Vacuum-Ultraviolet Electronic Circular

Vacuum-Ultraviolet Electronic Circular Dichroism of L-Alanine in Aqueous Solution Investigated by Time-Dependent Density Functional Theory Takayuki Fukuyama,† Koichi Matsuo,† and Kunihiko Gekko*,†,‡ Department of Mathematical and Life Sciences, Graduate School of Science, and Hiroshima Synchrotron Radiation Center, Hiroshima UniVersity, Higashi-Hiroshima 739-8526, Japan ReceiVed: April 6, 2005; In Final Form: June 7, 2005 The electronic circular dichoism (ECD) of L-alanine in the vacuum-ultraviolet region was calculated for various optimized structures using time-dependent density functional theory (TDDFT) to assign the CD spectrum observed experimentally in aqueous solution down to 140 nm [Matsuo, et al. Chem. Lett. 2002, 826]. The structure of L-alanine in vacuo was optimized using density functional theory (DFT) at the B3LYP/6-31G* level. Its hydrated structure was optimized with nine water molecules (six and three around carboxyl and amino groups, respectively) using DFT and a continuum model (Onsager model). The dihedral angles of carboxyl and amino groups in the optimized hydrated structure differed greatly from those in the crystal and in nonhydrated structures optimized using a continuum model only. The ECD spectrum calculated for the hydrated structure had two successive positive peaks with molar ellipticities of about 2000 deg cm2 dmol-1 at around 205 and 185 nm, which were close to those observed experimentally. These positive peaks were attributable to nð* transitions of the carboxyl group, with the latter peak also influenced by the ðð* transition of the carboxyl group that originates below 175 nm. A small negative peak observed at around 252 nm was also predicted from the hydrated structure. These results demonstrate that the hydrated water molecules around the zwitterions play a crucial role in stabilizing the conformation of L-alanine in aqueous solution and that TDDFT is useful for the ab initio assignment of ECD spectra down to the vacuum-ultraviolet region. I. Introduction Circular dichroism (CD) is very sensitive to the conformation of chiral molecules, which makes CD spectroscopy a useful tool for structural analyses of both biomolecules and organic materials.1,2 The CD spectrum in the vacuum-ultraviolet region, which is hardly measurable using a conventional CD spectro- photometer, can provide more detailed and new information on the structure of biomolecules based on the higher energy transition of chromophores. Since the 1970s, there has been a great deal of effort at several facilities to extend the short- wavelength limit of CD spectrophotometer using synchrotron radiation as an intense light source.3-6 We recently constructed a vacuum-ultraviolet CD spectrophotometer at Hiroshima Synchrotron Radiation Center that can measure CD spectra down to 140 nm in aqueous solutions due to all of the optical devices being kept under a high vacuum.7,8 In this spectropho- tometer, the optical servo-control system is newly introduced to control the photoelastic modulator accurately and to stabilize the lock-in amplifier in the vacuum-ultraviolet region, and the path-length of the optical cell is very short (from 1.3 to 50 ím) to minimize light absorption by the solvent water. A consider- able body of vacuum-ultraviolet CD data has been accumulated on biomolecules such as amino acids, carbohydrates, proteins, and nucleic acid.1,2,9-11 However, only a few limited theoretical assignments have been reported for electronic CD (ECD) spectra in the vacuum-ultraviolet region12,13 and for vibrational CD spectra (VCD) in the infrared region,14 because of the compli- cated relationship between chiroptical properties and molecular structure. The theoretical assignment of these vacuum-ultraviolet ECD spectra taking into account the electronic transition is indispensable for understanding details of the conformation of biomolecules in aqueous solution or physiological conditions. Some theoretical approaches have been developed to estimate ECD spectra from known structures of molecules or to determine the conformation of molecules from their CD spectra. The octant rule is useful for the conformation of molecules containing ketone or aldehyde groups, with the ð-SCF-CI-DV method being useful for twisted or conjugated ð-electron systems, and Tinoco’s method for very large molecules such as polypeptides and proteins.15-17 On the other hand, it remains difficult to calculate ECD spectra for molecules in aqueous solution because their various equilibrium conformations are complicatedly affected by hydration. The Onsager model (continuum model) includes the effects of the solvent ab initio by assuming a dielectric medium.18 However, density functional theory (DFT) has shown promise in evaluating the role of hydration in the structural optimization of biomolecules, because it introduces the electronic correlation effect into calculations of the confor- mation of molecules with high accuracy and with computational efficiency comparable with the Hartree-Fock (HF) method.19,20 Also, time-dependent density functional theory (TDDFT) has become useful for calculating electronic excitation spectra of valence transitions and has greatly improved calculations of ECD,21 as confirmed for helicenes by Furche et al. 22 In the present study, we applied TDDFT to assign the CD spectrum of L-alanine in aqueous solution in the vacuum- ultraviolet region. The vacuum-ultraviolet CD spectra of L- alanine have previously been measured in film23 and hexafluoro- 2-propanol,12 but we have recently succeeded in measuring its CD spectrum down to 140 nm in aqueous solution.9 This * Corresponding author. E-mail: gekko@sci.hiroshima-u.ac.jp. † Department of Mathematical and Life Sciences. ‡ Hiroshima Synchrotron Radiation Center. 6928 J. Phys. Chem. A 2005, 109, 6928-6933 10.1021/jp051763h CCC: $30.25 © 2005 American Chemical Society Published on Web 07/20/2005 Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Sticky Note helicene—百度词典 [网络释义]1.螺烯 Administrator Highlight Administrator Sticky Note alanine—百度词典 alanine ['ælənin] [词典释义]n. 1. 【化】【生化】丙氨酸 [网络释义]alanine 1.丙氨酸 2.丙胺酸 Alanine 1.丙氨酸 Administrator Highlight spectrum exhibited two successive positive peaks at around 203 and 184 nm and a shoulder at around 170 nm, which differ considerably from the peaks in a nonaqueous system probably because L-alanine exists in a zwitterionic form with hydrated water molecules in aqueous solution. We optimized the structure of L-alanine in aqueous solution by combining DFT and the Onsager model, and we calculated the ECD spectra using the TDDFT for the crystal and the optimized structures with and without hydration to assign the spectrum observed experimen- tally. This is the first study to demonstrate the usefulness of TDDFT in the theoretical analysis of vacuum-ultraviolet ECD of amino acids in aqueous solution. II. Theoretical and Experimental Methods Initial Structures of L-Alanine. The 36 initial structures of L-alanine were constructed with the standard molecular param- eters for bond lengths (C-C, 1.53 Å; C-O, 1.25 Å; C-N, 1.48 Å; C-H, 1.09 Å; and N-H, 1.03 Å) and bond angles (O-C- O, 125.00°; C-C-N, C-C-H, and C-N-H, 109.47°),24-28 by changing the dihedral angle of the COO- group (�) from -60° to 120° in increments of 30° and that of the NH3+ group (æ) from -60° to 60° in increments of 20°. The model structure of L-alanine and the definition of the dihedral angles are shown in Figure 1. Optimization of L-Alanine Structures. The optimized structure of L-alanine is closer to the experimentally measured structure when using the DFT method than when using the HF method.29 We therefore adopted the DFT method to optimize the structure of L-alanine at the B3LYP/6-31G* level. The effect of the solvent surrounding L-alanine was calculated using a continuum model (Onsager model) with the relative permittivity of water (78.39) and a recommended cavity radius for a solute volume. Optimization was performed with the Gaussian 98 program (Gaussian)30 on an H9000 VR360 computer (Hitachi) at the Information Media Center of Hiroshima University. Calculation of CD Spectra. CD is induced by the interaction between electric and magnetic dipole transition moments of chromophores. As for the relationship between absorption and the dipole strength, CD is related to the rotational strength, R, which is theoretically defined by2,31 where R0a is the rotational strength of the electric transition from the “0” to “a” states, íˆ and mˆ are the electric and magnetic dipole moments, respectively, and Im means the imaginary part of a complex number. The rotational strength is expressed in cgs units (erg cm3), which are conveniently transferred to a Debye-Bohr magnetron (1 DBM ) 0.9273 � 10-38 erg cm3 ) 0.9273 � 10-51 J m3). The final CD spectrum can be calculated using the following equations: where [ı] is the molar ellipticity, ìi is the wavelength of the ith transition, and ¢ì is the half bandwidth of a spectrum calculated assuming the Gaussian distribution. The CD spectra were calculated using Gaussian 98. The rotational strength, Ri, was first calculated using a TDDFT method at the B3LYP/6- 31+G** level and a polarized continuum model (PCM)32 to take the effect of the solvent into account. From the obtained rotational strength, CD spectra were calculated using eqs 2 and 3 with a ¢ì value of 12.5 nm. Far-UV CD Measurements. L-Alanine of reagent grade was purchased from Sigma and dissolved in double-distilled water at 0.1 g cm-3. The concentration of L-alanine was determined accurately by calibrating the moisture content. The far-UV CD spectrum was measured on a J-720W spectropolarimeter (Jasco) with a 10-mm-path-length quartz cell, an 8-s time constant, a 20-nm/min scan speed, and 9-times accumulation. III. Results and Discussion Rotational Strengths and CD Spectra of Initial Structures. To elucidate the effect of the dihedral angles of the COO- and NH3+ groups on rotational strength, the rotational strengths of 36 initial structures were first calculated for their lowest energy transitions without optimization. Figure 2 shows plots of the rotational strengths (R) as functions of dihedral angle (�) of the COO- group for six dihedral angles (æ) of the NH3+ group (from -60° to 60°). It is evident that the rotational strength of the lowest energy transition is more sensitive to the dihedral angle of the COO- group than that of the NH3+ group. The CD spectra of L-alanine between 260 and 140 nm were calculated for typical initial structures with the following four sets of � and æ values: (0°, 0°), (0°, 60°), (90°, 0°), and (90°, 60°). As shown in Figure 3, the CD spectrum for (90°, 0°) is similar to that for (90°, 60°) but differs markedly from the spectrum for (0°, 0°), indicating that the dihedral angles of the COO- group have a large effect on the ECD of L-alanine. Therefore, it is necessary to determine accurately the dihedral angle of the COO- group using an optimization method when Figure 1. Model structure and definition of dihedral angles of L-alanine (zwitterion form). Atoms of O, N, H, and C are colored red, blue, white, and green, respectively. � and æ indicate the dihedral angles of COO- (N1-C1-C2-O1) and NH3+ (C2-C1-N1-H2) groups, respectively; these angles were varied in increments of 30° and 20°, respectively, to obtain the 36 initial structures. R0a ) Im{〈¾0jíˆj¾a〉â〈¾ajmˆj¾0〉} (1) Ri ) 1.23 � 10-42 [ı]i¢ì ìi (2) [ı](ì) ) ∑ i [ı]i exp[-(ì - ìi¢ì )2] (3) Electronic Circular Dichroism of L-Alanine J. Phys. Chem. A, Vol. 109, No. 31, 2005 6929 Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Sticky Note ellipticity—百度词典 ellipticity [ɪ,lɪp'tɪsətɪ] [词典释义]n. 1. 【数】椭圆率 [网络释义]1.椭圆率 2.椭圆度 Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight calculating the ECD spectrum of L-alanine in the vacuum- ultraviolet region. Optimized Structures and ECD Spectra in Vacuo and in Water. The structure of L-alanine in vacuo was optimized with the four initial structures mentioned above. The averaged molecular parameters of the optimized structure (structure I) are listed in the third column of Table 1. As compared to the crystal structure (in the second column of Table 1),33 the N1- H3 bond is significantly stretched and the bond angle of H3- N1-C1 and the dihedral angles (� and æ) are remarkably changed. These results suggest that proton transfer from NH3+ to COO- groups is induced in vacuo, forming the nonionized structure of L-alanine. The structure of L-alanine in water was optimized using the Onsager model to take the effect of the solvent into account. In all of the four initial structures, the optimized structures converged on an identical structure: (�, æ) ) (5.6°, -5.2°). The � values of these optimized structures are in agreement with those (0 ( 10°) reported in previous works.28,34 The averaged molecular parameters of the optimized structures (structure II) are listed in the fourth column of Table 1. As compared to the crystal structure, stretching of the N1-H3 bond and a decrease in the bond angle of H3-N1-C1 still occur in the continuum model, but to lesser extents than found in vacuo. Figure 4 shows ECD spectra calculated for the optimized structures in vacuo (structure I) and water (structure II) using the molecular parameters listed in Table 1. The spectrum for the crystal structure was also calculated for comparison using the molecular parameters in the second column of Table 1. The spectra for the optimized structures in vacuo and water exhibit positive peaks at around 230 and 210 nm, respectively, followed by two negative peaks in the vacuum-ultraviolet region. The difference between the two spectra may be mainly ascribed to the differing ionization states of zwitterions in vacuo and in a dielectric medium. The crystal structure exhibits a small positive peak at around 220 nm, a negative peak at around 200 nm, and two positive peaks in the vacuum-ultraviolet region, which are similar to those in film.22 These three spectra of L-alanine differ markedly from that observed experimentally in aqueous solu- tion,9 which indicates that the optimized structure and CD spectra obtained using the continuum model only are imaginary, and therefore that the effect of hydration around zwitterions should be taken into account when determining the structure of L-alanine in aqueous solution. Optimization of the Hydrated Structure. Some experi- mental and theoretical studies have evaluated the amount of hydration of L-alanine. From NMR analysis, Kuntz showed that about six and three water molecules are bound to the COO- and NH3+ groups of side chains of polypeptides, respectively.35 These values are consistent with theoretical calculations on model compounds: the COO- group of CH3COO- has six hydrated water molecules,36 and each hydrogen atom of the NH3+ group of CH3NH3+ hydrates one water molecule.37 Recently, Frimand et al. showed that nine explicit water molecules are necessary for reproducing the VCD spectrum of L-alanine in water.14 We therefore optimized the hydrated structure of L-alanine with nine water molecules (six and three for the COO- and NH3+ groups, respectively) using a continuum model for the initial structures with four sets of dihedral angles (�, æ): (0°, 0°), (0°, 60°), (90°, 0°), and (90°, 60°). The following molecular parameters were used for water and its hydrogen bonds with zwitterions: O-H, 0.948 Å; H-O-H, 106.6°; COO-- - -H-O, 2.0 Å; and NH3+- - -O-H, 1.8 Å. The initial structure having only (�, æ) ) (90°, 60°) could be optimized, and the others could not retain the hydrated water molecules around the zwitterions. The optimized structure (structure III) is shown stereographically in Figure 5, and its molecular parameters are listed in the fifth column of Table 1. Six water molecules around the COO- group form a hydrogen- bond network with each other to restrict the rotation of this group. Each hydrogen atom of the NH3+ group forms a hydrogen bond with a water molecule, and two hydrated water molecules around the NH3+ group form a hydrogen-bond network with those around the COO- group. The lengths of the hydrogen bonds are between 1.75 and 1.95 Å, which are consistent with the result (1.8 Å) of a Monte Carlo simulation for the hydration of CH3NH3+.37 The bond lengths and bond angles of the optimized structure are close to those of the crystal structure, and stretching of the N1-H3 bond (as found for structure II) does not occur. On the other hand, the dihedral angles differ markedly from those for the crystal structure and structure II, probably due to the hydrogen-bond network around the zwitterions. To confirm the propriety of the nine water molecules in the optimized structure, an additional water molecule was added around the CH3 group of L-alanine. As listed in the last column of Table 1, the molecular parameters of the structure thus optimized (structure IV) are very close to those of structure III. This result indicates that the additional Figure 2. Rotational strength (R) as a function of the dihedral angle (�) of the COO- group at the lowest energy transition: æ ) -60° (60°), black line; -40°, red line; -20°, blue line; 0°, purple line; 20°, brown line; and 40°, green line. Figure 3. ECD spectra calculated for four typical initial structures of L-alanine: (�, æ) ) (0°, 0°), black line; (90°, 0°), red line; (0°, 60°), blue line; and (90°, 60°), purple line. 6930 J. Phys. Chem. A, Vol. 109, No. 31, 2005 Fukuyama et al. Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Sticky Note alanine—百度词典 alanine ['ælənin] [词典释义]n. 1. 【化】【生化】丙氨酸 [网络释义]alanine 1.丙氨酸 2.丙胺酸 Alanine 1.丙氨酸 Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight Administrator Highlight water molecule is removed from the initial structure and that the conformation of L-alanine in water is mainly determined by nine hydrated water molecules. ECD Spectrum of the Hydrated Structure. Figure 6 shows the rotational strength and ECD spectrum calculated for the optimized structure of L-alanine with nine hydrated water molecules (structure III). These hydrated water molecules were ignored in the calculation due to the computational limitations. Evidently, there exist many rotational strengths with positive and negative signs in the vacuum-ultraviolet region. The obtained ECD spectrum shows positive peaks at around 203 and 185 nm, negative peaks at 225 and 160 nm, and a small shoulder at around 170 nm. This spectrum is very different from that for structure II calculated using a continuum model (Figure 4), and both the wavelengths and the intensities of its peaks are similar to those observed experimentally except for a large negative peak at around 225 nm. This indicates that the continuum model is inadequate, and so its combination with the hydrated water molecules is indispensable for evaluating the effect of the solvent on ECD. At present, we cannot explicitly explain the large ne