Computational Approach to Evaluation of Optical Properties of

Subscriber access provided by University of Newcastle, Australia

Article

Computational approach to evaluation of optical properties of membrane probes Lina Johanna Nåbo, Nanna Holmgaard List, Casper Steinmann, and Jacob Kongsted J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.6b01017 • Publication Date (Web): 02 Jan 2017 Downloaded from http://pubs.acs.org on January 11, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Journal of Chemical Theory and Computation is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Journal of Chemical Theory and Computation

Computational approach to evaluation of optical properties of membrane probes Lina J. N˚ abo,⇤,† Nanna Holmgaard List,‡ Casper Steinmann,¶ and Jacob Kongsted⇤,† †Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark ‡Division of Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden ¶Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom E-mail: [email protected]; [email protected]

Abstract Computed optical properties of membrane probes are typically evaluated in the gas phase, i.e. neglecting the influence of the membrane. In this study, we examine how and to what extent a membrane influences the one- and two-photon absorption (1PA and 2PA, respectively) properties for a number of cholesterol analogs and thereby also evaluate the validity of the common gas phase approach. The presence of the membrane is modeled using the polarizable embedding scheme both with and without the e↵ective external field extension of the polarizable embedding model. The shifts in excitation energies and one-photon absorption oscillator strengths compared to gas phase are relatively small, while the 2PA process is more a↵ected. The electric field inside the membrane induces a larger change in the permanent electric dipole moment

1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

upon excitation of the analogs compared to in gas phase, which leads to an almost 2-fold increase in the 2PA cross section for one cholesterol analog. The relative trends observed in the membrane are the same as in the gas phase, and the use of gas phase calculations for qualitative comparison and design of cholesterol membrane probes in terms of absorption properties is thus a useful and computationally efficient strategy.

2


Page 2 of 29

Page 3 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

Introduction

Cholesterol (Chol) plays a vital role in biology. It is a crucial ingredient in eukaryotic cellular membranes, where it modulates both structure and functionality and is also involved in cell metabolism. 1–7 Trafficking of Chol to the cell membrane is carefully regulated, and unrestrained Chol accumulation is deleterious for cells and associated with a number of diseases like atherosclerosis or lysosomal storage disorders. 8,9 It is therefore desirable to be able to visualize the organization and dynamics of Chol. Powerful tools for such monitoring are fluorescence spectroscopy and microscopy. 8,10 However, since Chol does not display fluorescence, suitable fluorescent analogs capable of probing the intra-cellular transport and membrane organization of Chol are needed. Ideally, these probes should perturb the original structure minimally, but be traceable with high sensitivity and specificity. A number of intrinsically fluorescent Chol analogs as well as externally labeled Chol probes are currently used for imaging applications, but su↵er from various disadvantages. 11 The intrinsically fluorescent probes dehydroergosterol (DHE) and cholestatrienol (CTL) mimic the physicochemical and biochemical properties of Chol very well due to their close structural similarities 8,10,12–20 (see Figure 1). Compared to Chol they have two additional double bonds in the ring system. DHE di↵ers further in the structure of the aliphatic tail which is identical to that in ergosterol, the sterol predominantly found in the plasma membranes of fungi. However, these probes su↵er from low brightness and poor photo-stability 8,10,13–15 and are excited in the UV-region of the spectra, which makes them less suitable for live cell imaging. On the other hand, externally labeled probes such as NBD 21 - and BODIPY-Chol 22,23 are often bright and stable, but perturb the membrane quite di↵erently compared to Chol due to their large covalent attachments. 10,22,24–28 Consequently, the development of new fluorescent probes that retain the functionality of Chol while displaying favorable optical properties is still an active area of research. We have recently investigated a series of intrinsically fluorescent Chol analogs and evaluated their applicability as membrane probes using computational tools. 29 Two important 3


Journal of Chemical Theory and Computation H

H

!

HO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Erg%

H

!

HO

DHE%

H

!

HO

1b%

Page 4 of 29

H

!

HO

2b%

H

!

HO

3b%

!

H H

H

HO

Chol%

!

H HO

DHE%

!

H HO

CTL%

!

H HO

3a%

!

! Figure 1: Molecular structures for cholesterol (Chol) and the probes dehydroergosterol (DHE), cholestatrienol (CTL) and 3a.

criteria for such probes are 1) they should mimic Chol in the way they perturb the membrane structure, and 2) they should absorb and emit light efficiently, preferably in or near the visible region of the electromagnetic spectrum. The analogs’ abilities to mimic the membrane-ordering properties of Chol were evaluated based on classical molecular dynamics (MD) simulations, and their one-photon absorption (1PA) and fluorescence properties were calculated using electronic structure methods. The size of biological systems, e.g. cell membranes, presents a huge challenge for theoretical investigations, especially when there is a need for a quantum mechanical treatment, as in the study of electronic excitation processes. The computational cost quickly becomes unfeasible, and a preferred approach is to focus only on a smaller part of the system, thus leaving out what is expected to be less important details of the membrane. For this reason, our initial approach was to evaluate the optical properties of the probes in the gas phase as is commonly done, and it was assumed that the trends observed in the gas phase also apply for the probes when they are situated inside a membrane. The results from these gas phase calculations as well as the analysis of the MD simulations have been reported and discussed in detail in ref. 29. The next step, which is the focus here, is to examine the extent to which the membrane a↵ects the electronic transition properties of the probes. Understanding the role of the membrane is necessary to determine whether or not a gas phase approach is at all qualitatively useful for membrane probes, i.e. are the trends observed in gas phase also valid in the probes’ real environment? We aim to answer this question for the case of Chol membrane probes by examining the absorption

4


Page 5 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


properties of a selection of these probes while taking the surrounding membrane into account. The study is further extended with the evaluation of two-photon absorption (2PA) properties of the probes. Excitation of fluorescent probes through a two-photon process has several advantages in microscopy applications, as for example reduced photo-bleaching, low phototoxicity, and higher spatial resolution compared to one-photon excitation. 30 A third criteria for a widely useful fluorescent probe is therefore a large 2PA cross section. The two currently used intrinsically fluorescent Chol analogs DHE and CTL are chosen as test cases together with the most promising probe candidate 3a from the previous study 29 (structures are shown in Figure 1). The 1PA and 2PA properties are calculated for these probes, and the role and importance of the membrane environment are evaluated in both cases. To describe the e↵ect of the membrane on the absorption properties of the probes we employ the polarizable embedding (PE) model, 31,32 which is a quantum–classical embedding approach tailored for the calculation of environmental e↵ects on spectroscopic properties (see ref. 33 for a recent perspective). In particular, this model incorporates the electrostatic potential at the location of the probe created by the surrounding molecules, including both static and dynamic polarization between the molecules in the surroundings and with the probe itself. Furthermore, the e↵ective external field extension of the PE model (PEEEF) 34 is used to account for direct polarization of the surroundings by the perturbing electromagnetic field. The theoretical background for these embedding models is given in the Methodology section. Based on our studies we find that the e↵ect of the membrane on the excitation energies of the probes is a moderate red-shift (0.05 0.15 eV), and the trends and conclusions derived on the basis of gas phase calculations are also seen in the membrane environment. The 1PA strengths are only slightly modified by the presence of the membrane, and the e↵ects of the environment are most pronounced in the 2PA intensities, which are significantly enhanced in the membrane compared to in gas phase. The neglect of the EEF e↵ect leads to an overestimation of the intensity. Furthermore, the 2PA cross section is promising for probe

5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 29

3a, but very small for both DHE and CTL.

2 2.1

Methodology Theoretical Background

In this work, we employ the PE model to accurately account for the presence of the environment during an electronic excitation of a probe embedded in a membrane. In this model the part of the system of specific interest (here the central probe) is treated using quantum mechanics (QM), while the presence of the rest of the system (here the membrane, other probes, water and ions) is accounted for with classical embedding methods. The permanent charge density of the environment is described by electric multipole moments distributed at the atomic sites. Polarization of the environment by the quantum region and in the environment itself is also taken into account through the use of atomic polarizabilities which leads to induced dipole moments. Thus, the standard PE method accounts for the electrostatic interaction between the surrounding molecules and the quantum region. The energy functional in the PE model can be partitioned into three components

Etot = EQM + EPE + Eenv ,

(1)

where EQM is the energy of the quantum region (including wave function polarization) and Eenv is the internal energy of all molecules in the environment, including the electrostatic interaction between the permanent multipoles assigned to the atomic sites. The energetic contributions arising from the interaction between the quantum region and the environment are described by EPE , which consists of three terms 31,32

EPE = Ees + Eind + Edisp

6

rep .


(2)

Page 7 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ees and Eind are the electrostatic interactions of the quantum region with the permanent and induced charge distributions in the environment, respectively. The latter also includes the electrostatic interaction between the induced dipole moments in the environment. Edisp

rep

contains the energy terms related to dispersion and exchange-repulsion e↵ects. These are typically treated only at the energy level using a Lennard-Jones potential, which does not a↵ect the electronic properties of the quantum region, so they are not included in the following response expressions. The wave function/density of the quantum region is determined by minimization of the total energy Etot with respect to the wave function/density parameters. This procedure leads to a set of self-consistent field equations where the vacuum Hamiltonian ˆ QM ) is appended by a ground state PE embedding operator (H vˆPE = vês + vînd .

(3)

The first and second term on the right hand side of eq. 3 represent the electrostatic interactions of the quantum region with the permanent multipoles and induced dipoles in the environment, respectively.

A convenient way of addressing excited states and transition properties is through response theory, 35 which for density functional theory (DFT) is known as time-dependent DFT (TDDFT). 36,37 Within this formalism, the linear response equations for a molecule in a PE environment perturbed by an electric field at frequency ! are 34 h x!b = E[2]

!S[2]

i

1

![1]

Vb ,

(4)

where x!b is the first-order response vector (b denotes the x-, y- or z-component) describing the physical response of the wave function/density due to the perturbation, S[2] is the gen![1]

eralized overlap matrix, Vb

is the property gradient reflecting the perturbation and E[2] is

7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 29

the electronic Hessian with matrix elements q

[2]

j ˆ QM + vˆPE ), qˆj ]]|0i + h0|[ˆ Eij = h0|[ˆ qi , [(H qi , vˆPE ]|0i,

(5)

written here in a second quantization formalism. The optimized ground state for the quantum region is denoted |0i, and qî represents a one-electron excitation (i > 0) or de-excitation (i < 0) operator. The first term in eq. 5 includes the vacuum contribution and the static (ground-state) polarization of the environment, while the last term accounts for the dynamic polarization of the environment due to the change in the charge distribution of the quantum ![1]

region caused by the perturbation. The elements of the property gradient Vb

in standard

PE are of the form ![1]

Vb,i

= h0|[ˆ qi , Vˆb! ]|0i,

(6)

where Vˆb! is the perturbation operator that represents the perturbing field. Excitation energies and transition moments can be found from a pole- and residue analysis of the linear response function related to eq. 4. Explicitly, excitation energies are found by solving the generalized eigenvalue equation E[2]

!n S[2] xn = 0,

(7)

where xn represents the n’th excited state with excitation energy ~!n =

E0n , where ~ is the

reduced Planck constant. The corresponding oscillator strength (fn ) for 1PA is calculated based on the expression for the single residues of the linear response function: (Sa0n )2 = lim (! !!!n

! [1]

!n )hhVâ ! ; Vâ! ii = Va!n [1]† xn x†n Vb n

(8)

ˆ Sa0n is a Cartesian for the case when the perturbation operator is the dipole operator (µ). component of the transition moment between the ground state and the excited state n. The

8


Page 9 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


explicit formula for the 1PA oscillator strength of this transition is then

fn =

X 2 E0n (Sa0n )2 , 3 ab

(9)

summing over the Cartesian coordinates. Two-photon absorption is a non-linear process with a probability depending on the square of the intensity of the incoming light. Since two photons are absorbed simultaneously to reach the excited state, the frequency of the photons at resonance corresponds to half the excitation energy: ! = !n /2 =

E0n /(2~). The strength associated with 2PA is related to the single

residues of the quadratic response function in a similar manner as 1PA is related to the linear response function. Computationally, the (a, b)’th component of the 2PA transition moment (S) is 34 ![2]

0n Sab = Va ![2] x!b xn + Vb xa ! xn + Pab E[3]

!S[3] xa ! x!b xn ,

(10)

where Pab is the permutation operator and definitions for the remaining matrices can be found in refs. 35 and 38. For linearly polarized light with parallel polarization, the rotationally averaged 2PA strength h

2PA

i in atomic units (a.u.) can be obtained from the transition

moments as 39 h

2PA

i=

1 X 0n 0n⇤ 0n 0n⇤ (2Sab Sab + Saa Sbb ), 15 ab

(11)

where the star indicates complex conjugation. Finally, the 2PA cross section can be obtained from the rotationally averaged 2PA strength using the following expression: 39,40 2PA

=

N ⇡ 3 ↵ a50 ! 2 h c

2PA

i g(2!, !n ),

(12)

where N is an integer, ↵ is the fine structure constant, a0 is the Bohr radius, ! is the photon frequency in a.u., c is the speed of light and g(2!, !n ) is the lineshape function that describes spectral broadening. These quantities are explained in detail in ref. 39. Using a Lorentzian lineshape function for the broadening and assuming resonant conditions, the 2PA 9



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 29

cross section becomes 2PA

where

=

N ⇡ 2 ↵ a50 ! 2 h c

2PA

i,

(13)

is the half width at half maximum. 39

The PE response equations assume a perturbing electric field in the quantum region that is una↵ected by the surrounding molecules, i.e. the field acting on the molecule treated using quantum mechanics is identical to the applied external field (F! ). However, due to environment polarization this is not the case, as the surrounding molecules will be polarized directly by the applied field. This polarization will in turn produce a field that is oscillating at the same frequency as the applied field. In a dielectric continuum picture such environmental polarization leads to a screening of the applied field, but in atomistic approaches it may lead to either a screening or an enhancement of the external field. The e↵ect of environment polarization is accounted for in the e↵ective external field extension of the PE model (PEEEF), which is thoroughly outlined in ref. 34. The PE-EEF perturbation operator Vˆ¯b! = Vˆb! + vˆbPE (!)

(14)

represents the perturbation from the e↵ective external field (FEEF,! ), which is the sum of the applied external field and the field caused by the polarization of the environment that has been directly induced by the applied field. Because the perturbation operator enters the expression for the transition moment for both 1PA and 2PA (see eqs. 8 and 10), we note that the inclusion of direct environment polarization modulates the strength of absorption. On the other hand, it does not a↵ect the excitation energies since the frequency of the field is unaltered and eq. 7 has no dependence on Vˆ¯b! . The modification of the external field due to the environment can be expressed in terms of e↵ective external field tensors with elements 34 LEEF,! (R) ab

@FaEEF,! (R) = @Fb!

10


(15)

Page 11 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


at location R within the quantum region. A diagonal element with a value larger than one thus corresponds to an environment-induced enhancement of the field in that direction, while a value below one indicates a screening of the field. The inclusion of direct polarization of the environment in PE-EEF provides a more realistic representation of the absorption process than standard PE, which allows for a better comparison to full quantum-mechanical predictions or experimental results. In the following we will compare the PE and PE-EEF approaches numerically in addition to investigate the optical properties of the probes.

2.2

Computational details

The structures used in the 1PA and 2PA calculations were taken from ref. 29, where they were obtained from three 200 ns, periodic boundary condition MD trajectories of 1-palmitoyl-2oleoyl-phosphatidylcholine (POPC) membranes containing 30 mol-% DHE, CTL or 3a (i.e. 128 POPC lipids and 54 probes) solvated in 0.15 M KCl. The Lipid14 41 and GAFF 42 force fields were used for POPC and Chol analogs, respectively, TIP3P 43 for water, and the parameters developed by Joung and Cheatham 44 for the ions. A detailed description of the setup of the MD simulations can be found in ref. 29. Only the last frame from each trajectory was used to evaluate the optical properties of the probes. Centering the simulation box around one probe at a time produced 54 (finite-sized) structures. The relevant excitation energies and associated 1PA and 2PA strengths were then evaluated for the central probe in each structure using the PE model described in the previous section. Figure 2 illustrate an example structure of 3a probes (yellow) embedded in a POPC membrane patch (grey) where the central probe that constitutes the quantum region is represented by van der Waals spheres. The embedding potential for the POPC lipids have been taken from ref. 46 and consists of averaged atom-centered charges and isotropic electric dipole–dipole polarizabilities derived on the basis of quantum-mechanical calculations employing a fragmentation strategy. Averaged embedding parameters for water molecules were taken from ref. 47 and have been 11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2: One of the structures from the MD simulation of 54 3a probes (yellow) embedded in a membrane patch of 128 POPC lipids (grey) solvated in water (blue) with K+ (pink) and Cl (green) ions. Ions, lipid head groups and the 3a molecule constituting the quantum region are represented by van der Waals spheres. H atoms in lipid tails and in 3a molecules (except the quantum region) are omitted for clarity. The figure was produced with the Visual Molecular Dynamics program (VMD). 45

12


Page 12 of 29

Page 13 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


derived in a similar manner. These averaged parameters have been designed to give the most optimal representation of the electrostatic potential, including polarization. Embedding parameters for the 53 probes in the outer region (number 54 constitutes the quantum region) were calculated for this work from a single geometry that had been optimized at the B3LYP 48–50 /6-311++G** 51 level of theory. Atom-centered, restrained electrostatic potential (RESP) charges 52 were calculated using the Antechamber 53 module within AMBER 54 on an ESP obtained with Gaussian 09 55 at the B3LYP/aug-cc-pVDZ 56,57 level of theory. The polarizabilities were determined at the same level of theory and distributed to atomic centers using the localized properties (LoProp) method by Gagliardi et al. 58 as implemented in a development version of the Dalton program. 59 Isotropic polarizabilities for the Cl and K+ ions were obtained using LoProp in Molcas 60 with the ANO-S 61 basis set and the B3LYP functional. Excitation energies and oscillator strengths were computed using PE or PE-EEF implementations within the framework of TDDFT. All property calculations employed the range-separated CAM-B3LYP 62 exchange-correlation functional and the 6-311++G** basis set for the probe in the quantum region. The quantum region and embedding potential were constructed in the polarizable embedding assistant script in combination with FragIt. 63 Calculations were performed using a development version of the Dalton program together with PElib 64 and Gen1Int. 65,66 The 2PA cross sections reported have been calculated using eq. 13 with N = 4, thus assuming excitation by a single beam, and

= 0.1 eV. 39 It should

be mentioned that CAM-B3LYP has been shown to underestimate the 2PA cross section for neutral chromophores due to an underestimation of excited state dipole moments. 39 The presented absolute 2PA cross sections are therefore likely also somewhat underestimated, but we expect that relative trends across probes will be correctly reproduced.

13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3

Page 14 of 29

Results and discussion

The transition properties for 1PA and 2PA have been calculated for 54 identical probes inserted in a POPC membrane. The average excitation energy and corresponding 1PA oscillator strength and 2PA cross section for the lowest ⇡ ! ⇡ ⇤ transition of each probe are presented in Table 1. The subsequent ⇡ ⇤ ! ⇡ de-excitation is accompanied by fluorescence emission that allows the probes to be detected. The corresponding 2PA transition strengths are given in Table S1 of the Supporting Information. Note that the vacuum results (taken from ref. 29 for 1PA) are based on a single, quantum-mechanically geometry-optimized structure for each probe, while the PE and PE-EEF calculations are averages over 54 conformations in a single snapshot from an MD simulation. However, the 2PA cross sections for DHE and CTL are averages over three conformations only. All three values are given in Table S2 in the Supporting Information. Table 1: Average excitation energies ( E) in eV and corresponding average oscillator strengths (f ) and 2PA cross sections ( 2PA , 1GM = 10 50 cm4 photon 1 s 1 ) for the lowest ⇡ ! ⇡ ⇤ transition of three Chol analogs in vacuum or in the membrane modeled with PE or PE-EEF. Standard deviations are indicated in parenthesis. All quantities are calculated at the CAM-B3LYP/6-311++G** level of theory. Probe DHE

CTL

3a

Model vac PE PE-EEF vac PE PE-EEF vac PE PE-EEF

E 3.90 3.75 (0.16) 3.90 3.78 (0.15) 3.41 3.36 (0.15)

f 0.32 0.36 (0.02) 0.26 (0.02) 0.31 0.35 (0.02) 0.27 (0.02) 0.43 0.47 (0.03) 0.34 (0.03)

2PA

0.01 0.11* 0.07* 0.01 0.21* 0.13* 1.95 6.94 (3.57) 3.84 (1.99)

*Average over only three molecular structures, see Table S2.

The optical properties of DHE and CTL are very similar, as is expected since they have identical ring structures and thereby identical ⇡-conjugated systems. In general, the presence of the lipids, water molecules and ions surrounding the probes leads to a small red shift in the

14


Page 15 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


absorption maximum compared to in gas phase. Probe 3a displays the smallest shift of only 0.05 eV, which is not significant considering the magnitude of the fluctuations (the standard deviation is 0.15 eV). The fluctuations are dynamical temperature e↵ects caused by slight di↵erences in the conformations of both probe and neighboring molecules. Note that the gas phase calculations were performed at 0 K, so the temperature of 303 K will also lead to a shift in the average excitation energy due to distorted geometries. Another possible cause for a shift is the use of a force field to determine the geometries instead of a more accurate electronic structure method. The average excitation energy for the 3a probes calculated in isolation, but using the molecular geometries from the simulation, is blue-shifted by 0.04 eV compared to the geometry-optimized structure. However, inclusion of the membrane in the calculation leads to an overall red shift. Due to the alignment of the electric dipoles of the lipids and water molecules in a membrane, the center of the membrane acquires a positive potential known as the membrane dipole potential. 67 Because the dipole potential is operative over a relatively small distance, the field from this potential is large, in the 10 MV·cm 1 , 68 and is parallel (or anti-parallel for the lower leaflet) with the

order of 1

membrane normal (z-direction). Chol is known to increase the dipole potential and thereby the field inside a membrane. 69 Our calculated electric fields have local magnitudes up to 25 MV·cm

1

at the positions of the C atoms participating in the ⇡-conjugated system in

the probes, and even larger values are found at the positions of the O atoms (see Figure 3). Since the membrane field in this case is also more or less parallel to the change in dipole moment in the probes upon excitation (see green arrow in Figure 3), it is expected that the field stabilizes the excited state charge distribution in the probes and thereby lowers the energy of the excited state, leading to an expected red-shift in the absorption. The e↵ect of the environment on the 1PA strength is similar across the di↵erent probes. The standard PE model predicts an increase in intensity compared to in gas phase, while the PE-EEF model predicts a decrease. The increased absorption predicted by the PE model stems from increased transition dipole moments in the z-direction, i.e. parallel to the field.

15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3: The local electric field (magenta arrows) experienced by probe 3a in its electronic ground state in the solvated membrane, using a representative snapshot. Ground state dipole moment (blue) and di↵erence dipole moment upon excitation (green). The figure was produced with VMD.

16


Page 16 of 29

Page 17 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


However, the screening of the external field in the z-direction found by inspection of the EEF tensor (defined in eq. 15) leads to an overall decrease in the transition dipole moments in this direction (see Supporting Information). The approximation of an unaltered external field in the standard PE treatment thus leads to an overestimation of the 1PA absorption strengths of between 30 and 38 % for the examined probes.

3.1

Two-photon absorption

The gas phase calculations for DHE and CTL indicated only a very small 2PA cross section. Therefore, we only evaluate the environmental influence on the 2PA cross section for three representative geometries for each of these probes to inspect if the environment would induce a large increase in two-photon activity. As in the case of 1PA, the PE treatment enhances the intensity of absorption for all probes. The PE-EEF extension also leads to an increase in the 2PA intensity, but to a smaller extent than PE. The 2PA cross sections for DHE and CTL are however still too small to be considered useful experimentally, and we did not perform further calculations on these molecules. The probe 3a has a more promising 2PA cross section based on calculations performed in isolation, and we therefore calculated the intensity for all 54 structures using PE or PE-EEF to include the e↵ect of the environment. On average we see a 2-fold increase in 2PA activity (more than 3-fold without EEF e↵ects) induced by the environment. Furthermore, the 2PA cross section is very sensitive to the geometry of the probe and/or its neighbors, as seen from the large standard deviation. The origin of the large increase in 2PA induced by the membrane can be illustrated with the approximate two-state model (2SM) 70,71 for the 2PA, where only the ground state (0) and the final excited state (f ) are considered. Use of this model is reasonable in this case since the higher excited states in 3a are energetically well-separated from the ground and first excited states and also strongly electric-dipole forbidden. The elements of the transition

17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 29

moment in the 2SM (S2SM ) are of the general form 34 0f S2SM,ab =

⌘ 2 ⇣ 0f 0f 0f µa µ0f + µ µ , a b b !0f

where a, b = x, y or z, and !0f is the frequency corresponding to the excitation energy

(16)

E0f .

µ0f a is an element of the transition dipole moment from the ground to the final excited state, while

µ0f a is a component of the di↵erence electric dipole moment, i.e. the change

in the permanent electric dipole moment upon excitation (green arrow in Figure 3). To validate the 2SM for probe 3a, we used it to calculate the elements of S in the gas phase and compared them with the corresponding elements obtained by use of quadratic response (see eq. 10), and obtained qualitatively similar results (see Supporting Information). The following discussion of membrane-embedded probes is based on calculations that include EEF e↵ects. As already mentioned, the transition dipole moments are slightly decreased by the presence of the membrane and are therefore not responsible for the observed increase in 2PA. Moreover, the 2PA cross sections calculated for the 54 structures of 3a do not correlate with the magnitude of their transition dipole moments (data not shown), so the variation in transition dipole moments is not the cause of the observed variation in the 2PA cross sections. On the other hand, the 2PA cross section correlates well with the square of the magnitude of

µ, as shown in Figure 4 (recalling from eqs. 11–13 that the 2PA cross section

is proportional to the square of the transition moment). Since

µ has its largest component

in the z-direction, it interacts favorably with the membrane field, which leads to an almost 2-fold increase in

µ compared to in gas phase to obtain an energetically even more favorable

interaction. According to eq. 16, an increased

µ gives a larger 2PA transition moment and

thereby a greater 2PA cross section, in agreement with Figure 4. This conclusion can also explain why the 2PA activities of DHE and CTL are much smaller. In the gas phase,

µ is

calculated to be 0.29 and 0.32 Debye for DHE and CTL respectively, while it is 1.33 Debye for 3a. Even though

µ may increase due to the membrane field, it remains relatively small

18


Page 19 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4: The 2PA cross section for the 3a probes plotted against the square of the magnitude of the change in permanent electric dipole moment upon excitation, together with a linear fit. Both quantities have been calculated for membrane-embedded probes and include EEF e↵ects. Each point represents a di↵erent geometry of 3a. for DHE and CTL. In summary, we see that the relative trends in excitation energy and absorption strengths observed in gas phase are also found in the probes’ intended environment. The influence of the membrane and solvent on the one-photon transition properties is rather small, but twophoton processes are more a↵ected. The membrane field induces a larger charge reorientation in the probe upon excitation, which in turn leads to a stronger 2PA in the membrane compared to in the gas phase.

4

Conclusions

This article examines the influence of the membrane environment on the excitation energies and 1PA and 2PA strengths of Chol analogs with the aim of evaluating whether or not the use of gas phase calculations for prediction of absorption properties is a useful approach for such intrinsically fluorescent Chol probes. The shifts in excitation energies and 1PA oscillator strengths are relatively small for all probes. The largest e↵ect of the membrane is observed for the 2PA cross sections due to a membrane-field-induced increase in bilayer normal. Furthermore, it is observed that 19

µ along the

µ largely determines the 2PA cross section



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

for this class of Chol analogs, and a large

µ is therefore a criterion for future design of

similar efficient 2PA probes. It is also noted that EEF e↵ects are found to have a significant influence on both 1PA and 2PA properties of the Chol analogs. Ignoring these e↵ects as in the standard PE model leads to an overestimation of the 1PA oscillator strength by up to 38 %, while the 2PA strength is overestimated by as much as 81 % as seen for probe 3a. This work together with the previous report 29 present a computational approach to be used in the design of fluorescent membrane probes. Overall, the e↵ects of the membrane on both excitation energies and absorption strengths are qualitatively similar for the investigated Chol analogs, and the same relative trends in excitation energies and absorption strengths as observed in gas phase are consequently found when the analogs are embedded in the membrane. Performing gas phase calculations for qualitative comparison of absorption properties is thus a useful and computationally efficient strategy for the examined probes, and this conclusion is expected to be valid at least also for other intrinsically fluorescent Chol analogs in similar environments. However, since the membrane is shown to have a large e↵ect on some molecular properties it has to be included in the model in order to obtain quantitatively accurate results. In agreement with our previous study, 29 which identified 3a as an interesting Chol probe based on its ability to closely mimic the membrane properties of Chol and its favorable optical properties in the gas phase, we find a relatively strong 1PA also for membrane-embedded 3a probes. Furthermore, probe 3a has a noticeable 2PA cross section that is increased by the presence of the membrane. Altogether, these properties make it a very promising candidate for a Chol membrane probe that can be used with both 1PA and 2PA.

Acknowledgement Computational resources were provided by the DeIC National HPC Center at the University of Southern Denmark. N.H.L. acknowledges the Carlsberg Foundation for a postdoctoral fel-

20


Page 20 of 29

Page 21 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


lowship (Grant No. CF15-0792). C. S. thanks the Danish Council for Independent Research (the Sapere Aude program) for financial support (Grant No. 4181-00370). J. K. thanks the Danish Council for Independent Research (the Sapere Aude program), the Villum Foundation, and the Lundbeck Foundation.

Supporting Information Available Average two-photon transition strengths, individual 2PA cross sections for DHE and CTL, the average e↵ective external field tensor for probe 3a and evaluation of the two-state model for two-photon absorption are given in the Supporting Information.

This material is

available free of charge via the Internet at http://pubs.acs.org/.

References (1) Yeagle, P. L. Biochim. Biophys. Acta - Reviews on Biomembranes 1985, 822, 267–287. (2) Henriksen, J.; Rowat, A.; Brief, E.; Hsueh, Y.; Thewalt, J.; Zuckermann, M.; Ipsen, J. Biophys. J. 2006, 90, 1639–1649. (3) Ipsen, J. H.; Karlström, G.; Mourtisen, O.; Wennerström, H.; Zuckermann, M. Biochim. Biophys. Acta - Biomembranes 1987, 905, 162–172. (4) Vist, M. R.; Davis, J. H. Biochemistry 1990, 29, 451–464. (5) Xu, X.; London, E. Biochemistry 2000, 39, 843–849. (6) Silvius, J. R.; del Giudice, D.; Lafleur, M. Biochemistry 1996, 35, 15198–15208. (7) Ipsen, J.; Mouritsen, O.; Bloom, M. Biophys. J. 1990, 57, 405–412. (8) W¨ ustner, D. Chem. Phys. Lipids 2007, 146, 1–25. (9) Maxfield, F. R.; Tabas, I. Nature 2005, 438, 612–621. 21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(10) Maxfield, F. R.; W¨ ustner, D. Lipids; Elsevier BV, 2012; pp 367–393. (11) Sezgin, E.; Can, F. B.; Schneider, F.; Clausen, M. P.; Galiani, S.; Stanly, T. A.; Waithe, D.; Colaco, A.; Honigmann, A.; W¨ ustner, D.; Platt, F.; Eggeling, C. J. Lipid Res. 2015, jlr.M065326. (12) W¨ ustner, D. Curr. Pharm. Biotechnol. 2012, 13, 303–318. (13) McIntosh, A. L.; Atshaves, B. P.; Huang, H.; Gallegos, A. M.; Kier, A. B.; Schroeder, F. Lipids 2008, 43, 1185–1208. (14) Gimpl, G.; Gehrig-Burger, K. Bioscience Rep. 2007, 27, 335–358. (15) Schroeder, F.; Nemecz, G.; Gratton, E.; Barenholz, Y.; Thompson, T. Biophys. Chem. 1988, 32, 57–72. (16) Yeagle, P.; Albert, A.; Boesze-Battaglia, K.; Young, J.; Frye, J. Biophys. J. 1990, 57, 413–424. (17) Xu, Z.; Farver, W.; Kodukula, S.; Storch, J. Biochemistry 2008, 47, 11134–11143. (18) W¨ ustner, D.; Færgeman, N. J. Histochem. Cell Biol. 2008, 130, 891–908. (19) Mondal, M.; Mesmin, B.; Mukherjee, S.; Maxfield, F. R. Mol. Biol. Cell 2008, 20, 581–588. (20) Robalo, J. R.; do Canto, A. M. T. M.; Carvalho, A. J. P.; Ramalho, J. P. P.; Loura, L. M. S. J. Phys. Chem. B 2013, 117, 5806–5819. (21) Ramirez, D. M. C.; Ogilvie, W. W.; Johnston, L. J. Biochim. Biophys. Acta - Biomembranes 2010, 1798, 558–568. (22) Hölttä-Vuori, M.; Uronen, R.-L.; Repakova, J.; Salonen, E.; Vattulainen, I.; Panula, P.; Li, Z.; Bittman, R.; Ikonen, E. Traffic 2008, 9, 1839–1849.

22


Page 22 of 29

Page 23 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(23) W¨ ustner, D.; Lund, F. W.; Röhrl, C.; Stangl, H. Chem. Phys. Lip. 2016, 194, 12–28. (24) Mukherjee, S.; Zha, X.; Tabas, I.; Maxfield, F. R. Biophys. J. 1998, 75, 1915–1925. (25) Scheidt, H. A.; Muller, P.; Herrmann, A.; Huster, D. J. Biol. Chem. 2003, 278, 45563– 45569. (26) Milles, S.; Meyer, T.; Scheidt, H. A.; Schwarzer, R.; Thomas, L.; Marek, M.; Szente, L.; Bittman, R.; Herrmann, A.; Pomorski, T. G.; Huster, D.; M¨ uller, P. Biochim. Biophys. Acta - Biomembranes 2013, 1828, 1822–1828. (27) W¨ ustner, D.; Solanko, L.; Sokol, E.; Garvik, O.; Li, Z.; Bittman, R.; Korte, T.; Herrmann, A. Chem. Phys. Lipids 2011, 164, 221–235. (28) Robalo, J. R.; Ramalho, J. P. P.; Loura, L. M. S. J. Phys. Chem. B 2013, 117, 13731– 13742. (29) N˚ abo, L. J.; List, N. H.; Witzke, S.; W¨ ustner, D.; Khandelia, H.; Kongsted, J. Biochim. Biophys. Acta - Biomembranes 2015, 1848, 2188–2199. (30) Kyrychenko, A. Methods Appl. Fluoresc. 2015, 3, 042003. (31) Olsen, J. M.; Aidas, K.; Kongsted, J. J. Chem. Theory Comput. 2010, 6, 3721–3734. (32) Olsen, J. M. H.; Kongsted, J. Adv. Quantum Chem. 2011, 61, 107–143. (33) List, N. H.; Olsen, J. M. H.; Kongsted, J. Phys. Chem. Chem. Phys. 2016, 18, 20234– 20250. (34) List, N. H.; Jensen, H. J. A.; Kongsted, J. Phys. Chem. Chem. Phys. 2016, 18, 10070– 10080. (35) Olsen, J.; Jørgensen, P. J. Chem. Phys. 1985, 82, 3235. (36) Runge, E.; Gross, E. K. U. Phys. Rev. Lett. 1984, 52, 997–1000. 23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(37) Casida, M. E. in Recent Developments and Applications of Modern Density Functional Theory; Elsevier: Amsterdam, New York, 1996; Edited by J.M. Seminario. (38) Hättig, C.; Christiansen, O.; Jørgensen, P. J. Chem. Phys. 1998, 108, 8331. (39) Beerepoot, M. T. P.; Friese, D. H.; List, N. H.; Kongsted, J.; Ruud, K. Phys. Chem. Chem. Phys. 2015, 17, 19306–19314. (40) Peticolas, W. L. Annu. Rev. Phys. Chem. 1967, 18, 233–260. (41) Dickson, C. J.; Madej, B. D.; Skjevik, ˚ A. A.; Betz, R. M.; Teigen, K.; Gould, I. R.; Walker, R. C. J. Chem. Theory Comput. 2014, 10, 865–879. (42) Wang, J.; Wolf, R. M.; Caldwell, J. W.; Kollman, P. A.; Case, D. A. J. Comput. Chem. 2004, 25, 1157–1174. (43) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (44) Joung, I. S.; Cheatham, T. E. J. Phys. Chem. B 2008, 112, 9020–9041. (45) Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graphics 1996, 14, 33–38. (46) Witzke, S.; List, N. H.; Olsen, J. M. H.; Steinmann, C.; Petersen, M.; Beerepoot, M. T. P.; Kongsted, J. Submitted 2016, (47) Beerepoot, M. T. P.; Steindal, A. H.; List, N. H.; Kongsted, J.; Olsen, J. M. H. J. Chem. Theory Comput. 2016, 12, 1684–1695. (48) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (49) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200–1211. (50) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785–789. (51) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. 24


Page 24 of 29

Page 25 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(52) Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. J. Phys. Chem. 1993, 97, 10269– 10280. (53) Wang, J.; Wang, W.; Kollman, P. A.; Case, D. A. J. Mol. Graphics Modell. 2006, 25, 247–260. (54) Case, D. A.; Babin, V.; Berryman, J. T.; Betz, R. M.; Cai, Q.; Cerutti, D. S.; Cheatham, III, T. E.; Darden, T. A.; Duke, R. E.; Gohlke, H.; Goetz, A. W.; Gusarov, S.; Homeyer, N.; Janowski, P.; Kaus, J.; Kolossvry, I.; Kovalenko, A.; Lee, T. S.; LeGrand, S.; Luchko, T.; Luo, R.; Madej, B.; Merz, K. M.; Paesani, F.; Roe, D. R.; Roitberg, A.; Sagui, C.; Salomon-Ferrer, R.; Seabra, G.; Simmerling, C. L.; Smith, W.; Swails, J.; Walker, R. C.; Wang, J.; Wolf, R. M.; Wu, X.; Kollman, P. A. AMBER 14. 2014; University of California, San Francisco. (55) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09 Revision D.01. Gaussian Inc. Wallingford CT 2009. (56) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007–1023. 25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(57) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796–6806. (58) Gagliardi, L.; Lindh, R.; Karlström, G. J. Chem. Phys. 2004, 121, 4494–4500. (59) Aidas, K.; Angeli, C.; Bak, K. L.; Bakken, V.; Bast, R.; Boman, L.; Christiansen, O.; Cimiraglia, R.; Coriani, S.; Dahle, P.; Dalskov, E. K.; Ekström, U.; Enevoldsen, T.; Eriksen, J. J.; Ettenhuber, P.; Fernández, B.; Ferrighi, L.; Fliegl, H.; Frediani, L.; Hald, K.; Halkier, A.; Hättig, C.; Heiberg, H.; Helgaker, T.; Hennum, A. C.; Hettema, H.; Hjertenæs, E.; Høst, S.; Høyvik, I.-M.; Iozzi, M. F.; Jansik, B.; Jensen, H. J. Aa.; Jonsson, D.; Jørgensen, P.; Kauczor, J.; Kirpekar, S.; Kjærgaard, T.; Klopper, W.; Knecht, S.; Kobayashi, R.; Koch, H.; Kongsted, J.; Krapp, A.; Kristensen, K.; Ligabue, A.; Lutnæs, O. B.; Melo, J. I.; Mikkelsen, K. V.; Myhre, R. H.; Neiss, C.; Nielsen, C. B.; Norman, P.; Olsen, J.; Olsen, J. M. H.; Osted, A.; Packer, M. J.; Pawlowski, F.; Pedersen, T. B.; Provasi, P. F.; Reine, S.; Rinkevicius, Z.; Ruden, T. A.; Ruud, K.; Rybkin, V.; Salek, P.; Samson, C. C. M.; de Merás, A. S.; Saue, T.; Sauer, S. P. A.; Schimmelpfennig, B.; Sneskov, K.; Steindal, A. H.; Sylvester-Hvid, K. O.; Taylor, P. R.; Teale, A. M.; Tellgren, E. I.; Tew, D. P.; Thorvaldsen, A. J.; Thøgersen, L.; Vahtras, O.; Watson, M. A.; Wilson, D. J. D.; Ziolkowski, M.; ˚ Agren, H. WIREs Comput. Mol. Sci. 2014, 4, 269–284. (60) Aquilante, F.; De Vico, L.; Ferré, N.; Ghigo, G.; Malmqvist, P.-A.; Neogrády, P.; Pedersen, T. B.; Pitoˇ nák, M.; Reiher, M.; Roos, B. O.; Serrano-Andrés, L.; Urban, M.; Veryazov, V.; Lindh, R. J. Comp. Chem. 2010, 31, 224–247. (61) Pierloot, K.; Dumez, B.; Widmark, P.-O.; Roos, B. O. Theor. Chim. Acta 1995, 90, 87–114. (62) Yanai, T.; Tew, D. P.; Handy, N. C. Chem. Phys. Lett. 2004, 393, 51–57. (63) Steinmann, C.; Ibsen, M. W.; Hansen, A. S.; Jensen, J. H. PLoS ONE 2012, 7, e44480.

26


Page 26 of 29

Page 27 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(64) The PE library developers, PElib: The Polarizable Embedding library (development version). 2015; http://gitlab.com/pe-software/pelib-public. (65) Gao, B. Gen1Int Version 0.2.1. 2012; http://gitlab.com/bingao/gen1int. (66) Gao, B.; Thorvaldsen, A. J.; Ruud, K. Int. J. Quantum Chem. 2011, 111, 858–872. (67) Wang, L. Annu. Rev. Biochem. 2012, 81, 615–635. (68) Clarke, R. J. Adv. Colloid Interface Sci. 2001, 89-90, 263–281. (69) Starke-Peterkovic, T.; Turner, N.; Vitha, M. F.; Waller, M. P.; Hibbs, D. E.; Clarke, R. J. Biophys. J. 2006, 90, 4060–4070. (70) Cronstrand, P.; Luo, Y.; ˚ Agren, H. Chem. Phys. Lett. 2002, 352, 262–269. (71) Alam, M. M.; Chattopadhyaya, M.; Chakrabarti, S. Phys. Chem. Chem. Phys. 2012, 14, 1156–1165.

27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Graphical TOC Entry

28


Page 28 of 29

Page 29 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42



Computational Approach to Evaluation of Optical Properties of

Recommend Documents