon atoms, 7 nitrogen atoms, 2 oxygen atoms, and 11 hydrogen atoms. These add up to 98 valence electrons, 76 in socalled u orbitals and 22 in so-called a orbitals. (More correctly, neglecting the methyl group on thymine, the adenine-thymine pair is taken as a planar molecule with reflection symmetry in the molecular plane; therefore, the molecular orbitals are of A and B type; the 38 doubly occupied A orbitals are those commonly labeled as u orbitals; the 11 B orbitals are those commonly labeled a orbitals . ) 34  Unfortunately, no experimental technique will, at present, allow the detection of a rare tautomeric form present in proportions as low as lo4. In principle, this can be solved by means of theoretical calculations of the electronic transitions along the reaction coordinate. Although these studies may not be relevant to tautomeric equilibria in biological systems, they may lead to a better understanding of biological processes where tautomerism is supposed to be involved. Naturally, conclusions obtained in such a way cannot be quantitative; they are heuristic in their character and they allow us to come to   Le., they are intramolecular in nature, except the 4a*x and 11r*a transitions of the rare tautomeric form.
In fact, the 4x* + x transition is produced exclusively by the promotion of one electron from HOMO (T) to LUMO (A); the lla*x transition is due to the electronic promotion from HOMO (A) to LUMO + 4 (T). These transitions are strongly associated with the behavior of the two protons of the hydrogen bonds, NH-N and O-HN, since they are generated by the promotion of electrons localized in mixture orbitals, lone pair and x of adenine to localized orbitals in double bonds of thymine (C=O and C=C bonds). That is, an optical transition between levels originating from different bases would involve a charge transfer between the two bases. The same trend is observed in the A* + x triplet transitions ( Figure 5). Here the lowest energy transfer for the normal form is predicted to be 2.1 eV and that of the tautomeric form is calculated to be 4.1 eV. We can anticipate increased stability of the normal form relative to the right.
Similar effects are probably expected if the heavy atoms of the bases are allowed to relax their positions as the proton transfers occur. This alternative, although achievable in principle, would have been an exceedingly laborious procedure and was not considered in the present work. Calculations on the formic acid dimer35 in fact . Scheiner and C. W. Kern, Chem. Phys. Lett., 57,331 (1978);  (b) S. Scheiner and C. W. Kern, J. Am. Chem. SOC., 101, 4081 (1979). suggest that the barriers to double proton transfers may also be facilitated by uncoupling the motions of the protons or by zero-point vibrational deformation^.^^ All of these effects would tend to reduce the CNDO/S-CI barrier in both the ground and excited states.
As far as the a*u singlet and triplet transitions (Figures 2 and 4) of both normal and tautomeric forms is concerned, they are due to the promotion of electrons delocalized on both bases to orbitals localized in a single base a* (A or T) +-a(D). The delocalized u orbitals have a strong component of the lone-pair electrons belonging to the hydrogen bonds.
Previous ab initio c a l c~l a t i o n s~~~~~~-~~ have found the highest occupied and lowest unoccupied molecular orbitals (MOs) of each base to be of a symmetry. Our CNDO/S-CI calculations indeed agree with this result; in addition, we find the highest occupied and lowest vacant MOs of the A-T base pair to be of a symmetry as well. Clementi et al. 13 have reached a similar conclusion for the highest occupied MO of the guanine-cytosine base pair. First ionization potentials are thus predicted to be of a symmetry, and excitations of lowest energy are of a*a type. A more specific result of this method concerns the status of the lone pairs. Thus, although atomic "lone pairs" do not exist as such (pure) in molecules, the analysis of the coefficients of the atomic orbitals in the MOs shows very neatly that a large amount of "lone-pair character" may be assigned to the highest u levels in these heterocycles. Although deeper in energy than the highest a level, these "lone pairs" (or combined lone pairs) appear more ionizable than the other u electrons, with oxygen lone pairs more ionizable than nitrogen lone pairs.
The characterization of a double-minimum potential, typical of a double transfer, is given by the barrier height V and upper well height A. The variation of these parameters as a function of the energy of the normal form for each excited state (singlet and triplet transitions) below 10 eV is given in Figures 7 and 8.
The behavior of the barrier height V (Figure 7) for both the a*u and T*a singlet and triplet transitions is quite different from that shown in Figure 8 for the vari-  . Mely and A. Pullman, Theor. Chirn. Acta, 13, 278 (1969).  (40) L. C. Snyder, R. G . Shulman, and D. B. Neumann, J. Chern.   Phys., 63, 256 (1970).  1.27 X 10" 0.86 X 10" 2.81 X 10' 6.57 x 1 0 -2 7 1 ( n * +-u ) 14.42 2.98 X 2.16 X 1 0 " 1.04 X 10" 1.05 X 10' 9.50 x 1 0 -3 3 1 ( n * + n ) 16.57 4.05 X 10"' 1.22 X 10" 0.86 X 10"  profiles at energies below the ionization energy of the orbitals is involved in the transitions. The above-mentioned behavior of the singlet transitions is also observed for the triplet states. As suggested,14 the two-proton transfer in the A-T pair under irradiation can also be a cause of the phosphorescence band of DNA. Realization of such a possibility would mean that in the triplet state the two-proton mechanism takes place. 41 Equilibria and Tunneling. Although most experimental genetic systems do not require quantum theory for interpretations,@ the experiments of Freese and Freesea and KornbergU indicate that the high fidelity of DNA replication is due to an extremely sensitive hydrogen-bonddirected base-pairing process where any misincorporations are enzymatically connected afterward by "copy-editing" These enzymes would apparently discriminate against rearranged proton-electron configurations of the template strand which would therefore decrease the probability of observing most biological consequences generally associated with the replication of unusual tautomeric bases. Experiments designed to investigate the microscopic model7 of genetic information must therefore take into account the possibility of enzymatic masking of proton-electron arrangements which could have occurred before replication. Other experimental difficulties are exemplified by the fact that experimental investigation of proton tunneling reactions47 in well-defined chemical systems was delayed 20 yr after Bell4* formulated the process in terms of basic theoretical and experimental principles. This delay was not due to an absence of proton tunneling reactions but to an absence of "proper" experimental methods.49 Efforts to detect proton tunneling in a complicated ill-defined in vivo environment should likewise eliminate all possible "experimental difficulties" associated with detection. Thus, it is not surprising that direct experimental investigation of the microscopic model of genetic information is scarce; nevertheless, theoretical investigation^^^ continue to imply that quantum-mechanical properties of genetic information may be required to explain particular biological observations. However, the fact that the immediate environment of an in vivo molecular genetic system is essentially unknown severely restricts the information contained in most atomic and molecular model calculations. Thus any real qualitative success with such models is considered significant. Therefore, we have decided to investigate the tunnel effect in both singlet and triplet excited states of the A-T base pair in both normal and tautomeric forms.
The modes of proton transfer investigated thus far have allowed no motion of the heavy nuclei which were assumed to be stationary. Since the much bulkier atomic framework of the base pair is considerably less mobile than the protons being transferred, this is expected to provide a reasonably good basis for studying quantum-mechanical tunneling.
Rein and Harris" have estimated the equilibrium proportions of the tautomers formed as a result of the transfer of upper protons in the guanine-cytosine pair. They have also computed the times required for each of these protons to tunnel to the complementary base. Their results were based on semiempirical molecular orbital calculations on (primarily) the 9-electron system of the base pair which yielded double-well potentials for single proton transfers, contrary to the all-electron calculations reported by Clementi et al.13 and by Scheiner et al.35 in the ground state. Since our all-valence electron calculations of the double transfer in the excited states do, by contrast, yield double-well potentials, we have computed values for the equilibrium constant as well as the tunneling time and the classical oscillatory frequency associated with these modes.
The application of kinetic and quantum-mechanical principles to tunneling and equilibria in double-well potentials has been summarized in a convenient form by L O~d i n .~ The probability of an incident particle tunneling through a barrier is, in the WKB approximation, dependent upon the quantity are presented in Tables I and 11. Details of the meaning of and the assumptions made in the explicit calculation of the barrier parameter (eq 2), the tunneling probability g, the left and right oscillation frequencies fN and fT, the tunneling time 7 , and the equilibrium constant K have been described in a previous paper20 and will not be repeated here.
In these calculations we have neglected the correction due to zero-point vibrational energy in both minima for each excited state; i.e., it was assumed that the energies can be taken directly from the values corresponding to the minima. Of course, this assumption does not change the character of the values given in Tables I and 11.
It is evident that, if the time required by the proton to tunnel through the potential hill in the medium of the hydrogen bonds of the A-T base pair is small as compared to the lifetime of a singlet excited state s), the conditions will be particularly favorable for the appearance of ionic tautomeric forms and thus for irreversible mutation. In fact, the 13a*u singlet and triplet transitions (Tables I and 11) show that there exists a finite probability of double proton tunneling tautomerization which could be responsible for the partial loss of the genetic code. This is particularly true for the triplet state, since its lifetime is much longer than that of a typical singlet state.
The present calculation as proposed by Lowdin' is based on the phase-integral approximation, sometimes called the WKB method51 for unidimensional physical models, assuming that the barrier penetration is due to the movement of one proton in just one potential well. More generally, the problem which we are dealing with here is that of the double simultaneous displacement of two protons in both hydrogen bondings of the A-T base pair, in which the resulting potential is a two-dimensional double-minimum potential V(xl,x2) (see Figure 9).
According to the physical model proposed in Figure 9, the Hamiltonian of two particles (two protons) can be written (3) where x1 and x 2 are the support lines of the classical trajectories which contribute to the tunneling process. It can be observed that these two lines are not parallel, so that the coordinate of proton 2 can be expressed as a function of an angular parameter 4 x 2 = x1 + d sin 4 (4) Therefore, the Hamiltonian takes the form (3) potential of the hydrogen bond Ha; (4) sum of the potentials of the hydrogen bonds Ha and H, .
All curves refer to the ground state.
Clearly, the WKB method cannot be applied to the two-dimensional potential V(xl,r$) since this is a nonseparable potential. This means that the potential cannot be described as a sum of potentials of just one hydrogen bonding Vi(x), i.e.

(6)
The justification of the nonseparability of the potential V(xl,4) is found in the following facts. From the atomatom bond index curves of the A-T base pair for the single displacement,m a net transfer of electronic charge can be observed in the opposite direction to that of the proton's movement. On the other hand, the curves for the coupled motion of the two protons show the protonic and electronic currents to cancel each other, thus making the total current in the ring comprising the two hydrogen bondings and the rest of the system vanish. Therefore, it is not possible to decompose the concerted movement of both protons as the sum of the movements of each of them. A second justification is found by comparing the composition of the potentials for the single movement of the protons with the double-minimum potential of the concerted movement ( Figure 10).
It can be clearly seen that the sum of the potentials is not equal to the potential of the concerted movement of both protons. Further, a cooperativity effect seems to operate, since the potential due to the movement of a single proton is determined by the position of the second one in the other potential well. In Figure 10 it is considered that, when a proton is moved along the line constituting the hydrogen bond, the other is in its normal position; Le., the minima coincide with those of the potential of the coupled motion of both protons; in this case the coincident minimum represents the normal position of the A-T base pair. A similar result could, of course, be obtained if the movement of one proton is performed as the second one is in the tautomeric position, giving the same relative context, there exists the possibility of simultaneous double proton tunneling tautomerization for excitation energies higher than 12 eV. This is particularly true for the triplet state (see Table 11).
The tautomerization processes must have other origins, Le., electronic charge transfer derived from donor-acceptor interaction with other molecules or ionization effected by radiation.
The effects just discussed, though important, are probably less significant than the uncertainty in rate introduced by limitations of our knowledge of the barrier shape. Actually, if it should be possible to analytically represent the potential V(X,$J), the problem of calculating the tunneling process could be carried out by using the different methods that at present are available. Among these can be mentioned the one developed by Gutzwillelb2 as applied to single-minimum potentials of multidimensional and nonseparable problems. More recently, Colemanm working in Minkowski space and in four-dimensional Euclidean space" has shown that the double-well problem is closely related to the concept of "instantons" or "solitons", what should be the solution of the equation of motion for a classical particle in a symmetrical double-minimum potential as shown in Figure ll. Thus, when a rotation of the time to a Euclidean imaginary time is performed, the potential V(x) is inverted to -V ( X ) .~~ On making use of this idea, ChangM studied the tunneling phenomenon involving two degrees of freedom. He found the most probable escape path in phase space (which links the initial and final states) and the classical trajectories between the relative maxima and applied this philosophy to the classical problem of the inversion of ammonia.
Another factor not explicitly considered in the present work is the sensitivity of fN, fT, T , and K to the barrier shape since different approximations could lead to results qualitatively not concordant. For this reason, the double proton tunnel tautomerization may be considered an interesting subject not concluded yet, and as such it would deserve more attention as a possible source of nonradiative process. Finally, the role of H bonds in the hypochromism of the double-stranded polynucleotides calls for further studies of model compounds. A study along these lines is underway and will be published at a later time.