Ab Initio Study of the Two-Photon Circular ... - ACS Publications

446

J. Phys. Chem. B 2007, 111, 446-460

Ab Initio Study of the Two-Photon Circular Dichroism in Chiral Natural Amino Acids Branislav Jansı´k† and Antonio Rizzo* Istituto per i Processi Chimico-Fisici del Consiglio Nazionale delle Ricerche (IPCF-CNR), Area della Ricerca, Via G. Moruzzi 1, I-56124 Pisa, Italy

Hans A° gren Theoretical Chemistry, Royal Institute of Technology, Roslagstullsbacken 15, SE-10691 Stockholm, Sweden ReceiVed: August 18, 2006; In Final Form: October 18, 2006

Two-photon circular dichroism spectra calculated within an origin-invariant density functional theory approximation in the absorption region where the lowest electronic excited states appear are presented for all 19 essential amino acids in the gas phase. A comparison of intensities and characteristic features is made with the corresponding two-photon absorption and one-photon circular dichroism spectra for each species. Also, the contributions of the electric dipole, magnetic dipole, and electric quadrupole transitions to the rotational strengths are analyzed in some detail. The remarkable fingerprinting capabilities of the two-photon circular dichroism spectroscopy are highlighted.

1. Introduction Chiral molecules exist in two mirror-image forms that cannot be superimposed by simple rotation. A collection of chiral molecules shows circular dichroism due to electric-dipolemagnetic-dipole interactions and therefore interacts differently with left- and right-handed circularly polarized light.1-3 Since many biological molecules are chiral, linear circular dichroic (also known as electronic circular dichroism, ECD)3,4 spectra have been commonly used in biochemical research, often providing complementary structural information to what can be obtained from X-ray Bragg refraction or nuclear magnetic resonance experiments. The chiral feature thus has important consequences for the fingerprinting of enantiomers of drug molecules or the analysis of proteins where the identification of amino acid left- or right-handed forms often can be accomplished by the recording of a CD absorption spectrum. CD can also occur for achiral molecules or even within the dipole approximation, as long as the experimental setup as a whole is chiral. In recent years increasing attention has been given to nonlinear optical processes,4-7 whose combination with circular dichroism can provide new and unexpected applications in biological and materials research. Among a great number of effects or processes, two-photon absorption8,9 and secondharmonic generation4,7 constitute nonlinear processes that would be most interesting to study in this respect. Two-photon absorption (TPA) is based on the probability that two low-energy photons will simultaneously arrive at a fluorophore and induce a coherent electronic excitation normally obtained by a single high-energy photon so that, for example, the simultaneous absorption of two red photons will excite a molecular ultraviolet transition. This brings about 3D confocality and a substantially improved penetration depth as compared with linear absorption. * Corresponding author. E-mail: [email protected]. Tel.: +39-050-3152456. Fax: +39-050-315-2442. † Current address: Teoretisk Kemi, Kemisk Institut, Aarhus Universitet, Langelandsgade 140, 8000 Aarhus C, Denmark. E-mail: [email protected].

These features have been utilized in various applications in biological research for collecting information from subcellar events within organized tissue environments with deep imaging into tissue, while restricting the phototoxicity and so-called photobleaching (photooxidation) to the area being imaged. Thus we speculate that this 3D confocality and penetration aspect of two-photon absorption can bring in new applications if combined with the fingerprinting of circular dichroism as a new tool for biomolecular recognition. So far TPA has been almost exclusively applied to nonpolarized or linear polarized light. On the other hand, TPA possesses very particular polarization dependencies, the most apparent difference with respect to linear absorption being that the cross section is polarization-dependent even for randomly oriented molecules.4,10,11 However CD, i.e., the differential absorption of circularly polarized light,12,13 has attracted to date less attention in connection to TPA. Two-photon absorption circular dichroism (TPCD), i.e., the difference in two-photon absorption of left and right circularly polarized light, is closely related to the phenomenon of circular intensity difference in Rayleigh and Raman scattering predicted by Barron and Buckingham.14 It was analyzed by Tinoco,15 Power,16 Andrews,17 McClain,11 and Harris.18 In refs 19 and 20 we have presented an approach, based on modern analytic response theory, which enables an ab initio determination of TPCD with accuracy and efficiency. On the experimental side, there is a very limited amount of data available, as two-photon circular dichroism is an effect on the detection edge, and until recently experimental evidence has been scarce. That situation has now changed with the development of the modified Z-scan techniques by Markowicz and co-workers.21 As follows from the works of Markowicz and co-workers, the measurement of nonlinear circular dichroism is a delicate undertaking. This refers not only to the general sensitivity and small size of the effect per se but also to the fact that there are a number of competing nonlinear processes that can interfere in the measurements, such as light-induced linear birefringence and dichroism due to the light-induced orientation of molecules (see for instance refs 2226), which are intensity-dependent. The outcome in terms of

10.1021/jp0653555 CCC: $37.00 © 2007 American Chemical Society Published on Web 12/19/2006

Circular Dichroism in Chiral Natural Amino Acids

J. Phys. Chem. B, Vol. 111, No. 2, 2007 447

an average quantity will also be dependent on the particular phase of the sample. Thus, a reliable instrument for theoretical prediction could be valuable for separation of the different contributing mechanisms from the observable effect. Nonlinear circular dichroism has been seen in liquids of chiral molecules in single-beam experiments where polarization is modulated from circular right-to-left and in pump-probe experiments where the modulation of the polarization of the probe (or pump) yields pump-induced CD on the probe.27 Also, multiphoton optical rotatory dispersion28 and two-photon optical rotation29 have been observed, the latter process being theoretically related to TPCD through the Kramer-Kro¨nig relation. Using the tools developed and discussed in our recent work,19,20 we present here a comprehensive ab initio study of two-photon absorption circular dichroism for the chiral amino acids commonly occurring in nature. These all have a common backbone of a carboxylic acid group and an amino group attached to a saturated carbon atom referred to as the R-carbon. Although over 300 amino acids are present in nature, only 20 of them are commonly found as constituents of mammalian proteins. These amino acids cannot be synthesized by the organism from other available resources and must be supplied from outside. They are therefore known as the essential amino acids. In this work the qualitative trends among the spectra of the amino acids with similar chemical character are identified, and their spectral features, to be observed in the gas phase, are compared mutually and also with the corresponding ordinary two-photon absorption spectra on one hand and with the linear absorption dichroic spectra on the other. The relative contribution of the electric dipole, electric quadrupole, and magnetic dipole transitions to the rotational strengths is also analyzed in some detail. The comparison of the three spectroscopies is used to indicate which kind of additional fingerprinting capability of TPCD can be expected with respect to ECD and TPA. 2. Theory Two-photon circular dichroism arises from the difference in TP two-photon absorption of left (δTP L ) and right (δR ) circularly polarized light. The symbol δ indicates the two-photon absorption coefficient, and its CGS units are cm4 s mol-1 photon-1. The phenomenon, which is part of the vast area of high-order optical activity,30-34 has been theoretically described by Tinoco,15 Power,16 and Andrews17 in the 1970s. In ref 19 we have given the definitions and discussed our computational approach to the ab initio determination of TPCD spectra. In ref 20 we presented a selection of origin-invariant approaches, of which the one based on Tinoco’s original formulation,15 labeled as the “TI” approach, is employed in our present study. In this section we therefore briefly outline the theory. A full derivation is given in refs 19 and 20. 2.1. Definitions. Two-photon absorption circular dichroism is a differential effect observed when two photons (in our case, of equal frequency ω), at least one of which being of circular polarization, are absorbed, inducing a transition from the initial state | 0〉 to the final state | f〉 (pω0f ) 2ω is the energy difference). The difference in absorption can be written, following the original expression of Tinoco 15,20 as TP δTP L - δR )

2 2 4 (2π) ω g(2ω)NA f TP R 15 c03(4π0)2

(1)

where fRTP is the two-photon circular dichroism rotatory strength. In eq 1, g(2ω) is the normalized line shape, NA is

Avogadro’s number, c0 is the speed of light in vacuo, and is 0 the vacuum permittivity. In ref 20 we have shown that the twophoton circular dichroism rotatory strength fRTP, in the particular formulation which we dubbed as the “TI” approach, is written as f TP

R

TI TI ) -b1BTI 1 (ω) - b2B2 (ω) - b3B3 (ω)

1

BTI 1 (ω) )

3

p,0f p,f0 M Fσ (ω)P Fσ *(ω) ∑ Fσ

(3)

3

+,0f p,f0 u Fσ (ω)P Fσ *(ω) ∑ Fσ

(4)

p,0f ∑F M p,0f FF (ω)][∑P σσ (ω)] σ

(5)

ω 1

BTI 2 (ω) )

2ω BTI 3 (ω) )

1 3

ω

[

(2)

p,0f p,0f +,0f where the tensors P Rβ (ωβ), M Rβ (ωβ), and u Rβ (ωβ) are defined through the following sum-over-states expressions (general case ωR + ωβ ) ω0f):

P

p,0f Rβ (ωβ)

)

1

∑P n∑ *0

p M

p,0f Rβ (ωβ)

)

1 p

u

+,0f Rβ (ωβ)

∑P n∑ *0

1

) βFσ p

(µpR)0n(µpβ)nf ωR - ω0n

(6)

(µpR)0n(mβ)nf ωR - ω0n

∑P n∑ *0

(7)

0n p nf (T+ RF) (µσ)

ωR - ω0n

(8)

P takes care of the permutation of the couples (operator/ associated frequency) whereas the Levi-Civita βFσ tensor in eq 8 implies Einstein summation over repeated indices (F and σ). The parameters b1, b2, and b3 depend on the polarization and propagation status of the beam, and they are tabulated for a few combinations in Table 2 of ref 15. Also, the notation (XR)0n indicates the matrix element 〈 0 | XR | n 〉 of the R-Cartesian component of the operator X between the ground | 0 〉 and excited | n 〉 electronic states. The operators X appearing in the infinite summations are the velocity operator µp

qi

∑i m piR

µpR )

(9)

i

involving a sum over the linear momentum pi of all particles of mass mi and charge qi; the magnetic dipole operator m

mR )

qi

qi

∑i 2m liR ) ∑i 2m (ri × pi)R i

(10)

i

involving the position ri and angular momentum li operators; and the mixed length-velocity form of the quadrupole operator + (TRβ ), defined as + ) TRβ

qi

∑i m (piRriR + riRpiR)

(11)

i

When the dichroism is computed in atomic units through eq 1, a multiplication by the conversion factor of ≈1.89679 × 10-50

448 J. Phys. Chem. B, Vol. 111, No. 2, 2007

Jansı´k et al.

yields the value in CGS units. If the frequency ω, the line shape g(2ω), and the TPCD rotation strength fRTP are all given in au, the dichroism in the CGS unit is obtained via multiplication by the factor 4.67299 × 10-32. Equation 1, the TI equation, can be proven to yield origininvariant results for the observable value (the circular dichroism) independent of the completeness of the one-electron basis set employed in the calculation.20 In our original computational study (ref 19) we employed the expression arising in the full length formulation of the theory of TPCD once the interaction between molecule and radiation was approximated, introducing the traditional electric dipole, µ

µR )

∑i qiriR

∑i

qiriRriβ

(13)

R

) -ib1B ω1 0(ω) + b2B ω2 0(ω) - ib3B ω3 0(ω) (14) B

ω0 1 (ω)

)

ω

B ω2 0(ω) ) B ω3 0(ω) ) [

∑ Fσ

0f f0 MFσ (ω)S Fσ *(ω)

∑ Fσ

2

(15)

(16) (17)

0f 0f 0f where the tensors SRβ (ωβ), MRβ (ωβ), and Q Rβ (ωβ) are defined as

1 p

M

0f Rβ(ωβ)

)

∑P n∑ *0

1 p

Q

0f Rβ(ωβ)

1

∑P n∑ *0

) βFσ p

(µR)0n(µβ)nf ωR - ω0n

(18)

(µR)0n(mβ)nf

∑P ∑n

ωR - ω0n

(19)

(qRF)0n(µσ)nf ωR - ω0n

(20)

The ω0 formulation, which can be proven to give the same results as those yielded by eq 1 in the limit of a complete oneelectron basis set and where the following relationships hold 0f f -ω2SRβ (ω)

(21)

p,0f 0f M Rβ (ω) f -ιωMRβ (ω)

(22)

P

u

p,0f Rβ (ω)

+,0f Rβ (ω)

δ

TP

)

(2π)2ω2g(2ω)NA 1 2

2

c0 (4π0)

30

{F[

∑F S0fFF(ω)]2 + (G + H)(

(2π)2ω2g(2ω)NA 1 δ 30 c 2(4π )2 0

0f 0f SFσ (ω)SFσ (ω))} ∑ Fσ

(25)

0

As with b1 , b2, and b3 (see above), the F, G, and H parameters take different values for different polarization and propagation conditions of the two photons. Note that the following relationship holds (cf. eqs 1 and 25 above) TP δTP L - δR

δ

TP

)

8 fRTP c0 δ

(26)

3. Computational Details 0f f0 QFσ (ω)S Fσ *(ω)

∑F M0fFF(ω)][∑σ S0fσσ(ω)]

0f SRβ (ωβ) )

(24)

0f Also, SRβ (ωβ) is the same tensor entering the expression of the two-photon absorption in the dipole approximation. For two photons of equal frequency, the latter is usually written as15,11

)

moment operators. In that formulation, which we labeled as the “ω0” approach in ref 20, the TPCD rotatory strengths read f TP

3 ˆ | 0〉] R ) Im [〈0 | µˆ | f〉‚〈f | m 4

f

(12)

and traced quadrupole q

qRβ )

we recall that the TPCD rotational strength fRTP is a quantity analogous to the ordinary ECD rotatory strength(1,4) fR

0f f -ω2QRβ (ω)

(23)

has the disadvantage of being otherwise origin-dependent. The results presented in this paper were obtained by exploiting Tinoco’s original TI fully velocity-based, origin-independent formulation, eq 1. The reader should refer to the discussion in ref 20 for a comparison of these and other approaches to the calculation of the TPCD rotational strengths. To end this section

The theoretical approach employed here and its computational application have been discussed in detail in refs 19 and 20. Analytic response theory represents a particular formulation of time-dependent perturbation theory, in terms of response functions, which provides a uniform, universal representation of the response of a system to external perturbations, applicable and implemented to all computational models (density-functional as well as wave-function models) and to dynamic and static perturbations alike. As shown in ref 19, properties like twophoton circular dichroism are calculated from analytically derived expressions at the frequency of the experiment where the summation over excited states is replaced by the solution of linear equations, without explicit knowledge of the excited states. This enables us to obtain the property of interest in a size-extensive manner, provided the underlying computational model is size-extensive. The recent development of timedependent density functional theory (DFT), with frequencydependent quadratic response theory beyond the adiabatic local density approximation,35 is a key step that makes modeling of TPCD a possible proposition within the frame of modern DFT. The approach adopted in ref 19 led to results which were, in principle, dependent on the choice of the origin of the interaction operators, albeit it was possible to show that such an origindependence was, rather surprisingly, quite contained. In ref 20 we have studied alternative approaches to the calculation of the TPCD and introduced expressions where the dependence of the observable on the choice of origin was also removed for incomplete basis sets. We exploit in this study one such approach, one which was proven to be more computationally efficient. We have calculated the one- and two-photon circular dichroism spectra and the two-photon absorption spectra for the six lowest excited states | f 〉 of all 19 chiral essential amino acids. The calculations involved neutral, gas-phase molecules. The initial geometry was taken from crystal structure data and then optimized employing the Becke three-parameters Lee,Yang, and



Figure 1. ECD, TPCD, and TPA spectra obtained at the DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for alanine (Ala) and isoleucine (Ile).

Parr (B3LYP)36-38 density functional and 6-31G(d,p) basis set.39,40 The six excited states energies ω0f were obtained as single residues of a linear response function.41 The two-photon circular dichroism rotatory strength fRTP was calculated within the TI formulation defined in ref 20 and briefly outlined in eqs p,0f p,0f +,0f 2-8 above. The P Rβ (ωβ), M Rβ (ωβ), and u Rβ (ωβ) tensors were then evaluated as single residues of the appropriate quadratic response functions within the response theory framework, for each final excited state | f 〉 at the frequency ω ) ω0f/2 . Whereas the sign of the response function is well-defined, it is not so for the residues; i.e., the two-photon type tensor and the remaining transition moment that can be obtained as single residues of a given quadratic function. In usual two-photon absorption calculations the quantity of relevance, the observable, is the squared amplitude, obtained by taking the square of the two-photon residue. Therefore, the lack of information on the sign of the latter is not consequential. This is, however, not the case of the TPCD, where the combination of two-photon transition amplitudes (see eqs 6-8) is crucially dependent on the sign of the individual residues. Care was therefore taken to compute all tensors at once for each given final state, within a common loop, to make sure that all phase factors were properly taken into account. All the property calculations were performed employing the B3LYP/DFT response.36-38 The aug-cc-pVDZ basis set42 was used throughout. Both the absorption and circular dichroism spectra were obtained, according to, respectively, eqs 25 and 1, assuming a Lorentzian as line shape function, g(2ω), with a width Γ of 0.1 eV and with maxima determined so that each Lorentzian, when integration is performed over the whole frequency spectrum, yields the value of the TPA strength (δ), TPCD (fRTP), or ECD (fR) rotational strength for the given excited state. The results shown and discussed in the following for the two-photon processes correspond to an experimental setup with two left

circularly polarized beams of equal frequency, propagating parallel to each other, originating from a single intense beam and absorbed simultaneously. For this arrangement, F ) -2, G + H ) 6, b1 ) 6, and b2 ) -b3 ) 2.15 The intensities of the two-photon spectra presented in the next section are of arbitrary units and normalized in each figure to the area of the two-photon absorption spectrum, thus allowing for the absolute comparison of the TPA and TPCD spectra. For this purpose the factor eq 26 (see also ref 19) was included into the scaling of the TPCD spectra. The ECD spectra, obtained by applying eq 24, are also given in arbitrary units. All calculations were carried out using a parallel, locally modified version of the DALTON 2.0 electronic structure program.43 4. Results and Discussion Despite the large number of amino acids that can be found in nature, only 20 are commonly found as constituents of mammalian proteins. Those are the so-called “essential amino acids”. Out of these 20, 19 are chiral. In Figures 1-10 we present two-photon absorption and one- and two-photon circular dichroism spectra obtained from the six lowest excited states of these 19 chiral essential amino acids. For the purpose of the presentation and discussion of the results, they can be subdivided into five categories, based on the nature of the side chain bonded to the R-carbon, with a classification (see ref 44) which is believed to reflect the fundamental properties of amino acids such as the types of biochemical reactions in which they are involved and their influence on protein structure and reactivity: 1. Amino acids with simple aliphatic side chains; alanine (Ala), isoleucine (Ile), leucine (Leu), and valine (Val) fall into this group (see Figures 1 and 2). 2. Amino acids with alcohol (-OH), thiol (-SH), and (-SCH3) groups on the aliphatic side chain; cysteine (Cys),


Jansı´k et al.

Figure 2. ECD, TPCD, and TPA spectra obtained at DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for leucine (Leu) and valine (Val).

Figure 3. ECD, TPCD, and TPA spectra obtained at DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for cysteine (Cys) and methionine (Met).

methionine (Met), serine (Ser), and threonine (Thr) are found in this group (see Figures 3 and 4). 3. Amino acids with a carboxylic acid or an amide group side chain, such as the aspartic (Asp) and glutamic (Glu) acids, asparagine (Asn), and glutamine (Gln) (see Figures 5 and 6).

4. Amino acids with strongly basic group side chains such as arginine (Arg) and lysine (Lys); proline (Pro), with its heterocyclic side chain, is also included in this set due to the basic properties of the imino (cyclic amine) group; glycine (Gly), the 20th essential amino acid, is not chiral, and therefore is not



Figure 4. ECD, TPCD, and TPA spectra obtained at DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for serine (Ser) and threonine (Thr).

Figure 5. ECD, TPCD, and TPA spectra obtained at DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for asparagine (Asn) and aspartic acid (Asp).

suitable for ECD or TPCD experiments. Yet we have computed its two-photon absorption spectrum, which is presented together with the spectra of Pro (see Figures 7 and 8).

5. Amino acids with aromatic side chains; this group includes histidine (His), phenylalanine (Phe), tryptophan (Trp), and tyrosine (Tyr) (see Figure 9 and 10).


Jansı´k et al.

Figure 6. ECD, TPCD, and TPA spectra obtained at DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for glutamic acid (Glu) and glutamine (Gln).

Figure 7. ECD, TPCD, and TPA spectra obtained at DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for arginine (Arg) and lysine (Lys).

As indicated in section 3, in each figure the two-photon spectra are normalized so that the TPA is contained between 0 and 1 units. The ECD spectra are also normalized so that in each figure maxima of absorption are contained within (1 units.

In order to give an idea of the absolute intensity of the TPA, TPCD, and ECD spectra across the whole set of amino acids, in Table 1 we report the relative areas of the portion of the spectra resulting from the convolution of the rotational strengths



Figure 8. ECD, TPCD, and TPA spectra obtained at DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for proline (Pro) and glycine (Gly). The latter, being the only nonchiral essential amino acid, yields no dichroic response.

Figure 9. ECD, TPCD, and TPA spectra obtained at DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for histidine (His) and phenylalanine (Phe).

yielding the absorption of the first six excited states. The most intense signal for the TPA process is given by Trp. If we assume that the area spanned by our TPA spectrum of Trp is equal to

1, the areas of the remaining TPA and TPCD spectra of the natural amino acids distribute as seen in Table 1. For example, whereas Pro and Asn span with their TPA spectra an area ca.


Jansı´k et al.

Figure 10. ECD, TPCD, and TPA spectra obtained at DFT/B3LYP/aug-cc-pVDZ level arising from the lowest six excited electronic states for tryptophan (Trp) and tyrosine (Tyr).

TABLE 1: Areas of the Portion of TPA, TPCD, and ECD Spectra Yielded by the First Six Excited States for All 20 Essential Amino Acids, Given Relative to the Area of the TPA Spectrum of Trp (for TPA and TPCD) and to the (Absolute) Area of the ECD Spectrum of Ile (for ECD)a Ala Ile Leu Val Cys Met Ser Thr Asn Asp Glu Gln Arg Lys Pro His Phe Trp Tyr Gly

TPA

TPCD × 100

ECD

0.52 0.42 0.54 0.13 0.33 0.43 0.21 0.22 0.74 0.14 0.19 0.15 0.24 0.38 0.80 0.28 0.33 1.00 0.49 0.27

1.37 (-1.26) 2.48 (0.08) 2.10 (1.13) 0.55 (-0.32) 0.92 (0.75) 1.19 (0.89) 0.58 (-0.53) 1.67 (1.49) 3.01 (3.01) 0.84 (0.28) 0.58 (-0.38) 0.65 (-0.13) 1.06 (0.43) 1.12 (0.63) 2.33 (-1.71) 0.84 (-0.84) 1.23 (1.19) 2.37 (-1.84) 1.17 (0.16)

0.81 (0.01) 1.00 (-0.43) 0.49 (-0.12) 0.38 (0.07) 0.21 (0.18) 0.34 (0.29) 0.86 (0.18) 0.53 (0.04) 0.80 (-0.45) 0.51 (0.11) 0.51 (0.18) 0.33 (0.25) 0.26 (0.16) 0.47 (-0.07) 0.34 (0.08) 0.21 (0.19) 0.92 (0.80) 0.28 (0.28) 0.38 (0.38)

a For the CD spectra (TPCD and ECD), both the absolute area (obtained by integrating the absolute value of the spectral function over the whole set of frequencies) and (in parentheses) the actual area (with it sign, resulting from the balance of negative and positive portions of the spectrum) are given. Note that the relative area of the TPCD spectra is given in hundredths of the reference unit.

80% and 74% that of Trp, the less intense TPA spectra are those of Val and Asp, with only 13% and 14% of the intensity of that yielded by Trp. For the circular dichroism spectra we report in Table 1 both the absolute area, that obtained by integrating the absolute value

of the spectral function and thus yielding the integrated rotational strength independent of the individual signs, and (in parentheses in Table 1) the actual area, resulting from a balance of negative and positive regions in the CD spectrum. Both values for the TPCD spectra are given relative to the (unitary) area of the TPA spectrum of Trp. As expected from eq 26, the intensity of the TPCD spectra is much lower than that of the corresponding absorption spectra, and therefore, TPCD entries in Table 1 are multiplied by a factor of 100. The most intense TPCD signal (measured on the absolute area) is given by Asn, ≈3% that of the TPA spectrum of Trp and a factor of 25 less intense than its absorption counterpart. As can be seen from Figure 5, the TPCD spectrum of Asn in the 2.05-3.6 eV region (where the signals arising from absorption associated to the lowest excited states appear) shows no transparencies, i.e., displays no change of sign, and therefore the absolute area coincides with the actual area. Ile yields an absolute area of about 2.5% relative to the reference TPA spectrum of Trp, but in this case the spectrum shows transparencies and a neat balance of negative and positive differential absorption areas, resulting in a very efficient cancellation of rotatory strength (actual area less than a thousandth of the reference, see Figure 1). Pro (Figure 8) and Trp (Figure 10) also yield quite intense (and somewhat similar) TPCD spectra, ca. 2.3-2.4% of the reference area in absolute terms, and both characterized by a strong negative absorption band. Val (Figure 2) and Ser (Figure 4) are instead the two species yielding the less intense TPCD spectra, 0.55% and 0.58% of the reference, respectively. Their TPCD spectra are again somewhat similar, with the most intense (negative) band in both cases in the 3.13.2 eV energy region. The areas of the ECD spectra are given relative to that of Ile (see again Figure 1), which displays the most intense differential one-photon absorption and for which the (absolute) area has



TABLE 2: Excitation Energy, pω0n, Parameters B TI 1 (eq 3), TI f TP B TI 2 (eq 4), and B3 (eq 5), and Rotational Strengths R (eq 2) and fR (eq 24) for Each of the Six Lowest Excited States of Ala, Ile, Leu, and Vala amino acid/ exc state (n) pω0n/eV Ala 1 2 3 4 5 6 Ile 1 2 3 4 5 6 Leu 1 2 3 4 5 6 Val 1 2 3 4 5 6

BTI 1

BTI 2

BTI 3

fRTP

fR

5.2735 8.3814 -6.5712 -1.6296 -40.4053 7.577 5.6770 18.7602 -2.4549 28.1968 -51.2579 29.389 5.9398 -11.5867 -2.0840 -7.8923 57.9037 -5.923 6.1272 8.7072 2.6137 1.5698 -54.3310 -6.299 6.4938 61.5346 -16.2491 12.5176 -311.6740 15.587 6.5153 -36.8723 25.6970 -12.4098 145.0200 -39.846 5.1863 0.1406 5.5864 -34.5365 6.1283 45.2143 6.2630 -24.7844 6.3212 -51.2308 6.4670 84.3387

-1.9546 -4.8418 -6.6178 27.354 -0.8707 14.4971 237.9540 -30.655 -3.1752 -21.0333 -307.0020 -5.020 9.3597 -8.4207 113.1460 4.623 12.5409 -3.7058 274.8910 -5.358 0.6124 105.2360 -296.7840 -24.841

5.3709 22.0248 -13.1105 17.8887 -70.1504 -6.248 5.6233 -7.1049 3.9002 -7.7363 19.3562 -20.495 6.0072 -72.2258 14.8630 -8.4186 386.7920 -1.396 6.0490 -4.1243 4.3183 8.6020 33.3130 14.871 6.2607 -31.6965 25.6659 -32.9577 72.9318 1.200 6.3176 38.4651 5.9974 14.6613 -213.4630 2.780 5.4566 5.6707 5.9706 6.2102 6.4272 6.5474

6.1370 -5.0487 -8.6136 18.7819 -2.6063 1.5017

0.0396 13.7280 -9.4451 11.084 -0.2202 3.4241 37.5810 -2.704 -1.6146 -17.9989 18.9127 11.555 1.0242 -3.1025 -120.9450 -16.031 3.0067 -2.4986 4.6274 1.250 -4.6110 1.7506 3.7127 0.381

a The TPCD rotational strength has been computed for two circularly polarized photons (b1 ) 6, b2 ) -b3 ) 2); atomic units where not explicitly specified.

been arbitrarily taken as unitary. Phe (Figure 9), Ser (Figure 4), Ala (Figure 1), and Asn (Figure 5) all have absolute areas within 80% of the ECD reference, with the spectrum of Ala where the (positive) rotational strength accumulated at a photon energy between 4.8 eV and the transparency occurring at ≈5.8 eV is compensated for almost entirely by the negative contribution of the bands beyond 5.8 eV. The weakest integrated (absolute) ECD rotational strengths are observed for Cys (0.21, see Figure 3), His (0.21, see Figure 9), and Arg (0.26, see Figure 7), all three characterized by intense positive absorption bands. Having presented and discussed the relative intensity of the TPA, TPCD, and ECD spectra of all amino acids, we can move on to discuss the features of the calculated spectra, grouped according to the criteria discussed at the beginning of the section. It is perhaps important to stress at this stage that, for example, ECD spectra of organic compounds of the size of those discussed here, of particular interest in the very recent literature,45,46 are nowadays rather routinely simulated, using for instance time-dependent DFT47 or even sophisticated fully ab initio approaches.48,49 A meaningful comparison of the results of computation with experimental data involves a provision for suitable models of the condensed phase and a thorough conformational analysis, including, if needed, zwitterionic forms. We limit our studies here to single stable conformations in the gas phase, our scope only being the in silico comparison of the three spectroscopies in the wide set of natural chiral amino acids. 4.1. Group 1: Ala, Ile, Leu, and Val. The spectra for the amino acids belonging to this group are collected in Figure 1 (Ale, Ile) and Figure 2 (Leu, Val). In Table 2 the excitation TI TI energies, the parameters B TI 1 (eq 3), B 2 (eq 4), and B 3 (eq 5) f TP with the rotational strengths R (eq 2), computed for the case of two circularly polarized photons ( b1 ) 6, b2 ) -b3 ) 2),

and fR (eq 24) are given for each of the six lowest electronic excited states of each molecule. The amino acids in this group are apparently those yielding the most effective dichroic response, both linear and nonlinear, with respect to all other groups, as indicated by the comparison of the integrated (absolute) areas in Table 1. Also, their TPA response is quite strong, albeit not as effective as that exhibited by the amino acids of group 5 (those with aromatic side chains) or those of group 4 (Arg, Lys, and Pro). The two excited states around 6.50 eV are responsible for the most intense peaks appearing in the high-energy region in all three panels devoted to Ala in Figure 1. Table 2 shows that the two states yield rotational strengths (both ECD and TPCD) of opposite sign. In the two-photon CD spectrum, they are largely due to the B TI 1 electric dipole-magnetic dipole related contribution. The TPCD spectrum of Val (Figure 2) is somewhat similar to that of Ala, more so in the higher photon energy region. Most of the intensity is due to the fourth state, responsible for the negative band around 3.1 eV. The ECD and TPCD spectra of Val differ notably in the 5.2-6.1 eV (ECD) photon energy region, with the single peak just above 2.8 eV in the TPCD spectrum splitting into two somewhat symmetric peaks separated by a valley in ECD. An alternation of somewhat equally intense positive/negative two-photon rotational strengths yields the peculiar TPCD spectrum of Ile (Figure 1), rather unique in the series of essential amino acids. The four highest excited states in Table 2 all concur to the large structured peak about as wide as 0.4 eV in the higher portion of the TPA spectrum. On the other hand, the third to fifth states do not yield a particularly intense response in the ECD spectrum. The TPCD spectrum of Leu is dominated by the intense peak at 3.0 eV, due to the third and (partly) fourth excited states, yielding a positive signal. Two side dips, with weaker negative strength, can be seen at around 2.69 eV (mainly due to the first excited state) and 3.16 eV (mainly attributable to the sixth excited state) (see Figure 2). It is this last state at an excitation energy of 6.32 eV that is mainly responsible for the most intense peak in the TPA spectrum. 4.2. Group 2: Cys, Met, Ser, and Thr. The discussion in this section will be made with reference to Figure 3 (Cys, Met) and Figure 4 (Ser, Thr) and to Table 3. A look at Table 1 shows that the amino acids gathered in this group are those yielding the weakest response to the two-photon solicitation, both in absorption and in circular dichroism, with respect to all the other groups identified at the beginning of the section. The average TPA absolute area (measured again relative to the TPA of Trp) is ≈0.3, just a bit lower than that of group 3 (next subsection) and smaller than the 0.40 of group 1 (previous subsection), 0.47 of group 4, and 0.52 of group 5. Concerning TPCD, the average absolute area is ≈1.1% that of the TPA spectrum of Trp, compared with, for example, 1.6% for the amino acids of the group 1. The three excited states lying within less than 0.1 eV of the region around 5.75 eV combine their strengths to yield the absorption dominating the TPA spectrum of Cys (see Figure 3). The same states also are responsible for the peaks in the same region in both the ECD and TPCD spectra. The latter in particular is somewhat similar to the TPCD spectrum of Arg (see Figure 7) and to a lesser extent to that of Thr (Figure 4), which belongs to the group discussed in this subsection. Also, the TPCD and ECD spectra of Cys are similar. Quite a difference can be seen instead between the ECD spectrum of Met (see Figure 3), dominated by the transition due to the fifth state at an excitation energy of 5.54 eV and the corresponding


Jansı´k et al.

TABLE 3: Excitation Energy, pω0n, Parameters B TI 1 (eq 3), TI f TP B TI 2 (eq 4), and B 3 (eq 5), and Rotational Strengths R (eq 2) and fR (eq 24) for Each of the Six Lowest Excited States of Cys, Met, Ser, and Thra

TABLE 4: Excitation Energy, pω0n, Parameters B TI 1 (eq 3), TI f TP B TI 2 (eq 4), and B 3 (eq 5), and Rotational Strengths R (eq 2) and fR (eq 24) for Each of the Six Lowest Excited States of Asn, Asp, Glu, and Glna

amino acid/ exc state (n) pω0n/eV

amino acid/ exc state (n) pω0n/eV

Cys 1 2 3 4 5 6 Met 1 2 3 4 5 6 Ser 1 2 3 4 5 6 Thr 1 2 3 4 5 6

BTI 1

BTI 2

BTI 3

fRTP

fR

4.8303 5.3981 5.2961 -15.2564 5.4750 9.1996 5.7231 -39.8845 5.7504 10.1395 5.8026 -5.4654

-4.8783 -4.1861 5.3706 -4.8106 3.5741 23.4631 -5.5277 -59.7100 -8.3571 6.0642 -2.2777 -4.2706

-31.0041 71.1759 -15.4193 130.9420 -31.9946 28.8068

-1.143 6.015 -1.840 6.430 6.620 -1.904

4.7577 -7.9592 5.0129 20.4510 5.2231 -47.2280 5.4685 5.2434 5.5440 -1.8917 5.5888 -17.6205

-2.2566 -3.1488 45.9708 -2.2718 1.5138 -115.1350 -2.7599 -52.1351 184.6180 1.1408 2.4038 -28.9346 -3.1810 -5.9892 5.7340 8.1161 -0.2564 88.9781

-2.272 -0.349 -1.485 3.579 22.373 0.718

5.6355 5.6995 6.2095 6.2769 6.3951 6.5659

6.6399 -2.6477 -0.8775 -36.2989 -6.109 -5.5548 8.7853 6.0428 27.8440 40.935 -3.6907 0.5075 -13.9746 -6.8201 -9.221 4.0047 -10.9998 2.7326 3.4368 -29.119 21.9598 4.1376 0.1570 -139.7200 7.408 -7.7767 1.9740 0.7653 44.2430 10.687

5.2977 -2.1587 5.5624 9.3392 5.7276 -3.8343 5.8660 -35.1251 6.2524 -22.4420 6.5033 4.9751

-1.7499 3.8922 -1.4492 8.3159 -7.2260 0.9484

-2.5947 -5.4652 0.4303 1.5292 5.5175 6.5548

11.2622 5.626 -74.7501 -5.096 26.7646 -18.476 197.1770 8.639 160.1390 18.300 -18.6377 -5.826

Asn 1 2 3 4 5 6 Asp 1 2 3 4 5 6 Glu 1 2 3 4 5 6 Gln 1 2 3 4 5 6

BTI 1

BTI 2

BTI 3

fRTP

fR

5.1239 -7.0732 -3.5545 12.3671 74.2822 -11.242 5.3557 22.3458 -11.2166 18.5981 -74.4454 8.982 5.4531 -85.4836 19.3324 -137.7140 198.8090 -42.389 5.7268 -32.1227 8.7365 77.3226 329.9090 -11.077 5.8361 -7.7833 -9.4202 -26.9724 11.5957 2.070 5.9297 -17.1697 11.1330 -5.2278 70.2966 18.427 2.6083 -1.0932 2.6985 4.2103 -2.1834 -3.7853

-9.2095 -2.5767 9.8023 5.8676 9.5571 13.8433

6.6791 -0.2895 -6.8233 2.1585 -2.1897 -0.9707

-5.4192 31.0606 -3.2522 9.5349 2.5860 -39.9949 -0.8277 -41.1778 23.0802 -6.8027 25.7274 -29.6637

10.833 4.403 16.164 -9.928 -0.566 -6.452

5.1337 -15.4387 3.2516 5.1810 -3.3733 2.3748 5.4556 13.1853 -1.4582 5.5753 3.1923 -0.0639 5.7183 -0.3371 0.0415 5.8302 19.2744 -14.3336

-13.7956 58.5378 -0.1867 15.1167 29.4108 -17.3738 0.4844 -18.0568 4.9487 11.8368 4.8645 -77.2504

-2.742 -1.322 -0.686 2.519 -1.939 24.041

5.2984 5.7276 5.7535 6.0071 6.1506 6.3340

6.3942 15.8369 -7.8112 -10.1214 10.7224 -6.5928

-64.9854 3.424 -3.8142 15.437 -54.2983 13.835 119.3040 -17.251 -23.0608 -13.085 84.6294 6.180

5.3825 12.0929 5.6038 6.2791 5.8667 5.5465 5.9468 -24.6613 5.9630 8.1454 6.2198 -15.0407



TPCD spectrum, where a major role is played instead by the third (and to a lesser extent second) excited state, yielding a sequence of positive and negative maxima and transparencies between 2.4 and 2.8 eV. The fifth excited state lying ≈6.40 above the ground electronic state dictates the features of the TPCD spectrum of Ser (Figure 4). Almost 95% of the rotation strength here is due to the B TI 1 contribution. The same state is much less effective in the ECD process, to which a more important contribution is given in the same frequency region by the fourth excited state placed at 6.28 eV. The intense peak around 5.70 eV in the ECD spectrum somehow disappears in the TPCD spectrum. The intense peak at 2.8 eV in the TPA spectrum of Thr (Figure 4), due essentially to the second excited state lying 5.56 eV above the ground state, turns into the only, relatively weak, negative peak of the corresponding TPCD spectrum, which is characterized on the other hand by the two (positive) peaks at 2.93 eV, mainly due to the fourth state, and 3.13 eV, related to the rotation strength of the fifth excited state. The spectrum is not dissimilar from that predicted for Met (Figure 3), discussed just above. The ECD spectrum is quite complex, with two leading peaks of opposite sign and very close intensity (see Table 3) due to the third and fifth excited states. 4.3. Group 3: Asn, Asp, Glu, and Gln. The spectra of Asn and Asp, belonging to our third group, are shown in Figure 5, whereas those of the other two amino acids, Glu and Gln, are given in Figure 6. Excitation energies and rotational strengths, those of the TPCD process split into their three contributions according to eq 2, are listed in Table 4. As for the systems in the previous group, the response in the two-photon process is generally weaker than average in the set of natural amino acids, at least within the region of photon energies considered in this work. In contrast,the intensity of the ECD spectra of this group

is stronger than average, and the group scores second behind group 1 in this particular ranking list, with an average absolute area ca. 54% that of the ECD spectrum of Ile, compared to the 67% of group 1, which includes Ile. The TPCD spectrum of Asp in Figure 5 is, together with that of His, which will be discussed below (see Figure 9), the only one missing the phenomenon of transparencies. This is the result of a combined effect of the first and, in particular, the third and fourth excited states, all exhibiting intense positive rotational strengths and thus cancelling the effect of the negative (also quite intense) rotation strength of the second state located at an excitation energy of 5.36 eV. The TPA spectrum is very similar to that of the TPCD, with its magnification of about 20 times and with the central peaks very effectively burying the small peaks and shoulder appearing on the side of the differential absorption spectrum. The ECD spectrum is mainly characterized by the intense negative peak at 5.45 eV, associated with the third excited state, and it has some similarities with that of the other amino acid in Figure 5, Asp. The two spectra are, in a broad sense, quasi mirror images, even if the former (ECD of Asn) is more intense (see Table 1). The negative band at about 5.95 eV for Asp combines the rotation strengths of the fourth and fifth excited states lying very close to each other around that photon energy. The TPA spectrum of Asp is dominated by the two maxima at ≈2.7 eV and ≈2.95-3.00 eV, roughly corresponding to the first and fourth (and fifth) states in Table 4. These same states contribute with rotation strengths of opposite sign to those of the TPCD spectrum. The TPCD spectrum of Glu is split in two regions, a lower photon energy region extending to ≈2.75 eV, which is the result of the positive rotation strength of the lowest excited state, and a higher energy region where the combined effect of the four negative rotation strengths of the third to sixth excited state yield



TABLE 5: Excitation Energy, pω0n, Parameters B TI 1 (eq 3), TI f TP B TI 1 (eq 4), and B 1 (eq 5), and Rotational Strengths R (eq 2) and fR (eq 24) for Each of the Six Lowest Excited States of Arg, Lys, and Proa amino acid/ exc state (n) pω0n/eV Arg 1 2 3 4 5 6 Lys 1 2 3 4 5 6 Pro 1 2 3 4 5 6

BTI 1

5.0877 15.9993 5.3566 -10.6623 5.4532 1.9380 5.4958 -0.6229 5.6714 -1.3489 5.7907 -24.5039

BTI 2 -4.5710 2.8437 -2.3353 2.6853 -3.5638 23.9719

BTI 3

fRTP

-9.7789 -106.4120 10.5909 79.4679 6.3753 5.7930 -4.3930 -10.4189 0.9935 17.2081 1.7028 102.4850

fR

-2.278 -1.044 16.675 3.377 0.282 -4.078

5.3105 -18.7257 4.2542 -8.7323 86.3810 16.938 5.3960 0.0885 -15.4440 4.8389 40.0349 -17.351 5.5489 -11.9876 11.2577 -5.4205 38.5694 13.456 5.6921 -25.4868 7.2842 4.4077 147.1680 4.751 5.7614 17.4149 -5.5051 14.9649 -63.5491 0.345 5.7933 13.3658 -9.1368 -29.3281 -120.5770 -23.565 4.8843 16.1514 5.2540 -8.1543 5.6081 103.3660 5.7682 1.0982 5.8612 -12.4975 6.0178 0.6735

-1.8450 5.3591 9.2892 -0.6435 -6.7603 3.8687

-8.0037 -109.2260 10.944 8.7379 55.6833 -1.846 91.6147 -455.5470 -11.513 -0.2972 -5.8964 11.472 16.8038 122.1130 0.271 28.4698 45.1614 -3.400


the structure shown in Figure 6. To some extent the situation is similar for Gln, on the right panel of the same figure. In this case the rotation strength of the sixth state is remarkably greater than that of the states nearby, and the structure in the negative side of the spectrum of Glu reduces here to a single negative peak and a weaker structure on the lower energy side. The sixth excited state yields the strong peak which dominates the ECD spectrum of Gln. The same state competes with the first and second excited states at 5.13 and 5.18 eV for the largest contribution to the TPA spectrum. Positive (below 5.9 eV) and negative (above 5.9 eV) contributions characterize the ECD spectrum of Glu, with a prevalence of the former (see Table 1). 4.4. Group 4: Arg, Lys, Pro, and Gly. As indicated above, we included in this group Arg and Lys (cf. Figure 7) and Pro (see Figure 8). The data necessary to account for and reproduce the dichroism spectra for these three systems is collected in Table 5. In Figure 8, the TPA spectrum of Gly is also included. Due to its achirality, this essential amino acid does not display optical activity, and therefore no dichroism can be observed. The three chiral amino acids in this group are those yielding on average the weakest response in the ECD experiment, with an average absolute area of the spectra shown in this work ca. 36% that of the ECD spectrum of Ile, our reference for unit absolute area. On the other hand, their response to two photons is quite remarkable, second in intensity to the amino acids of group 5 (discussed in the next subsection and which includes the reference, Trp) for TPA and to the those of group 1 for TPCD. Most of this is due, on the other hand, to a single system, Pro, which seems to be a quite strong two-photon absorber, both in the direct and in the differential experiment. The first excited state of Arg displays a strong negative twophoton rotational strength, shown by the intense negative peak at about 2.55 eV in the TPCD spectrum (see Figure 7). The second and last excited states have instead strong responses of opposite (positive) sign, which leads to a transparency just above 2.6 eV and to the intense peaks of the higher portion of the TPCD spectrum. The first and last (sixth) excited states

determine the structure of the corresponding TPA spectrum, whereas it is the strong one-photon rotation strength of the third state lying at an excitation energy of 5.45 eV that largely dominates the ECD spectrum of Arg. Note that for this particular TI state the B TI 1 and B 3 (electric dipole-magnetic dipole transition related) contributions tend to cancel each other in the TPCD spectrum, thus leaving a dominant electric dipoleelectric quadrupole contribution (B TI 2 ), a rather uncommon occurrence. The TPCD spectrum of Lys displays a single transparency a bit below 2.9 eV, separating the region of positive area yielded by the first four excited states from that of the negative area given by the two rather strong rotatory strengths of the fifth and sixth excited states. The corresponding ECD spectrum shows an alternation of peaks and dips, reflecting the alternation of positive and negative rotation strengths of similar intensity shown for states 1, 2, 3, and 6 in Table 5. Pro yields very characteristic intense two-photon spectra, the TPA one displaying a sequence of peaks of increasing intensity as the photon energy increases. The corresponding TPCD spectrum is largely dominated by the big negative peak around 2.80 eV, almost entirely due to the strong differential absorption of the third excited state. For this state the effect is to a very large extent due to an electric dipole-magnetic dipole transition, the quadrupolar contribution being negligible, less than 5% (cf. Table 5). That same state (with an excitation energy of ≈5.6 eV) competes with the first excited state located at 4.88 eV and the fourth at 5.77 eV for predominance in the ECD spectrum. Gly displays a TPA spectrum in the 2.3 eV-3.9 eV photon energy region covering an area ca. 27% that of the reference, Trp. The six low-lying excited states have excitation energies of 5.58, 5.71, 6.11, 6.14, 6.54, and 6.80 eV, respectively, and the most intense peak, located around 2.8 eV in the spectrum of Figure 8, appears to be due to the combined effect of the first two (very close lying) excited states. 4.5. Group 5: His, Phe, Trp, and Tyr. The last group of amino acids in our classification includes His and Phe (whose spectra are shown in Figure 9), Trp, and Tyr (see Figure 10). Excitation energies and rotation strengths are collected in Table 6. These amino acids, all exhibiting aromatic side chains, are very efficient two-photon absorbers, and they also appear to be able to display rather intense (compared with the natural amino acids distributed in the other four groups) TPCD spectra. Phe has a notable ECD response, its spectrum spanning an absolute area only 92% that of the reference ECD spectrum of Ile, but is balanced by the rather weak spectra of His, Trp, and Tyr, which makes this class of natural amino acids second only to group 4 for its reduced sensitivity in the ECD experiment. The TPCD spectrum of His is, as that of Asn (Figure 5), missing transparencies. A quasi-transparency appears at about 2.75 eV where the positive rotation strength of the second excited state almost manages to compensate the two negative rotation strengths bracketing it due to the first and third excited states (see Figure 9 and Table 6). The fifth state, lying at 5.84 eV, yields the most intense rotational strength, almost all due to the B TI 1 contribution, and it is responsible for the most intense signal at ca. 2.9 eV in both TPCD and TPA spectra. The sixth state, at 5.89 eV, also partly contributes in both cases. In the ECD spectrum, despite its size, the rotation strength of the fifth state has to struggle against those of the fourth and sixth states, lying close by and characterized by an opposite sign, to yield a peak (at about 5.8 eV) of comparable intensity to that appearing at about 5.55 eV. The latter is the result of the constructive interference of the two rotation strengths of


Jansı´k et al.

TABLE 6: Excitation Energy, pω0n, Parameters B TI 1 (eq 3), TI f TP B TI 2 (eq 4), and B e (eq 5), and Rotational Strengths R (eq 2) and fR (eq 24) for Each of the Six Lowest Excited States of His, Phe, Trp, and Tyra amino acid/ exc state (n) pω0n/eV His 1 2 3 4 5 6 Phe 1 2 3 4 5 6 Trp 1 2 3 4 5 6 Tyr 1 2 3 4 5 6

BTI 1

BTI 1

BTI 1

fRTP

fR

5.2402 14.1474 -6.2624 8.0905 -56.1785 1.867 5.5370 -6.6521 5.5232 3.0572 34.9810 6.579 5.5908 7.1592 -5.6521 1.7337 -28.1834 5.007 5.6847 1.3831 0.6982 9.4053 9.1154 -4.745 5.8357 35.5728 -6.3131 -1.2391 -203.2890 10.957 5.8923 -17.3438 1.0513 -14.1790 73.6019 -4.725 5.2309 10.7696 4.2922 2.9222 -67.3576 0.173 5.3535 -8.6838 4.8939 -33.1776 -24.0402 6.552 5.4147 -31.5795 -1.2147 38.3267 268.5600 -19.515 5.5429 -5.5769 -5.3543 18.9300 82.0299 21.654 5.6399 40.9232 0.4628 38.4682 -169.5280 1.632 5.6982 -37.6641 10.6432 -26.9513 150.7950 52.851 4.5114 -2.6986 4.2688 -13.4788 -19.3036 4.6035 79.9226 -18.7779 -46.5919 -535.1640 4.7192 4.9639 -3.4379 49.2362 75.5649 4.7721 -0.6286 1.1783 -0.1915 1.0319 5.0965 -50.7662 1.0906 -100.1040 102.2090 5.1706 -3.9275 9.5315 -0.6964 3.1093

0.121 4.882 4.829 0.097 9.000 2.876

4.8660 11.4402 1.7262 -2.9502 -77.9935 4.229 4.9876 7.8222 -10.8274 11.0899 -3.0988 -2.606 5.0676 -26.2904 -6.7176 33.2181 237.6140 1.618 5.2740 41.2265 14.9323 58.4745 -160.2750 20.764 5.3951 -2.3516 7.5435 -31.4561 -63.8894 -3.194 5.5686 -13.7526 6.3804 15.0357 99.8263 8.994


the second and third excited states, lying in that region within 0.06 eV of each other. The third excited state of Phe, 5.41 eV (see Table 6), dominates the TPCD spectrum on the right panel of Figure 9, also thanks to the support coming from the strength of the fourth state lying nearby. The net effect of the negative interference between the fifth and sixth excited states, lying within 0.06 eV between 5.64 and 5.70 eV, under the influence of the strong band centered around 2.7 eV, is the appearance of a second weaker peak at around 2.85 eV. The rotation strengths of the third and fourth excited states somehow quench each other in the ECD spectrum of Phe, with the net result of the strong rotation strength associated with the sixth excited state playing the major role. Note that the TPA spectrum is made by a band with very little structure. Trp is perhaps the most active two-photon absorber natural amino acid of this study, both direct and differential. Its second excited electronic state, with an excitation energy of 4.60 eV, displays the largest two-photon rotation strength of the whole set (-535.16 au, cf. Table 6), only 7% of which is attributed to electric dipole-electric quadrupole transitions. This rotation strength gives the peak characterizing the TPCD spectrum of Trp in Figure 10. Other features are the transparency located at ≈2.45 eV and the weaker positive peak at 2.55 eV, due to the far from negligible rotation strength of the fifth excited state. It is this state ( ω05 ) 5.10 eV) which is mainly responsible instead for the main peaks observed in both the TPA and ECD spectra. The latter is the sole example in this study of a electronic CD spectrum missing transparencies, and it is also unique among the 38 CD spectra presented and discussed here in the fact that all six rotation strengths have the same sign, and therefore the absence of transparencies is by no means due to interference effects, as observed above, for example, in the case of the TPCD spectra of Asn and His. Finally, the TPCD spectrum of Tyr

shows an alternation of dips and peaks resulting from the alternation of quite intense positive (third and sixth excited states, see Table 6) and negative (first, fourth, and fifth excited states) rotation strengths. The dip at ca. 2.65 eV in the TPCD spectrum is mirrored in Figure 10 by the maximum of the TPA spectrum, a maximum with a shoulder on its left side, at about 2.50 eV. A sequence of peaks located on the positive side of the axis, the most intense around 5.27 eV and due to the fourth excited state, appears in the ECD spectrum of Tyr. 5. Summary We have performed a thorough ab initio study of the response of the 20 essential natural amino acids to intense circularly polarized electromagnetic radiation, thus simulating their twophoton absorption and two-photon circular dichroism spectra in a region of frequencies spanning the lowest part of the electronic excitation manifold. Also, the corresponding electronic (one-photon) circular dichroism spectra have been computed, thus allowing a comprehensive comparison of three spectroscopies on a large pool of systems of obvious biological interest. The essential step behind this work has been the recent development of the tools needed for an efficient calculation of the TPCD rotation strength, performed by resorting to analytical response theory within the DFT wave function model.19 The process has involved the introduction of origin-invariant approaches allowing for the rigorous solution of the problems introduced by the use of limited-expansion basis sets and truncated N-electron wave function models in approximate calculations of properties involving perturbations of at least magnetic dipole and electric quadrupole order.20 We were therefore able to perform extended calculations of the residues of the quadratic functions contributing to the two-photon rotation strengths according to Tinoco’s original formulation15 of the theory of TPCD. We have used basis sets of double-ζ quality and a DFT model resorting to the B3LYP density functional, and we have performed calculations for the lowest six excited electronic states of all essential natural amino acids. Tinoco’s full velocity origin-invariant expressions, which, as demonstrated in ref 20, yields the most efficient computational implementation in the calculation of TPCD, was exploited. Following standard approaches, TPA and ECD strengths were also computed. The resulting TPA, TPCD, and ECD spectra, for the specific experimental setup where circularly polarized radiation is employed, have been presented and discussed in detail. A comparison of the integrated absorption and differential rotation strengths within the whole range of amino acids was carried out. This has permitted us to establish that the amino acids with side aromatic chains appear to be the most effective ones in yielding, on average, strong two-photon absorptions in the lowphoton-energy range where the six lowest electronic excited states appear. Those yielding the most intense circular dichroism signal (either one- or two-photon) are the amino acids with aliphatic side chains, as Ile and Leu for TPCD and Ile and Ala for ECD. Asn, Pro, and Trp also exhibit somewhat intense TPCD bands, just as well as Ser and Asn do with respect to ECD. For each amino acid we have analyzed the spectra, highlighting the analogies and the differences, and attempted to rationalize the features of each spectrum in terms of the rotational strengths. For the TPCD, these have been given explicitly in terms of the molecular parameters including all information on the molecular response to the external perturbation. This allows for both a trivial extension of our study to all possible choices

Circular Dichroism in Chiral Natural Amino Acids of photon polarization and geometrical setup and an in-depth analysis of the relative importance of electric dipole-magnetic dipole and electric dipole-electric quadrupole contributions to the observable. The latter appear to be in the vast majority of cases rather small, albeit seldom truly negligible. This study confirms that TPCD has in principle very peculiar fingerprinting capabilities and could be powerfully employed as an additional convenient tool for investigation of biological samples, in connection with other currently established spectroscopies as TPA, ECD, and Raman optical activity, ROA.3 The latter, especially in its natural vibrational manifestation,50-54 appears to be profoundly influenced by changes in electronic and structural properties of the molecule. Of special interest would be to explore the possibility of correlating specific TPCD features with functional groups and in some cases, individual bonds, such that the total spectrum could be considered as a linear combination of elementary spectra. This conceptual “building block principle” approach could provide a useful starting point for the interpretation of spectra of very complicated molecules. The ultimate goal would be to explore the limits of such approaches in the case of amino acids and to determine which building blocks can be considered best for descriptions of the TPCD spectra and also for larger protein complexes. This kind of analysis, on the other hand, requires an in-depth analysis of the electronic structural characteristics of the molecular systems and the ability to identify the characteristics of each excited state and connect those properties to the local features of the system being subjected to excitation. This task, albeit of unquestionable interest, is quite complex, and we consider it at this stage beyond the scope of this work. Finally, a few words about the quality and reliability of our results is in order. TPCD is a nonlinear optical property involving high-order molecular properties and requiring the calculation of transition strengths involving magnetic dipole and electric quadrupole interactions. In our experience these are rather demanding quantities, calling for proper treatment of the environment, for the use of extended and diffuse basis sets and of adequate wave function models. Concerning the latter, DFT/ B3LYP was recently proven to perform quite well in calculations of nonlinear optical properties of systems such as benzene55 and hexafluorobenzene,56 and it is at this stage the best choice, at the very least in terms of the ratio between cost and efficiency, for systems of the size related in this work. Note that recently the very promising qualities of the DFT/Coulomb Attenuating Method B3LYP (DFT/CamB3LYP)57,58 model in computing two-photon absorption spectra were highlighted by the authors of ref 59. The more serious limitation in our case is probably that connected to the use of basis sets of double-ζ quality. In ref 20 we have shown that results obtained for the TPCD rotation strengths of a system of reduced size as twisted hydrogen peroxide with a double-ζ basis set were still quite distant from those yielded by the corresponding triple-ζ set. We report here the same arguments employed in ref 20. Basis sets of triple-ζ size are not yet affordable for large systems of biological interest, and anyhow we cannot go beyond double-ζ quality. However, “large” molecules show different, improved, basis set convergence, as the manifold of basis functions at distant atoms helps to fill the one-particle basis at a specific site. We are witnessing the fast development of linear and sublinear scaling correlated approaches, and the current limitations on the size of basis sets may soon be gone. It is a fact, on the other hand, that the nonnegligible long-range interactions appearing with diffuse basis sets are still likely to force the use of smaller basis

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